CLIMATE ABSOLUTE RADIANCE AND REFRACTIVITY OBSERVATORY ( CLARREO )

The Climate Absolute Radiance and Refractivity Observatory (CLARREO) is a mission, led and developed by NASA, that will measure a variety of climate variables with an unprecedented accuracy to quantify and attribute climate change. CLARREO consists of three separate instruments: an infrared (IR) spectrometer, a reflected solar (RS) spectrometer, and a radio occultation (RO) instrument. The mission will contain orbiting radiometers with sufficient accuracy, including on orbit verification, to calibrate other space-based instrumentation, increasing their respective accuracy by as much as an order of magnitude. The IR spectrometer is a Fourier Transform spectrometer (FTS) working in the 5 to 50 μm wavelength region with a goal of 0.1 K (k = 3) accuracy. The FTS will achieve this accuracy using phase change cells to verify thermistor accuracy and heated halos to verify blackbody emissivity, both on orbit. The RS spectrometer will measure the reflectance of the atmosphere in the 0.32 to 2.3 μm wavelength region with an accuracy of 0.3% (k = 2). The status of the instrumentation packages and potential mission options will be presented. * Corresponding author.


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The Pathfinder for the Climate Absolute Radiance and Refractivity Observatory (CLARREO), 2 or CLARREO Pathfinder (CPF), is a cost-capped NASA directed mission for demonstration 3 of key technologies necessary for the full CLARREO mission. CLARREO is a Tier 1 mission 4 recommended by the 2007 NRC Earth Science Decadal Survey. The CLARREO mission's 5 primary objective is to produce highly accurate climate records to test climate projections in 6 order to improve climate models and ultimately enable sound policy decisions. This objec-7 tive is accomplished through accurate decadal satellite observations traceable to the Système 8 international d'unités (SI units) that are sensitive to key climate variables, including climate 9 feedbacks, responses, and radiative forcings. Uncertainties in such climate variables drive 10 current climate model projection uncertainties.

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In 2016, funds were appropriated for a Pathfinder mission, to demonstrate essential mea-

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CPF will provide highly accurate spectral reflectance measurements enabled by a RS spec-18 trometer operating between 350 nm and 2300 nm (> 95% of reflected solar energy) with 19 continuous spectral coverage with a broadband uncertainty < 0.5% and spectral uncertainty 20 < 1% (k=2) 1 . The RS spectrometer will be capable of pointing to the sun and moon for cal- and an 4) Improved lunar spectral irradiance calibration standard. 35 1 We use the general coverage factor k; k = 2 means a 95% confidence level (2σ) for a Gaussian distribution.

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The full CLARREO mission aims to provide highly accurate and SI-traceable decadal change 206 observations sensitive to the most critical but least understood climate forcings, responses, 207 and feedbacks. The required accuracy is determined by the need to detect projected decadal 208 changes in climate above the background signal of natural variability. The full CLARREO 209 mission measurement requirements have, therefore, been driven by the need to detect these 210 small, but critical, climate change-scale trends, rather than instantaneous instrument noise 211 levels. The CLARREO Pathfinder will demonstrate the capability of the technology and 212 methodology within the RS spectrometer portion of the CLARREO mission to achieve the 213 high absolute accuracy levels needed to achieve these goals. 214 The CLARREO Pathfinder requirements were derived from the full CLARREO mission 215 requirements. Unlike most missions, CLARREO must consider the impact of its science 216 requirements on multi-decadal time scales. This suggests that requirement metrics must 217 be stated in terms of accuracy of decadal climate trends and in terms of time to detect 218 those trends. The former is more relevant to climate model testing; the latter is more easily 219 discussed in terms of relevance to the timing of societal decision making in a cost/value sense. 220 Having determined the CLARREO mission requirements using the rigorous methodology 221 considered below, the CLARREO Pathfinder mission requirements have been stated such 222 that the CPF would serve to demonstrate that the CLARREO mission calibration and 223 inter-calibration capabilities are achievable. However, the currently expected lifetime of the 224 CLARREO Pathfinder (one year) is less than that of the full CLARREO mission (five years), 225 making it difficult to establish a climate benchmark. 226 The science community has struggled to make rigorous, quantitative climate monitoring re- Even a perfect observing system would be limited in its ability to measure long-term climate 235 forcing and response  due to the noise of the climate system's natural 236 variability (e.g. ENSO, 3 -5 years). Such natural variability creates a "floor" for required 237 accuracy in climate trends, meaning that climate observations need to have uncertainties 238 smaller than natural variability. The key, therefore, is to quantify the relationship between 239 natural variability and observing system accuracy. Von Storch andZwiers, 2001, Weatherhead et al., 1998], and the CLARREO team has used 244 this approach to quantify and compare the impact of different sources of uncertainty to 245 determine mission requirements. Although CLARREO/CPF data will not only be used to 246 determine trends, trend analysis provides a critical insight into the mission science require-247 ments and to the utility of the observations for decadal climate change science. 248 Here, an accuracy uncertainty factor, U a , for climate trend accuracy is defined as the ratio of 249 trend uncertainty for a real climate observing system to that of a perfect observing system 250 limited only by natural variability. The factor is unitless and can be applied generally to 251 any climate variable. A perfect observing system would have a U a value of 1.0. Any real 252 observing system will have uncertainties that increase the value of U a above 1.0. Using the 253 results of Leroy et al. [2008] on the relationship between trend uncertainties for perfect and 254 real observing systems, we can determine the accuracy uncertainty factor U a as follows. 255 U a = 1 + σ 2 cal τ cal + σ 2 noise τ noise + σ 2 orbit τ orbit σ 2 var τ var ments across diverse climate variables, each with their own estimates of natural variability. 283 The method also avoids the costs of pursuing perfection that may not add much value to 284 observing climate trends, and provides a quantitative "floor" for climate accuracy. In par-285 ticular, Equation 2.1 shows that when error sources are a factor of 2 to 3 below the level of 286 natural variability, we have reached the point of greatly diminished returns from any further 287 increase in accuracy. 288 We can also define an analogous uncertainty factor, U t , that is the ratio of the time to detect 289 a trend using a real observing system to the time to detect a trend using a perfect observing 290 system .

