Spectrally Dependent CLARREO Infrared Spectrometer Calibration Requirement for Climate Change Detection

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a b a b b c XU LIU, WAN WU, BRUCE A. WIELICKI, QIGUANG YANG, SUSAN H. KIZER, XIANGLEI HUANG, c a a a XIUHONG CHEN, SEIJI KATO, YOLANDA L. SHEA, AND MARTIN G. MLYNCZAK a NASA Langley Research Center, Hampton, Virginia b Science Systems and Applications, Inc., Hampton, Virginia c Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, Michigan

(Manuscript received 28 September 2016, in ﬁnal form 8 February 2017)

ABSTRACT

Detecting climate trends of atmospheric temperature, moisture, cloud, and surface temperature requires accurately calibrated satellite instruments such as the Climate Absolute Radiance and Refractivity Ob- servatory (CLARREO). Previous studies have evaluated the CLARREO measurement requirements for achieving climate change accuracy goals in orbit. The present study further quantifies the spectrally dependent IR instrument calibration requirement for detecting trends of atmospheric temperature and moisture profiles. The temperature, water vapor, and surface skin temperature variability and the associated correlation time are derived using the Modern-Era Retrospective Analysis for Research and Appli- cations (MERRA) and European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis data. The results are further validated using climate model simulation results. With the derived natural variability as the reference, the calibration requirement is established by carrying out a simulation study for CLARREO observations of various atmospheric states under all-sky conditions. A 0.04-K (k 5 2; 95% confidence) radiometric calibration requirement baseline is derived using a spectral fingerprinting method. It is also demonstrated that the requirement is spectrally dependent and that some spectral regions can be relaxed as a result of the hyperspectral nature of the CLARREO instrument. Relaxing the requirement to 0.06 K (k 5 2) is discussed further based on the uncertainties associated with the temperature and water vapor natural variability and relatively small delay in the time to detect for trends relative to the baseline

case. The methodology used in this study can be extended to other parameters (such as clouds and CO2)and other instrument conﬁgurations.

1. Introduction calibrate other satellite instruments so that data such as those from operational weather sounders and from the The CLARREO mission has been proposed to pro- Earth energy budget instruments can be used to improve vide the essential observations for climate change on climate change detection. decadal time scales with high accuracy that are traceable To detect an accurate trend for a geophysical pa- to International System of Units (SI) standards. The rameter, the observation system has to be able to sepa- demand for high absolute calibration accuracy of the rate the natural variability from anthropogenic climate Climate Absolute Radiance and Refractivity Observa- changes. Therefore, even for a perfect observation sys- tory (CLARREO) instrument is driven by the need to tem, one has to make sufﬁciently long observations to accurately determine the climate trend with minimum minimize the contribution from the natural variability. time delay relative to a perfect observation system For a perfect observation system, the trend uncertainty (Wielicki et al. 2013) and by the need to accurately for a selected geophysical parameter is statistically de-

termined by its variability svar and autocorrelation time tvar as has been explained by both Weatherhead et al. Denotes content that is immediately available upon publica- (1998) and Leroy et al. (2008a). How the measurement tion as open access. uncertainty affects the trend detection uncertainty is

quantiﬁed by the accuracy uncertainty factor Ua Corresponding author e-mail: Xu Liu, xu.liu-1@nasa.gov (Wielicki et al. 2013), where Ua is given as