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U t = 1 + σ 2 cal τ cal + σ 2 noise τ noise + σ 2 orbit τ orbit σ 2 var τ var 1/3 (2. 2) The only difference between Equations 2.1 and 2.2 is that there is a cubed root on the right 292 side of Equation 2.2, rather than a square root. Since the values of U a and U t are always 293 greater than 1, because the creation of a perfect observing system is not possible, Equations 294 2.1 and 2.2 can be combined and simplified to show that that is, that the degradation of trend accuracy for time to detect trends is only 2/3 of the 296 degradation for accuracy in trends. For example, the CLARREO mission's goal for trend 297 accuracy to be within 20% of a perfect observing system (U a = 1.2), equivalently requires 298 that the time to detect trends is within 13% of a perfect observing system (U t = 1.13). If a 299 perfect observing system could detect a temperature trend with 95% confidence in 20 years, 300 then the CLARREO observing system could detect the same trend with 95% confidence but 301 with 13% more time required: 23 years instead of 20 years.

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The framework defined by Equations 2.1 -2.3 gives a simple but powerful way to under-303 stand the value of observing system accuracy both for climate trend accuracy, relevant to 304 tests of climate predictions and for time to detect trends, and relevant for public policy 305 decisions. They also provide a way to compare consistent metrics across a wide range of 306 climate variables and a wide range of uncertainty sources in climate observations.

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Here we will show an example applying the accuracy uncertainty factor to determine cli-308 mate change scale-relevant absolute accuracy requirements by focusing on determining the 309 requirements for the CLARREO reflected solar spectrometer, which will be demonstrated 310 by the CPF. 311 Uncertainty in climate sensitivity is driven by the uncertainty in cloud feedback, which is re trends (Fig. 3a), the perfect ain shows the need for long clirate trends in SW CRF (Fig. 3b).
ect trends? Using Leroy et al. nalogous uncertainty factor o detect a trend using a real e to detect a trend using a pera ratio can be defined for any al confidence bound desired. from Leroy et al. (2008b), (2) en Eqs. (1) and (2) is that the de of the equation becomes a are always greater than 1, and and (2) show that (3) g Eq. (3) is that the degradation to detect trends is only twor accuracy in trends. For examment that U a < 1.2 equivalently w do we interpret the meaning serving system could detect a % confidence in 20 years, then ystem could detect the same in 23 years (13% more time). imple but powerful way to erving system accuracy for both tests of climate predictions) and ublic policy decisions). They also onsistent metrics across a wide s well as a wide range of sources servations. We strongly encourmore rigorously understand and n requirements across the wide riables (ECVs) (GCOS 2011).  ship between absolute calibration accuracy and the accuracy of decadal cloud forcing trends. The results are shown for a perfect observing system (black curve) and for instruments with varying levels of absolute calibration uncertainty (colored curves). The relationship between RS absolute accuracy and SW CRF trends is shown. This illustrates the dramatic effect of measurement accuracy on both climate trend accuracy (yaxis) and the time to detect trends (x-axis). Accuracy improvements beyond CLARREO approach diminishing returns compared to a perfect observing system.
Radiative Forcing (CRF) natural variability was determined using a 10-year time series of 318 globally and annually averaged CERES data. Additionally, the Student-t distribution was 319 used to account for the short 10-year record of CERES data available. The natural variabil-320 ity estimates determined using CERES data were compared to that of the average of five   The full CLARREO accuracy requirement for the reflected solar spectrometer of 0.3% (k=2) 352 provides an observing system very close in accuracy to a perfect observing system. For the 353 technology demonstration to be provided by the CLARREO Pathfinder, the absolute accu-354 racy requirement is expected to be comparable (see Section 4.1). This accuracy requirement 355 is a factor of 5 to 10 improvement in absolute accuracy compared to operational sensors.   [Goldberg, 2007] arose 367 from the critical need for satellite sensor inter-calibration for research and applications in 368 weather, climate, and natural resources. A major benefit to GSICS activities that is missing 369 from the current observing system, however, are SI-traceable reference radiometers with high 370 absolute accuracy to serve as anchors to the GSICS system. Inter-calibrating two operational 371 instruments, while beneficial, does not include the transfer of SI-traceable absolute accuracy 372 unless at least one of the instruments can serve as such a reference [Goldberg, 2007] The length of the groundtrack is proportional to the duration of the opportunity. The number of opportunities over the year to intercalibrate MetOp is found to be 772; ISS groundtracks during these opportunities are displayed in Fig. 3. The latitude of the ISS subsatellite point at the beginning of each opportunity for JPSS intercalibration is plotted over the course of one year in Fig. 4, where time t 5 0 corresponds to the instant of autumnal equinox. The sinusoidal behavior has a 60-day period, which corresponds to the length of the cycle in nodal alignments for the ISS and a sun-synchronous orbit. A similar plot has been constructed for MetOp, but it is omitted in the interest of conciseness. As one would expect, the main difference in the two plots consists of a phase shift corresponding to the difference in local times of the nodal crossings of JPSS and MetOp.
Details of the ISS instrument swath during two intercalibration opportunities are provided in Fig. 5. the ISS instrument is directed at nadir, the width of the swath is 100 km.) During some opportunities, the swaths extend as far as latitudes 52.188N or 52.188S.
The duration of each JPSS intercalibration opportunity is shown in Fig. 6, depending on whether solar zenith angle u 0 is taken into account. According to Minnis et al. (2008), measurements of reflected solar radiation are useful for intercalibration only when u 0 # 758. This constraint is left out of account in the top plot of Fig. 6, whereas the constraint is applied at the ISS instrument boresight target in determining the durations shown in the bottom plot. The constraint affects the duration at three times during the year, for only a few days each time, and reduces the total yearly duration from 1.41 to 1.36 days. The 60-day nodal alignment cycle is evident in these results. The opportunities having the longest durations, nearly 300 s, occur over near-equatorial latitudes as both spacecraft are ascending or descending together through the equatorial plane. Secondary maxima of  The ISS is well-suited to serve as a platform from which to obtain RS radiance measurements 428 that can be used to inter-calibrate instruments in sun-synchronous LEO. The ISS orbit  show that the numbers of samples that can be obtained from ISS are sufficient to inter-437 calibrate well-behaved sensors in sun-synchronous LEO and GEO to the accuracy required 438 for monitoring long-term climate change (Section 2.1).

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A unique feature of the CPF RS spectrometer is its on-orbit 2-dimensional pointing ability;  Inter-calibration on orbit is achieved by comparing the sensor measurements to observations 472 by CLARREO that are coincident in time, space, and viewing angle, as described above, and 473 considered to be the reference or true observations. Generally, the inter-calibration process

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Because of the physical nature of polarization in an optical system and its linear response, it 485 is reasonable to assume that inter-calibration offsets A 0 or A p will be very similar, and that 486 the polarization effect will be contained in the difference of inter-calibration gains, G 0 or G p .

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Obtaining inter-calibration gain for non-polarized and polarized cases, and attributing the 488 difference to the polarization effect, then imager sensitivity to polarization and its relative 489 uncertainty can be written as (2.5) The first term, σ ∆g /∆G, is random relative error of inter-calibrated gain difference, depen-491 dent on inter-calibration sampling. The second term, σ p /P , is the relative uncertainty of 492 the degree of linear polarization, which we obtain by applying the PDMs (see Appendix B).

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It is important to emphasize that σ p is the accuracy of P averaged over a large ensemble of 494 inter-calibration samples, and not the instantaneous error of the PDMs.
The uncertainty in the first term, σ 0 , is radiometric uncertainty of inter-calibrated VIIRS 507 reflectance for unpolarized measurements. The following steps are required to derive σ 0 : where σ clarreo is the accuracy of the CLARREO RS spectrometer, σ intercal is the error con-520 tribution from inter-calibration noise over an autocorrelation time period, and σ residue is 521 error associated with target sensor remaining error contribution (e.g. instrument month-522 to-month relative stability). These error sources are of different types: bias and random.

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If the difference between CLARREO and imager measurements has remaining offset/gain, 524 then Equation 2.7 will have additional error terms depending on the quality of performed 525 inter-calibration (remaining inter-calibration offsets and gains).

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The second term in Equation 2.6 is the error contribution due to inter-calibrated instrument 527 sensitivity to polarization determined from inter-calibration with CLARREO, uncertainty 528 of sensitivity to polarization, the degree of linear polarization and its uncertainty. When  target sensor remaining error contribution (e.g. instrument month-to-month relative stability). These error sources are of di↵erent types: bias and random. If the di↵erence between CLARREO and the imager measurements has remaining o↵set/gain, then Equation 2.13 will have additional error terms depending on the quality of performed inter-calibration (remaining inter-calibration o↵sets and gains).
The second term in Equation 2.12 is the error contribution due to inter-calibrated instrument sensitivity to polarization determined from inter-calibration with CLARREO, uncertainty of sensitivity to polarization, the degree of linear polarization and its uncertainty. When P > 0 (and p > 0), sensor's radiometric error increases. For a fixed value of sensitivity to polarization, m, it is a function of P, p , and m . The mean m and uncertainty m are obtained from inter-calibration with CLARREO as described above. The degree of polarization and p are obtained from the PDMs.  Figure 2.36: (a) Resulting imager relative radiometric error (k = 1) versus degree of polarization. Imager sensitivity to polarization is set to 3% (k = 1). Colored curves show cases for different PDM uncertainty, p : 5% (black), 10% (green), and 15% (blue). Red dashed line shows the error level for unpolarized radiances. (b) Estimated relative error of sensitivity to polarization for PDM accuracy of 5% (black), 10% (green), and 15% (blue).
We performed numerical estimates for three di↵erent levels of PDM accuracy ( p ): 5%, 10%, and 15%, using Equations 2.12 and 2.13, and estimated nominal polarized and not-polarized sampling uncertainties . The resulting imager radiometric uncertainty is shown in Figure 2.36a as a function of degree of polarization. Colored curves show results for PDM accuracy at 5% (black), 10% (green), and 15% (blue). The red dashed line shows the Figure 2.5: (a) Resulting imager relative radiometric error (k = 1) versus degree of polarization. Imager sensitivity to polarization is set to 3% (k = 1). Colored curves show cases for different PDM uncertainty, σ p : 5% (black), 10% (green), and 15% (blue). Red dashed line shows the error level for unpolarized radiances.
We performed numerical estimates for three different levels of PDM accuracy (σ p ): 5%, 10%, show that reduction in PDM accuracy from 5% to 15% can cause an increase in uncertainty 542 of inter-calibrated sensitivity to polarization by a factor of four for fully polarized light.