DOI: 10.1175/JCLI-D-16-0704.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/06/21 02:30 PM UTC 3980 JOURNAL OF CLIMATE VOLUME 30 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 21 s2 t 1 s2 t 1 s2 t spectral coverage of the far IR from 200 to 645 cm , U 5 1 1 cal cal instru instru orbit orbit . (1) a s2 t which is not currently included in hyperspectral sounders var var such as the Cross-Track Infrared Sounder (CrIS), the Atmospheric Infrared Sounder (AIRS), and the Infrared The variable U defines the ratio of the trend detection a Atmospheric Sounding Interferometer (IASI), will allow uncertainty of a real system over that of a perfect system. the CLARREO instrument to measure nearly half of the The measurement uncertainty includes the calibration outgoing longwave radiation currently unobserved by s , instrument noise s , and orbit sampling error cal instru current sounders and will provide additional information s uncertainties, with their associated autocorrela- orbit on cirrus clouds and upper-tropospheric water vapor. The tion times t , t , and t . We can derive the cali- cal instru orbit CO atmospheric emission lines with various trans- bration requirement as follows: 2 mittances will provide vertical temperature profile in- sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi formation. The H2O emission lines will provide water (U2 2 1)s2 t 2 s2 t 2 s2 t s 5 a var var instru instru orbit orbit (2) vapor vertical profile information. The window spectral cal t cal regions will provide information on surface skin temperature and surface emissivity. The broad spectral cov- In this paper, we assume that calibration uncertainty is the erage will enable the CLARREO instrument to dominant factor of the total measurement uncertainty. characterize cloud-top height, cloud phase, cloud Other factors such as the uncertainty due to instrument amount, and cloud particle size. random noise can be minimized by performing spatial and Because of the hyperspectral nature of the IR in- temporal averaging of the observed spectra. Wielicki et al. strument, information from one channel may be highly (2013) have concluded that the orbital sampling error is correlated with others. For example, the CO2 n2 perpen- small compared to natural variability even with just one dicular vibrational band near 15 mm has P, Q, and R 8 90 orbit. Equation (2) can be further simplified as branches. The R branch, which is located on the shorter- sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wavelength side of the Q branch, has similar information (U2 2 1)t content as the P branch, which is on the longer-wavelength s 5 a var s , (3) cal t var cal side of the Q branch. We can tolerate larger calibration errors for those channels in the CO2 P branch as long as we where scal is the observation accuracy for a geophysical can accurately calibrate the spectral region that covers the parameter that can be achieved assuming some value for R branch (or vice versa). Based on this rationale, we may the trend detection uncertainty factor Ua. It should be be able to relax the calibration requirement for spectral noted here that the calibration requirement scal defined in regions where the transmittances of the Fourier transform Eqs. (2) and (3) is not the direct spectral calibration re- spectrometer (FTS) optics or the detector sensitivities are quirement imposed on the instrument. It is the observa- low (e.g., at spectral band edges). tion accuracy uncertainty of geophysical parameters that The details of this study are contained in sections 2 are essential to climate change study. To obtain the and 3. Section 2 of this paper describes the efforts to derive spectral calibration requirement for the Fourier- natural variability values using deseasonalized MERRA transform-based IR instrument of CLARREO, the in- (Rienecker et al. 2011) and ECMWF interim reanalysis verse relationship between the spectral calibration error (ERA-Interim; Dee et al. 2011) data, which include and the associated error for the geophysical variables the information from multiple decades of satellite data. needs to be established. The attribution of the change in Our approach follows the trend analysis methodology of the measured IR spectra to climate change signals (i.e., Weatherhead et al. (1998) and Leroy et al. (2008a).Both changes in temperature, water vapor, cloud property, and methods assume the representation of climate anomalies surface property) has been studied using spectral finger- in a time series using a linear trend model with noise printing methods (Leroy et al. 2008b; Huang et al. 2010; processes (natural variability) embedded and correlated Kato et al. 2011). We use a similar method to perform the amongsuccessivemeasurements. Climate anomalies here inversion of radiance change to the geophysical parameter can be viewed as a linear combination of the climate change. Our goal is to characterize a spectrally dependent trends [a0 in Eq. (4)], the climate variations associated with instrument calibration requirement so that we can accu- known climate forcing factors, and the natural variability: rately detect the atmospheric temperature and moisture Y(t) 5 a t 1 C(t) 1 «, (4) profile changes within the uncertainties defined by scal. 0 The nominal design of the IR spectrometer of 2 CLARREO has a 0.5-cm 1 spectral resolution with a where Y is the climate anomalies as a function of time t, 2 spectral coverage from 200 to 2000 cm 1. The additional C is the contribution of climate forcing factors, and « is