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The CLARREO team has developed a framework for estimation of the resulting uncertainty One of the objectives of the CPF mission is the calibration of broadband radiance for CERES.

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For this endeavor, the required spectral coverage is a critical parameter for the CPF RS    Figure 2.37b all-sky averages. Therefore, in terms of total radiation, measurements do not need to cover the entire spectrum but only the range in which su cient reflected solar energy is enclosed. The minor correction from the uncovered spectral regions can be made using the radiative transfer calculations. Signal aliasing arises when a signal is discretely sampled at a rate that is insufficient to cap-568 ture the changes in the signal. In the case of inter-calibration, spectral reflectance aliasing 569 will result in additional systematic uncertainty, which can be avoided with a proper sam- Earth's reflectance spectra, outside of molecular absorption, are relatively smooth, and these 575 spectral regions are the high priority for the CPF inter-calibration objectives.

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To estimate the expected biases due to CLARREO (and therefore CPF) RS spectral sam-577 pling, we used theoretical calculations (MODTRAN) and the SCIAMACHY Level-1B data 578 product (SCI NL 1P) to obtain nadir spectral reflectance with wavelengths ranging from 240 579 nm to 1750 nm [Bovensmann et al., 1999]. The impact of spectral resolution is tested using a energy can be corrected and estimated spectral biases are below 0.1% for wavelength outside absorption regions. For the water vapor absorption bands, challenge remains due to sensitivity to the spectral features of atmospheric water vapor.

CLARREO InfraRed In-orbit Standard
In addition to providing valuable data for benchmarking the Earth's climate and assessing climate models, the reference observations provided by CLARREO are also anticipated to be very useful for satellite inter-calibration. In fact, the relatively short-term inter-calibration benefits are anticipated to be a major contribution to a CLARREO mission. In order for the accuracy and traceability of CLARREO to be beneficial to other concurrent sensors, the inter-calibration methodology and resulting inter-calibration uncertainty must be robust and well understood. There are many approaches used for satellite inter-calibration [e.g. Chander et al. 2013]. This section describes the use of CLARREO to serve as a reference for infrared satellite inter-calibration and quantifies the uncertainty in determining radiometric biases observed between CLARREO and sun synchronous sounding sensors such as the Atmospheric InfraRed Sounder (AIRS), the Cross-track Infrared Sounder (CrIS), and the Infrared Atmospheric Sounding Interferometer (IASI). and results hard to duplicate. Alternatively, common reusable software helps to alleviate 632 some of these problems.

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The MIIC framework multi-tiered architecture that is planned to support the CLARREO  The LEO-LEO SCIAMACHY/MODIS inter-calibration server-side spectral and spatial convolution functions provide even greater reductions in data network transmission. SCIAMACHY Level-1B data have 5287 spectral bands, 240 -1748 nm, and footprint sizes of 30 km ⇥ 240 km at nadir. Spectral convolution of MODIS Band 1 (0.65 µm) relative spectral response (RSR) values with hyperspectral SCIAMACHY data reduces the 5287 spectral values to one simulated reflectance value. Spatial convolution of 1 km MODIS pixels with 30 km ⇥ 240 km SCIAMACHY footprints accounts for a reduction factor of 7000 at nadir.
Histogram analysis and spectral and spatial resampling required for OSSE/observation comparisons have the potential for several orders of magnitude savings in data transmission. In addition to the substantial reductions in data transfer, there is a more important qualitative benefit provided by services such as the MIIC Framework. New collaborative research becomes more feasible as critical data centers such as NOAA's NCDC and NASA's ASDC support value added services along with remote access to their data.
Costs to transfer and store large volumes of data sets for inter-comparison studies are signif-  Assuming that the RS instrument is preforming well on orbit and the mission is extended Site 3 on the outboard side of ELC-1, providing views in the ram, port, and nadir directions; 744 and 2) Site 8 on the inboard side of ELC-1, providing wake, starboard, and nadir views.

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The primary technical performance measures that the team is evaluating involve lunar and  full mission spectral fingerprint benchmarks (L2 and L3 data products).

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• The CLARREO Pathfinder budget will support full Level 0 processing but will not 780 support complete Level 2 and 3 processing. No level 2 or 3 processing is planned.