Unauthenticated | Downloaded 10/06/21 02:30 PM UTC 1JUNE 2017 L I U E T A L . 3981 the natural variability. The effects of major climate forcing factors, including volcanic eruptions, solar cycle forcing, El Niño–Southern Oscillation (ENSO) variability, and the quasi-biennial oscillation (QBO), in the time series data have been accounted for in our linear regression analysis. Although ENSO and QBO are classified as ‘‘internal’’ forcing factors, the success of including them in the climate model simulations (Philander et al. 1992; Takahashi 1996) proves the fea- sibility of separating them from other uncharacterized natural variations. If the response of the climate variation to major climate forcing factors can be reliably estimated using representative indices (to be discussed in section 2), removing these climate signals from the anomalies will greatly facilitate the linear trend analysis by reducing the uncertainties caused by the naturally occurring variations. Other contributors to natural variability, including the Pacific decadal oscillation (PDO) and Atlantic meridional overturning circulation (AMOC), are not included in this analysis because of their insignificant impact within a decadal scale as compared with ENSO. Our goal in this paper is not to derive an accurate climate trend but rather to systematically characterize the temperature and water vapor anoma- FIG. 1. Flow diagrams describing the procedures used in sections 2 lies in order to derive the magnitude of natural vari- and 3. ability at all significant atmospheric altitudes. Our results obtained from one set of reanalysis data (e.g., MERRA) can be validated using the results from the calibration errors on the time to detect climate trends other reanalysis dataset (e.g., ERA-Interim). and how the CLARREO IR can be used in synergy with In addition to the comparison study between results current and future operational sounders to decrease the from the MERRA data and those from ERA-Interim time needed to detect the temperature climate trends data, we further compare the reanalysis results with accurately. Fig. 1 shows flowcharts summarizing the those from a general circulation model (GCM) simula- procedures used in sections 2 and 3 to derive the in- tion made by the NOAA/Geophysical Fluid Dynamics strument calibration requirement. Laboratory (GFDL) for phase 5 of the Coupled Model Finally, we present our conclusions on the method- Intercomparison Project (CMIP5). Natural variability ology developed in this study and how we can improve for the vertical profile of temperature and moisture and the work in future studies. the surface skin temperature are calculated and presented. Our goal is to derive reliable natural variability 2. Natural variability study values svar that can be used to define the calibration requirement scal. Continuous time series for temperature, water vapor, Section 3 discusses the simulation study to establish and surface skin temperature are obtained from the baseline for the spectral calibration requirement and MERRA and ERA-Interim data. Both time series how the requirements for specific channels are modified datasets consist of monthly mean results of the satellite to accommodate the instrumentation concerns. We observation era (from January 1979 to December 2013). summarize the information content difference between The MERRA data are obtained from Goddard Earth channels in various wavelength regions and illustrate Sciences Data and Information Service Center as daily how scal changes in correspondence to the change in means for 1.25831.258 latitude–longitude grid boxes. spectral calibration errors. Limiting factors that de- The monthly mean values are derived from the daily termine the calibration requirement are discussed. We means. The ERA-Interim data are available as monthly then present feasible spectral calibration requirement means for 38338 latitude–longitude grid boxes. Global solutions that take potential engineering concerns into mean or zonal mean values are calculated as the consideration. In section 3, we also discuss the impact of weighted average of all the nonmissing gridbox values.

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The weights used are the cosines of the central latitudes ENSO, and QBO in the quasi-decadal signal in the of each grid box. Anomalies are calculated using the tropical stratosphere with regard to temperature and deseasonalized global mean time series data by sub- ozone attributed to the 11-yr solar cycle. Although the tracting the monthly mean data in all years from each QBO’s signature in the lower-troposphere to surface re- individual monthly data value. Both temperature and gion has been neglected in the papers as mentioned water vapor data of MERRA and ERA-Interim are above, Powell and Xu (2013) showed the globally dis- collected as vertical profile layer quantities on pressure tributed response of tropospheric temperature to the grids extending from 1000 to 1 hPa. Both pressure grids QBO and that most of the statistically significant area was are divided into 37 levels, although their pressure level over the mid-to-high latitudes. values are not identical. Atmospheric temperature and ENSO is usually characterized by the Southern Os- water vapor variability are obtained by applying trend cillation index (SOI) (Wigley 2000; Santer et al. 2001), analyses on the time series anomalies for each layer and the multivariate ENSO index (MEI) (Lean and Rind estimating the standard errors. 2008; Foster and Rahmstorf 2011), or sea surface tem- The preindustrial control run (piControl) from the peratures for the Niño-3 and Niño-3.4 regions (Angell GFDL CM3 (Donner et al. 2011) is also used in this 2000; Santer et al. 2001). Solar influence can be char- study. Global mean values are again calculated as the acterized using monthly sunspot numbers (Foster and weighted average of all the gridbox values with a Rahmstorf 2011), the solar 10.7-cm radio flux (Crooks 2831.58 latitude–longitude spatial resolution and a and Gray 2005; Powell and Xu 2013), ultraviolet solar 23-layer pressure grid (1–1000 hPa). We apply a similar radiation flux integrated in the Hartley band (240–270 nm) procedure as mentioned in the previous paragraph to (Chiodo et al. 2014), or total solar irradiance (Lean and deseasonalize the time series data and extract trend and Rind 2008; Foster and Rahmstorf 2011). The choice of natural variability out of the deseasonalized data. QBO proxy indices include zonal wind time series at 30 and 10 hPa (Chiodo et al. 2014; Powell and Xu 2013) a. Temperature or principal components of averaged stratospheric Major climate forcing factors that have been taken zonal wind indices (Crooks and Gray 2005). The vol- into consideration for the global temperature trend canic aerosol effect has been estimated using global study generally consist of ‘‘external forcings,’’ which stratospheric aerosol optical depth (AOD) (Foster and include short-term volcanic eruption and solar vari- Rahmstorf 2011; Powell and Xu 2013; Crooks and Gray ability, and ‘‘internal variability,’’ which includes ENSO 2005). Our multiple-regression experiments show that and QBO. The relative influence of each climate forcing the choice of characteristic proxy for climate forcing factor can be estimated by performing multiple re- factors in general is believed to have an insignificant gression of temperature against their proxy data. By effect on the trend analysis, and the uncertainty of a removing contributions from these factors, a linear certain climate forcing signal as a result of the in- trend, which represents the climate change due to an- accuracy of the proxy indices has negligible impact on thropogenic factors, can then be derived. Previous cli- the analysis for other climate forcing signals. mate trend studies have focused on the impact of the We choose MEI (Wolter and Timlin 2011) to char- above known factors on temperature variations in dif- acterize ENSO. The multivariate ENSO index, which is ferent atmospheric regions. Effects of ENSO and vol- derived from sea level pressure, sea surface wind, sea canoes on the global surface temperature trend were surface temperature, air temperature, and cloud frac- illustrated in various papers (Wigley 2000; Lean and tion, provides a more complete and flexible description Rind 2008; Foster and Rahmstorf 2011). Angell (2000) of the nature of the coupled ocean–atmosphere system studied the influence of ENSO in tropospheric temper- and is less vulnerable to occasional data glitches in the ature variations. Santer et al. (2001) accounted for the monthly update cycles and thus more suitable for the effects of both volcanoes and ENSO in tropospheric global ENSO impact study. We use the zonal average of temperature trends. The influence of solar activity on the 30-hPa zonal wind at the equator (NOAA/NCEP surface temperature was addressed by both Lean and 2016) as the QBO index, and monthly sunspot numbers Rind (2008) and Foster and Rahmstorf (2011). Crooks (SILSO 2015) are used as a proxy for solar activity. We and Gray (2005) used an ECMWF dataset for the period characterize volcanic influence by the AOD data from 1979–2001 to study the influence of the 11-yr solar cycle a global stratospheric aerosol optical thicknesses data- on atmospheric temperature and zonal winds with vol- base (GISS 2016), which are derived from optical ex- canic, ENSO, and QBO signatures being extracted as tinction data (Sato et al. 1993). part of the multivariate regression analysis. Chiodo et al. Considering the delayed response of temperature (2014) investigated the relative role of volcanic eruptions, anomaly to the climate forcing factors, the multiple

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FIG. 2. Global air temperature anomaly at 70 hPa derived using (left) MERRA and (right) ERA-Interim data. (top) The temperature anomaly without accounting for ENSO, volcanic eruption, and solar cycle effects (blue curves); temperature anomaly after the subtraction of the volcanic eruption effect and the solar signals (dark green curves); and the derived linear trend (red lines) after the subtraction. Regression-based estimations for (middle top) ENSO (red curves), (middle) volcanic influence (black curves), (middle bottom) solar signal (green curves), and (bottom) QBO (cyan curves). regression analysis is carried out with optimally lagged stratosphere and that in the troposphere. Generally climate forcing signals, and the naturally occurring speaking, volcanic aerosol induces strong heating in the temperature « is given as follows: stratosphere and cooling in the troposphere. Solar activity influence is much stronger in the stratosphere as « 5 2 2 2 t 2 1 t T(t) a0t a1E(t 1) a2Q(t 2) compared with its influence in the troposphere, while 2 1 t 2 1 t ENSO influence is stronger in the troposphere. Figure 4 a3S(t 3) a4V(t 4), (5) illustrates the influence of different forcing factors on the global surface skin temperature trend. The multiple where T(t) is the temperature anomaly, and E(t), Q(t), regression analysis gives similar results for both S(t), and V(t) are MEI, QBO index, sunspot number, and MERRA and ERA-Interim temperature records. Both AOD in time series, respectively. We carry out the lag- results demonstrate a cooling temperature trend at correlation analysis using values from 0 to 24 months for 70 hPa and a warming trend in lower-tropospheric and each of the four factors and then select the lag values (t1, surface temperature. With the attribution of different t2, t3,andt4) that correspond to the best fit. Once the lag climate forcings fully accounted for, naturally occurring values are obtained a multiple regression is performed variations of temperature at specific altitudes can then to obtain the «(t) with climate trend a0 and other factors be estimated and validated with the climate model removed. Figures 2 and 3 are examples that demonstrate simulation results. the influence of climate forcing factors on global tem- Figure 5 compares the temperature variability from perature data from MERRA and ERA-Interim at 70 reanalysis data with that from the 35-yr-long GFDL and 975 hPa. Figures 2 and 3 clearly illustrate the dif- CM3 piControl output. The CMIP5 piControl ex- ference between the climate forcing signature in the periment with GFDL CM3 imposes nonevolving,