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Level 4 processing is limited to that sufficient to demonstrate inter-calibration for the 782 Clouds and the Earth's Radiant Energy System (CERES) and Visible Infrared Imaging

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• If CPF is judged to be highly successful, meaning that the team has advanced the tech-

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The CLARREO science value matrix (SVM) is a concept that has been used to clarify impact is a unique strength, but it can also complicate derivation of the mission priorities and 806 requirements. The science value matrix is one of the tools used to help with this challenge, 807 assisting the team in converging on and justifying its decisions and recommendations.

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For a SVM to be a useful tool, the "value" needs some method of quantification. The 809 science value matrix approach is based on the CLARREO team's work and discussions in 810 Section 2. The Science Value of a Science Objective, SV so , is computed using the following 811 product: F si is the science impact factor, F cov is the global coverage factor, F cv is the calibration 813 verification factor, F crl is the climate record length factor, F ta is the trend accuracy factor,  Baseline mission, will be discussed.

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Science Impact Factor

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The science impact factor, F si , serves to capture both the importance of the science objective The science impact factors, third column from the left in Table 3    20% of a perfect observing system is met. This accuracy level is assumed to be 100% of 956 the capability value. As accuracy in decadal change trends reduces below this, the accuracy 957 value factor is reduced proportional to the loss of accuracy. In particular, the trend accuracy 958 value factor is defined as: As the CLARREO MCR Level 1 requirement goal is to be within 20% of a perfect observ-

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ing system, F a = 1.0 when the trend accuracy requirement is met, F ta > 1.0 when CPF 961 measurements achieve trend accuracy better than requirement, and F ta < 1.0 when CPF 962 measurements exceed the 20% accuracy limit.

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The accuracy values used in The trend accuracy metric discussed above is relative to a perfect observing system. While Here, if it is assumed that there will be multiple CLARREO missions, the first would con- year of data (as is the current lifetime of the CLARREO Pathfinder). Even though highly 1012 accurate, it would not anchor the long-term record well because of high natural variability.

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As a result, in the science value matrix for the first two CLARREO missions, the square 1014 root dependence of record length is included. In particular, the climate record length metric 1015 is chosen as where ∆t is the number of years of CLARREO data with a 70% likelihood of survival 1017 on-orbit. Using this metric, the length of the initial CLARREO record (for example, the 1018 CLARREO Pathfinder) will be accounted for in determining the accuracy of the climate 1019 trends that can be achieved by the mission, even in the long term.         The SI-traceable accuracy advancement will be determined relative to ensemble means and 1121 for spectral reflectance relative to the global mean reflectance. To calibrate the spectrome-1122 ter relative to SI-Traceable standards, the CLARREO Pathfinder RS instrument will have 1123 the ability to observe the sun and the moon as stated in Section 4.2. It will also take 1124 spectral reflectance measurements of the Earth at nadir to demonstrate its inter-calibration 1125 capabilities.

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To achieve reference inter-calibration of other reflected solar sensors, the CPF RS instru-1127 ment will provide constraints to the effective offset, gain, non-linearity, and sensitivity to 1128 polarization of a target sensor.

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CLARREO Pathfinder is a technology/technique demonstration mission and therefore will 1131 only produce Level-1 data products. Level-0 data from the CPF RS instrument will be 1132 collected and archived at a data center, the location of which has yet to be identified.

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Additionally, these Level-0 data will be processed into Level-1 products, which will also be Level 1 through Level 4 data products. All data that will be archived at data centers will 1144 be available to the community for independent verification of the CPF instrument team's 1145 results.  The CPF RS spectrometer's measurements of Earth-reflected radiance will be used to cal- to determine the ratio of the Earth-reflected radiance to the solar irradiance measurement.

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The geometric differences between an Earth-viewing radiance measurement and a solar irra-1174 diance measurement requires the retrieval of a directional-hemispheric reflectance. Thus, the 1175 RS sensor will function like a band-ratio radiometer. The instrument is based on an Offner 1176 imaging spectrometer design, which is capable of limiting spectral smile on the focal plane. The instrument will operate as a push-broom imager with a reliance on heritage hardware, 1178 reduction of sensor complexity, and solar-and lunar-source based calibration. 1179 data set that, when collected globally, reduces sampling biases for climatologically significant spatial and temporal averages over annual means. The instrument spectral range and spectral sampling requirements are motivated by inter-calibration of the broadband (CERES) and narrowband radiometers (VIIRS), respectively. The spatial sampling 0.5 km ground-fieldof-view is for achieving a quality cloud masking, and spatial coverage is motivated by the CLARREO RSS "benchmark" global sampling at nadir. In order to achieve the reference inter-calibration mission objectives, the CLARREO RS instrument will be designed to allow the boresight to be pointed along selected lines of sight within the fields of view of orbiting target sensors, as illustrated in Figure 2.33. The primary data product from the RS instrument is spectral reflectance. The current operational plan for the RS instrument is to determine the ratio of the output of the instrument while viewing an Earth scene, to that of the instrument while viewing the Sun. Taking into account the geometry di↵erences between a radiance measurement (while viewing the Earth scene) and an irradiance measurement (the solar measurement) permits the retrieval of a directional-hemispheric reflectance. Thus, the RS sensor will function like a band-ratioing radiometer. The instrument is based on an O↵ner imaging spectrometer design, which is capable of limiting spectral smile on the focal plane. The instrument will operate as a push-broom imager with a reliance on heritage hardware, reduction of sensor complexity, and solar-and lunar-source based calibration. Among the critical aspects of the CPF instrument concept is its ability to satisfy the unprece-  The primary sources of error in transferring prelaunch calibration to orbit is expected to be 1226 changes in stray light behavior and polarization sensitivity.

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The solar irradiance (E solar,λ ) measured by CLARREO can be written in terms of the sensor output while viewing the sun (S solar i,λ ) and responsivity (R i,λ ) of the i th detector and in a given wavelength band, λ, as shown below.
T attenuator is the transmittance of the attenuator used in viewing the sun, and A attenuator 1228 is the area of the attenuator's aperture. The summation over x solar and y solar serves to 1229 integrate the output from a single detector over the full solar disk needed to measure solar 1230 irradiance.

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The Earth-reflected radiance measured by CLARREO can be written as where A sensor is the area of the sensor's entrance pupil, Ω sensor is the solid angle of the sensor's collection field of view, R i,λ is the detector response, and S earth i,λ is the spectrally-resolved signal from the ith detector while viewing Earth. The Bidirectional Reflectance Distribution Function (BRDF) is determined by the ratio between the Earth-reflected radiance (L earth i,λ , Eqn. 4.2) and the solar irradiance (E solar,λ , Eqn. 4.1).
where θ 0 is the solar zenith angle at the TOA. It is assumed that any temporal changes in 1232 response between the solar and Earth views, R i,λ and R i,λ , respectively, will be minimal and 1233 changes in solar irradiance between the Earth and solar view will also be minimal. If these 1234 differences are negligible, then detector response for the sun and Earth view cancels out. In 1235 this case, the absolute radiometric calibration is not used for the BRDF retrieval, but it is 1236 required for establishing SI-traceability. bsolute solar irradiance measurements to show the sensor did not change going to orb isagreement between reported solar irradiance and predicted values mean that the sens odel requires modification. Stellar and lunar views provide information regarding the optic uality of the sensor. Temporal changes in the sensor are evaluated using these techniqu s well. The sensor model can be thought of as the numerical abstraction of the physic nstrument, encapsulating knowledge of both optical physics and empirical results gaine rom laboratory analysis. Disparities between laboratory results and model predictions guid odel improvements. This is a continuous process that ultimately yields a sensor model read or use after launch as illustrated in Figure 4.3. critical part of the calibration is developing SI-traceable data by characterizing the sens o SI-traceable, absolute radiometric quantities during pre-launch calibration to the electr att (prelaunch calibration box shown in Figure 4.3). Pre-launch absolute calibration i Evaluation of sensor performance on orbit uses combined calibration, validation, and ver-1263 ification activities. One approach planned for validation of the RS on-orbit calibration is 1264 comparison to ground-based measurements propagated through the atmosphere to predict 1265 at-sensor radiance. Another radiometric calibration/validation activity will be comparisons 1266 to other sensors (e.g. airborne sensors). The main difficulty with validation for CLARREO 1267 RS will be ensuring that the validation data sets also have sufficient radiometric quality.

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The operations plan for the RS lunar verification observations specifies that measurements 1277 of the moon will be acquired at phase angles between 5 • and 10 • . Although this range is 1278 relatively small, the lunar irradiance cannot be considered constant across this range. As an 1279 example, Figure 4.4 shows irradiance spectra from one night of ground-based observations 1280 during which phase angle changed from 6.65 • to 9.55 • over about 9 hours. The difference 1281 between the two spectra ranges from 10% to 12% depending upon the wavelength band.  The CLARREO Pathfinder RS instrument is likely to be an imaging spectrometer with a 1292 ∼10 • cross-track FOV. From low Earth orbit, the moon's diameter subtends about 0.5 • . To 1293 make a lunar irradiance measurement, the entire disk must be spatially sampled, which for an 1294 imaging spectrometer typically means scanning it in the along-track direction. Generating 1295 the irradiance from the scan data involves concatenating the scan lines into a spectral image, 1296 then spatially summing the radiance pixels and multiplying by their IFOV: where E m is the measured lunar irradiance, Ω p is the pixel IFOV in steradians, L i is the 1298 radiance measure of the i th pixel, and the summation is over all pixels on the moon's disk.

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using the reference lunar spectral irradiance generated for the particular conditions (phase and librations) of the RS Moon observations, by the USGS ROLO model [Kie↵er and Stone, 2005]. These model-generated reference spectra can be used to develop normalization factors, or to correct the observations to a standard geometry, such as 7 phase and zero librations. .4: ROLO model-generated lunar irradiance spectra produced for a ground-based spectrometer. The observation times differ by 9 h 21 m, and the phase difference is 2.9 . The irradiances differ by 10% to 12%, spectrally dependent.
As described in sections 4.1.2 and 4.2.1, the CLARREO RS instrument is an imaging spectrometer with 100 km swath, or ⇠10 cross-track field of view (FOV). From low Earth orbit, the Moon presents a disk about 0.5 in diameter. To make a lunar irradiance measurement, the entire disk must be spatially sampled, which for an imaging spectrometer typically means 106 Figure 4.4: ROLO model-generated lunar irradiance spectra produced for a ground-based spectrometer.
The observation times differ by 9 hours and 21 minutes, and the phase difference is 2.9 • . The irradiances differ by 10% to 12%, so the moon cannot be considered constant between 5 • and 10 • phase angles.
Recommended best practices suggest oversampling the moon in the along-track direction