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FIG.3.AsinFig. 2, but for global air temperature anomaly at 975 hPa. preindustrial conditions that do not include volcanic and the GFDL CM3 is smaller than 0.05 K after we eruption inﬂuences and assumes constant solar forcing subtract those two external forcing inﬂuences from the (Taylor et al. 2009). The difference between tropospheric reanalysis temperature anomaly data. The discrepancy temperature variation from MERRA, ERA-Interim, among the three sets of results is much larger at high

FIG.4.AsinFig. 2, but for the global surface skin temperature anomaly.

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FIG. 5. Standard deviation of the temperature anomaly residual derived from MERRA, ERA-Interim, and GFDL CM3 data. (left) Standard deviation derived for MERRA and ERA-Interim temperature anomaly free of volcanic and solar forcing (blue and green solid curves, respectively); variance of GFDL CM3 temperature (red solid curve); and standard deviation of MERRA and ERA-Interim obtained after subtracting the linear trend and all four major climate forcing inﬂuences (blue and green dashed curves, respectively). (right)

Corresponding autocorrelation time tvar calculated using the AR(1) model. The legend for the curves in (right) is as in that shown in (left). altitude, starting from the tropopause (located at 100– accurate way to calculate autocorrelation time, which 200 hPa) and extending into the stratosphere. Errors requires the calculation of autocorrelation coefficients embedded in the multiple regression analysis, un- at all lags. A method by Weatherhead et al. (1998) has certainties associated with the reanalysis data, and the been widely used for the climate trend detection. inaccuracies of the climate model can all affect the ac- Phojanamongkolkij et al. (2014) compared the two curacies of the derived temperature variance. But the methods and concluded that the choice of the method consistency among the tropospheric temperature vari- depends on the autocorrelation characteristics of the ance from both reanalysis and climate model results data. For simplicity, we follow the method used by gives us confidence to establish a solid standard error Weatherhead et al. (1998) and treat the residual as a first- estimation baseline for temperature variance that is key order autoregressive [AR(1)] process. Different autocor- to set the calibration requirement of CLARREO. relation time values are plotted in Fig. 5 (right). Figure 5 also demonstrates that although ENSO and We use Eq. (3) to establish different CLARREO

QBO make trivial contribution to the temperature calibration requirements defined by svar and tvar in variation in the stratosphere, their contribution below Fig. 5. Figure 6 shows the calculated scal,givenatrend 100 hPa can be as large as 0.1 K. It should be noted that accuracy uncertainty factor Ua of 1.2 and an ENSO plays a much more dominant role than QBO in instrument-defined autocorrelation time tcal of 5 yr. the troposphere as illustrated in Fig. 3.Thesvar value The value of Ua and tcal are chosen to be consistent shown in Fig. 5 (left) is the standard deviation of the with those used by Leroy et al. (2008a) and Wielicki temperature residual after we subtract the linear et al. (2013). The most stringent calibration re- trends and prescribed forcing effects from the time quirement comes from the observation requirement for series data. The proper estimation of natural temper- lower-tropospheric temperature. Depending on ature variation also requires the autoregressive anal- whether we include the internal climate forcing (QBO ysis to estimate the autocorrelation time tvar. Leroy and ENSO) as natural variability or not, the scal ranges et al. (2008a) presented a theoretical way to define an from 0.033 to 0.055 K (k 5 2; 95% confidence). This

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TABLE 1. Statistics of surface skin temperature variability (Ua 5 1.2 and tcal 5 5 yr).

svar tvar scal Surface skin temperature anomaly (K) (month) (K) ERA-Interim (free of external forcing) 0.27 4.4 0.045 MERRA (free of external forcing) 0.28 5.1 0.054 GFDL CM3 (piControl run) 0.31 8.6 0.078 ERA-Interim (free of all forcing) 0.24 3.1 0.041 MERRA (free of all forcing) 0.24 3.4 0.045

demonstrate global average water vapor variation from MERRA and ERA-Interim. The poor agreement of long-term water vapor trend between the reanalysis outputs is well known, but reasonable agreement for short-term fluctuations can be expected (Dessler and Davis 2010). The ENSO signals from two reanalysis FIG. 6. Calibration requirement associated with the temperature models agree well since they correlate more strongly variance and the autocorrelation time shown in Fig. 5, given a trend with short-term fluctuations than the long-term trend. accuracy uncertainty factor Ua of 1.2 and an instrument-defined The standard deviation plots demonstrated in Fig. 9 autocorrelation time tcal of 5 yr. also show much better agreement between water vapor variations than the comparison between trends from means that a CLARREO-like satellite system needs the two reanalysis models. We apply a similar analysis to achieve an observation accuracy of 0.033–0.055 K as has been applied to the temperature anomalies in (k 5 2) for lower-tropospheric temperature to ensure section 2a to establish the observation requirements for the desired climate trend detection ability. The ob- the global water vapor trend study. The requirements servation requirement for surface skin temperature are plotted in Fig. 10. Although there is a large dis- trend detection is approximately 0.045 K (k 5 2) (see crepancy between the trend derived from ERA-Interim Table 1) when QBO and ENSO contributions are ex- water vapor anomaly and that from MERRA, the cluded from the natural variability. ENSO signals extracted from both water vapor datasets are similar in scale. The magnitudes of the long-term b. Water vapor water vapor natural variations obtained by subtracting the linear trend and the ENSO signals are in reasonable Similar to the analysis applied to temperature, we agreement. seek to decompose the water vapor in an observational time series with a multiple linear regression form and investigate the attribution of the known climate forcing 3. IR instrument calibration requirement trade factors to the global water vapor variations. The natu- study rally occurring water vapor variations can thus be given The CLARREO IR instrument is designed to have by subtracting the linear trend and associated climate sufficient spectral resolution, spectral coverage, and forcing contributions from the globally distributed water global spatial sampling so that the space–time-averaged vapor anomaly data: spectra can be used to ‘‘fingerprint’’ climate change signals. The radiometric calibration requirement for the « 5 2 2 1 t H(t) a0t a1E(t 1). (6) CLARREO IR instrument is based on the consideration that the errors in the attributed climate signals in- Our studies show that the dominant climate forcing troduced by the radiometric calibration inaccuracy factor that affects the water vapor variations in the should be less than the natural variability measurement troposphere region is the ENSO. Including volcanic requirements. The natural variability measurement re- contribution in Eq. (6) produces insignificant difference. quirements, predominantly driven by the requirements Li and Sharma (2013) concluded that although CMIP3 for temperature and the water vapor observations, are data show strong negative correlation between volca- established in sections 2a and 2b. We first derive the nic aerosol optical depth and water vapor, the reanalysis inverse relationship to quantify the attribution of the data only show weak correlation on a global scale, spectral radiance change to temperature and moisture which is consistent with our finding. Figures 7 and 8 and then carry out a simulation study by using synthetic

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FIG. 7. Global water vapor anomaly at 800 hPa derived using (left) MERRA and (right) ERA-Interim data. (top) The water vapor anomaly without accounting for ENSO effects (blue curves), water vapor anomaly after the subtraction of ENSO effects (dark green curves), and the derived linear trend (red lines) after the subtraction. (bottom) Regression- based estimations for ENSO (red curves) signals. spectral errors that resemble realistic CLARREO in- and low optical transmittance near band edges and by strument characteristics. A practical calibration require- checking the corresponding error introduced in temper- ment can thus be established by considering possible ature and moisture, using the natural variability mea- calibration errors resulting from low detector sensitivity surement requirements as the reference.

FIG.8.AsinFig. 7, but for the global water vapor anomaly at 1000 hPa.

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FIG. 9. (left) Standard deviation of the water vapor anomaly derived from MERRA (blue) and ERA-Interim (green); standard deviation derived from the global average water vapor times series data (solid curves); standard deviation calculated after the subtraction of the ENSO signal (dashed curves); and standard deviation for GFDL CM3 water vapor (red solid curve). (right) Corresponding lag-1 autocorrelation time.

The spectral dependent relationship between the required accuracy. The spectral calibration error DRcal outgoing IR radiation change and the temperature and will introduce errors in the geophysical variables such as water vapor ﬁngerprints can be characterized as atmospheric temperature and moisture proﬁles:

DR 5 SA 1 r, (7) D 5 STS21S 21STS21D X ( ) Rcal . (9) where DR represents the IR spectral fingerprints, S is the spectral signature (fingerprint) matrix, A represents the climate forcing factors, and r is the error vector that accounts for errors such as the radiation fluctuation caused by natural variability and the nonlinearity residual as a result of ignoring higher-order contributions. For climate observing system simulation experiments (OSSEs) using different climate models, signal shape uncertainty is also included in r (Leroy et al. 2008b; Huang et al. 2010). Optimal detection techniques can be used to determine the amplitude of multiple climate signals with a prescribed signature matrix S. The least squares solution (Hasselmann 1997) is given as

2 2 2 A 5 (STS 1S) 1STS 1DR, (8) where S is the covariance of the residual r. In this study, we take into account the instrument FIG. 10. Calibration requirement associated with the water vapor calibration error in the inversion process explicitly. Our variance and the autocorrelation time shown in Fig. 9, given a trend goal is to ﬁnd out how much calibration error we can accuracy uncertainty factor Ua of 1.2 and an instrument-deﬁned tolerate in order to detect a climate variable change to a autocorrelation time tcal of 5 yr.