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The basis of SIRCUS is a well-understood tunable laser source that can be coupled to Disagreement means the sensor model requires improvement based on the on-orbit data, including an additional set of characterization measurements. Solar and lunar views provide information regarding temporal changes in the sensor once on-orbit traceability is established. Thus, the key to the RS on-orbit calibration is the prelaunch, SI-traceable calibration. The required 0.3% uncertainty is fully traceable to the electric Watt by applying tunable laser sources and detector-based standards. Calibration systems, such as NIST's Spectral Irradiance and Radiance Responsivity Calibrations using Uniform Sources (SIRCUS) facility, provide such standards and a capability to understand stray light, spectral response, and polarization sensitivity at the level necessary for CLARREO [Brown et at., 2000]. The basis of SIRCUS is a well-understood tunable laser source that can be coupled to a fiber optic system providing both radiance and irradiance sources. The output of the source is determined via detector standards characterized against the Primary Optical Watt Radiometer (POWR). The planned calibration traceability to SIRCUS is shown as a stepwise sequence in Figure 4.31. It begins with a substitution radiometer that is used to calibrate the tunable laser source, known as the POWR Laser. In a second step, the POWR unit is moved and replaced by the CLARREO Transfer Radiometer (CXR) based on a silicon-trap detector for the visible and near infrared and indium-gallium arsenide detectors at longer wavelengths. The stated accuracy to calibrate a transfer radiometer in irradiance mode using POWR is 0.09%(k = 3). The upper portion of Figure 4.31 shows these steps.
The accuracy of such a radiance-based calibration has been demonstrated in NIST facilities to an expected accuracy of 0.2% for k=3. Once the CXR is calibrated, it is moved to the CLARREO Calibration Laboratory to calibrate the output of the sources used in the calibration of the RS instrument. in Section 4.2 and summarized in Figure 4.3, with emphasis on the laboratory-based absolute radiometric calibration. The SOLARIS test plan is shown in Figure 4.31. Attention is paid to developing credible uncertainties for characterizing possible degradation of the attenuator system. Emphasis of the laboratory testing is on the radiometric and spectral characterizations since the current state of the art of geometric and spatial calibration approaches are su cient for CLARREO mission requirements, assuming that stray light, scattered light, and ghosting analysis are radiometric properties. The importance of stray light in the reflectance retrieval makes characterization and modeling of stray and scattered light critical for SOLARIS, and the field-based measurements of the Sun and surface reflectance retrievals essential to demonstrate understanding of the error budgets. SOLARIS testing will lead to an end-to-end instrument performance model and error budgets with measured uncertainty magnitudes and peer reviewed measurement accuracy traceability chains, all of which are applicable to CLARREO. The path to an SI-traceable error budget leads to the CLARREO-required absolute uncertainties of 0.3%(k = 2). Figure 4.32 shows the three phases of SOLARIS integration and testing that leads to this level of accuracy: (1) 3% absolute uncertainty; (2) 1% absolute uncertainty; and (3) 0.3% absolute uncertainty. Current budgetary restrictions result in limitations on the available calibration and sensor hardware such that the CDS goal is to demonstrate < 1% absolute uncertainty with a path to 0.3%. SOLARIS will show these uncertainties for reflectance retrieval using direct solar irradiance to demonstrate SI-traceability of reflectance through both source-and detectorbased standards.
The testing in each of the three phases is described below. All three phases follow the general philosophy to accomplish the following: (1) Develop and evaluate calibration protocols leading to an SI-traceable calibration of the SOLARIS; (2) Develop a physically-based spectrometer   and stability, detector-to-detector uniformity, and linearity. Testing of the relative spectral 1554 response for the detectors was via a standard monochromator approach.

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The data collected permitted evaluation of detector noise, dark current level and stability, relative spectral response, conversion e ciency (CE) level and stability, detector-to-detector uniformity, and linearity. Testing of the relative spectral response for the detectors was via a standard monochromator approach. Grating Characterization: Characterization verified grating performance and its dimensional metrology. Dimensional metrology determined the size, shape, radius of curvature, and conic constant. The metrology also permitted assessing the optical quality of the grating through direct microscopic means. Optical characterization made use of the test configuration shown in Figure 4.33. Spectral evaluation made use of narrowband interference filters permitting determination of key spectrometer performance variables. Sample images from the high resolution imager at the end of the optical train are provided in Figure 4.33 as an example of the utility of these data. The horizontal and vertical size of the image provides the spatial and spectral quality of the grating. The top image demonstrates the e↵ect of a manufacturing artifact that was observed during the direct metrology of the grating. Altering the positioning of the grating, proper ba✏ing and slit design mitigated the impact of this artifact in the integrated system, as shown in the bottom image of Figure 4.33.
Optical Elements: The telescope and spectrometer optics were evaluated in like fashion to the grating. Dimensional metrology at the end of fabrication determined the size and shape of each element, including radius of curvature and conic constant. The metrology also evaluated the mechanical aspects of the elements and their associated mounts.
Performance characterization evaluates the quality of the surface finish and reflection e ciency as a function of wavelength. Surface figure of the optical elements was evaluated using standard optical interferometry techniques to evaluate wavefront error, and this was done under varying The imagery and model output are remarkably similar, save for slight rotational di↵erences in the orientation of the patterns.
The spectral reflectance of the coatings of the mirrors was also measured to allow prediction of the sensor signal to noise. The spectral resolution of the reflectance measurements was sufficient to allow it to be combined with grating and detector response. Initial characterizations of the mirrors demonstrated that the coatings did not meet the required spectral reflectance at shorter wavelengths. The mirrors were recoated to ensure that the signal-to-noise would be su cient in the ultraviolet while being as free as possible from spectral absorption features in the coating.  The spectral reflectance of the coatings of the mirrors was also measured to allow prediction reflectance at shorter wavelengths. The mirrors were recoated to ensure that the signal-1591 to-noise would be sufficient in the ultraviolet while being as free as possible from spectral 1592 absorption features in the coating.

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The imagery and model output are remarkably similar, save for slight rotational di↵erences in the orientation of the patterns.
The spectral reflectance of the coatings of the mirrors was also measured to allow prediction of the sensor signal to noise. The spectral resolution of the reflectance measurements was sufficient to allow it to be combined with grating and detector response. Initial characterizations of the mirrors demonstrated that the coatings did not meet the required spectral reflectance at shorter wavelengths. The mirrors were recoated to ensure that the signal-to-noise would be su cient in the ultraviolet while being as free as possible from spectral absorption features in the coating. Depolarizer: The quartz-quartz wedge depolarizer approach was selected for SOLARIS due 1594 to its compactness and its wide use in similar applications.

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Characterization of the pinholes to date has relied on measurements performed by the manu-1631 facturer as well as preliminary measurements with a laser-based system [Brown et al., 2000].

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Future measurements will include imaging approaches using electron microscopy or similar 1633 approaches to evaluate the shape, size, and total area of the pinholes.

Spatial dimension
Spatial dimension Absolute Radiometry Tests: The use of SIRCUS is the key to achieving calibration against both NIST standards and with respect to SI-traceable standards. The di culty with a SIRCUS-based approach for absolute spectral response is the time-consuming nature of the measurements.   The benefit of a nearly monochromic source is that collimating that source will provide a 1659 singular point on the imaging spectrometer's output.

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The image shown in Figure 4.12 resulted in a modification to the SOLARIS optical train to 1665 add a baffle that removes this feature.  signal-to-noise ratio (SNR), noise characteristics, and detector-to-detector variability. These will make use of full-field, full-aperture sources and thus include all detectors in the evaluations. Thus, a portion of the relative radiometry process will be assessment of the temporal stability and spatial uniformity of the sources.
An initial evaluation of SOLARIS noise characteristics included data collected in three sweeps with 50 frames collected for exposure times varying from 5 to 900 ms. Collections at 5, 10, 15, 20, 25, and 30 ms were made at 10 frames per second, while those at 50, 100, 150, 200, and 250 ms were done at 3 frames per second. The last four exposure times of 300, 500, 700, and 900 ms included SOLARIS images at 1 frame per second.
Determining the dominant noise types is important for CLARREO because the climate record relies on averaging thousands of spatial data points over time to remove short-term reflectance variations in the Earth-atmosphere system. This allows the SNR requirement for CLARREO Relative Radiometry Tests: Parameters covered under the relative radiometry term in-1667 clude signal-to-noise ratio (SNR), noise characteristics, and detector-to-detector variability.

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These will make use of full-field, full-aperture sources and thus include all detectors in the 1669 evaluations. Thus, a portion of the relative radiometry process will be assessment of the 1670 temporal stability and spatial uniformity of the sources.

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An initial evaluation of SOLARIS noise characteristics included data collected in three sweeps 1672 with 50 frames collected for exposure times varying from 5 to 900 ms. Collections at 5, 10, 1673 15, 20, 25, and 30 ms were made at 10 frames per second, while those at 50, 100, 150, 200, 1674 Reflected solar radiation from the Earth's ocean-atmosphere system (320 nm to 2300 nm wavelength range) can be significantly polarized by the Earth's surface and by atmospheric components. E↵ects from polarization of reflected light bias radiometric performance of various operational spaceborne instruments, such as MODIS and VIIRS, and imagers in geostationary orbits. It is essential to evaluate and correct for this bias in order to perform accurate measurements of reflectance at the top-of-atmosphere [Lyapustin et al., 2014]. CLARREO goal is to perform on-orbit inter-calibration with the target instrument by providing observations coincident in time, and matched in space and viewing geometry. The inter-calibration process consists of iterative adjustments to the target sensor calibration to account for the polarization e↵ects with respect to the observations made by CLARREO . Knowing the inter-calibrated instrument's on-orbit sensitivity to polarization and polarization state of reflected light would determine the radiometric polarization correction.

A. Empirical Polarization Distribution Models
Feasibility of the on-orbit inter-calibration have been demonstrated using existing data -by developing the Polarization Distribution Models (PDM) as functions of viewing scene type and geometry [Nadal and Breon, 1999;Lukashin et al., 2013]. A state of light at the top of the atmosphere is fully specified by three parameters: total radiance, I), degree of linear polarization, P , and angle of linear polarization, . Constructing a PDM is providing mean values and uncertainties for P and for every scene type globally, and as function of solar and viewed geometry.
The only available dataset containing the polarization parameters measured on orbit was collected by the POLarization and Directionality of the Earth's Reflectances (POLDER) instrument onboard the Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL ) satellite. The satellite was operational between 2004 and 2013 and was flying as a part of the A-Train formation at 705 km altitude.