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To have a direct illustration of the effect that spectral regions. The hyperspectral feature of CLARREO allows calibration errors may impose on the temperature and the vertical profiling of atmospheric properties with water vapor retrieval, spectral signatures of various cli- high vertical resolution. We also expect that a mate forcing factors can be decomposed into the linear CLARREO-like instrument can, under a wide range of combination of the radiance change resulting from the cloudy sky conditions, provide atmospheric information change of geophysical parameters associated with each from below clouds as long as the cloud optical depth is corresponding climate forcing factor: not too high. Figure 14 plots the effective emissivity of water and ice clouds as a function of cloud optical dR depth. Even with cloud optical depth as high as 4, the SA 5 DX. (10) dX effective cloud emissivity is less than 0.9 in most spectral regions (non-opaque). This conclusion is further sup- Equation (7) can thus be rewritten as ported by the nonzero values of the temperature, water vapor, and surface skin temperature Jacobians below DR 5 KDX 1 r0 , (11) 0 clouds as shown in Figs. 11, 12 and 13. It should be noted where DR is the space–time-averaged radiance change, that the cloud optical depth values are in reference to a and K is the Jacobian (dR/dX) for instantaneous ob- visible wavelength at 550 nm. The infrared cloud optical servation and defines the spectral shape and magnitude depths can be estimated from the visible cloud optical of the response of radiance to the change of atmospheric depth according to the following formula: parameters. The term DX represents the change of atmo- Q (y) spheric parameters at a certain geographical location after t(y) 5 e t(vis), (15) 0 Q (vis) a certain observation time interval. The residual term r0 e is the nonlinear residual [R(X 1DX) 2 R(X)] 2 KDX. Equation (11) can be further expanded as follows: where t is the optical thickness and Qe is the cloud ex- 0 tinction coefficient, y represents the infrared channel DR 5 K DX 1 K(DX 2 DX) 1 r . (12) 0 frequency, and vis represents the visible wavelength The residual in Eq. (13) includes two parts: the space– (550 nm). The infrared cloud optical depths are usually time-averaged radiance signal uncertainty due to the smaller than those at 550 nm because Qe(vis) is usually 2 natural variability of atmospheric parameters and the and Qe in the IR spectral region is usually smaller than 2. space–time-averaged nonlinearity errors. The optimal The Jacobians are shown as the change of top-of- detection method can be used to give the solution: atmosphere (TOA) brightness temperature (BT) to the change of the geophysical parameters. The top-left D 5 K TS21K 21K TS21D panels of Figs. 11, 12, and 13 illustrate a case with a cloud X ( s ) s R, (13) visible optical depth as thick as 3.95. The spectral sig- where Ss is the covariance matrix that accounts for both nature of water vapor absorption from below the clouds postfit residuals in Eq. (13). Hence, the effect of cali- is still clear (Fig. 12, top left), and the contribution of bration error DRcal on the retrieved atmospheric pa- surface emission to TOA radiance is nonnegligible rameters can be established as follows: (Fig. 13, top left), indicating non-opaqueness of the cloud. D 5 K TS21K 21K TS21D The effect of spectrally dependent radiometric cali- Xcal ( s ) s Rcal . (14) bration errors of the CLARREO IR instrument on the

How DXcal is affected by DRcal can be partially illustrated fingerprints of the space–time-averaged variations of by the spectral characteristics of the Jacobian K. Figures 11, temperature and water vapor vertical profiles, being 12, and 13 are sample plots of air temperature T, water mathematically expressed in Eq. (14), are estimated via vapor (H2O), and skin temperature (Tskin) Jacobians, simulation studies. We used a global atmospheric profile respectively. We can see from Fig. 11 that the spectral database (Borbas et al. 2005), which consists of 15 704 change in the narrow CO2 absorption band (600– globally selected temperature, water vapor, and ozone 2 800 cm 1) can be attributed to the change in the profiles at 101 vertical pressure levels. We chose this vertical atmospheric temperature. Figures 11 and 12 database because it was carefully selected from global together show that observational errors of temperature radiosondes, ECMWF forecast profiles, and various and water vapor profiles in the lower troposphere other data sources (Seemann et al. 2008; Martins et al. (about 200–900 hPa) can be ascribed to radiance errors 2016). Both temperature and water vapor profiles 2 in the 200–600- and 1210–2000-cm 1 wavenumber have large dynamic ranges and representative global

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FIG. 11. Temperature Jacobian (dBT/dT) plots under different sky conditions. (top left) Cloud located at 106.6 hPa with a visible optical depth of 3.95. (top right) Cloud located at 205.5 hPa with a visible optical depth of 2.21. (bottom left) Cloud located at 397.0 hPa with a visible optical depth of 1.36. (bottom right) Clear sky. coverage (Martins et al. 2016). There is no cloud in- redundant radiative transfer calculations at numerous formation in the database, so we matched these atmo- monochromatic frequencies (Liu et al. 2006). For the 2 spheric profiles with various cloud conditions, including CLARREO IR instrument with 0.5-cm 1 spectral res- clear sky, thin cloud, and opaque cloud cases. The phase olution, only a few hundred monochromatic radiative of the cloud is determined according to the temperatures transfer calculations are needed to accurately represent at the cloud altitude. The cloud optical depth at 550 nm the whole spectrum. PCRTM has been used to retrieve and cloud particle sizes are randomly assigned. The atmospheric and cloud properties from hyperspectral IR ranges of effective radius for water and ice clouds measurements (Liu et al. 2009) and in an atmospheric are 2.5–15 and 5–35 mm,respectively.Weuseafast fingerprinting study (Kato et al. 2011). PCRTM provides principal-component-based radiative transfer model analytical solutions of the Jacobians as direct outputs (PCRTM) to simulate TOA radiance and generate the and is a well-suited tool for the calibration study Jacobians associated with the temperature, water vapor, presented here. surface properties, and cloud parameters (Liu et al. Numerically, the Jacobian K is a linear approximation KTS21K 2006, 2007, 2009, 2016; Yang et al. 2016). The advantages for radiative transfer equations. s is usually ill- of the PCRTM include fast computational speed and conditioned and regularization is needed to solve for DX high accuracy. It takes about 0.02 s to compute one in Eq. (14). We have applied two constraints in our CLARREO radiance spectrum using an Intel 1.6-GHz spectral fingerprinting process. One is to reduce corre- CPU. The root-mean-square errors of the PCRTM rela- lations between matrix elements by projecting temper- tive to a line-by-line radiative transfer model (Clough et al. ature and moisture vertical profiles onto PC space as 1992) are less than 0.03 K. The fast speed of the PCRTM is described by Liu et al. (2009). The other one is to add the achieved by compressing the CLARREO spectra into Tikhonov regularization to the cost function. By con- the principal component (PC) domain and by removing verting the profiles into PC space using selected leading

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FIG. 12. Water vapor Jacobian [dBT/dlog(H2O)] plots under different sky conditions. (top left) Cloud located at 106.6 hPa with a visible optical depth of 3.95. (top right) Cloud located at 205.5 hPa with a visible optical depth of 2.21. (bottom left) Cloud located at 397.0 hPa with a visible optical depth of 1.36. (bottom right) Clear sky. principal components, we can improve the conditional chosen as a multiple of the identity matrix I such that K TS21K G 5 lI l number of the s matrix. In this study, the vertical . The damping factor is chosen in the way that K TS21K temperature and water vapor profiles have 101 pressure the subspaces of the kernel matrix s with smallest levels when calculating the Jacobian matrix K. After PC singular values can be dampened so that the inversion compressing, we only need to retain 20 temperature PC operation will not amplify the contribution of trivial scores and 15 water vapor PC scores. The Tikhonov features. We adopt a regularization scheme that em- regularization method, if applied here to find the solu- ploys different damping factors for temperature and D K TS21K tion to Eq. (14), amounts to finding the solution of X, water vapor of the kernel matrix s . The scheme is which gives a least squares fit to DR but penalizes so- based on our experience in temperature and water vapor lutions by minimizing the cost function: retrievals using hyperspectral data such as IASI (Liu et al. 2009). Since the atmospheric temperature and K TD 2D T S21 K TD 2D 1 GD 2 ( X R) s ( X R) X . (16) water profiles have different units and they are com- pressed into the PC domain, the state vector X elements The solution to Eq. (14) can be rewritten as have large difference in values. To reduce the contributions from PCs with small scores, we take the diagonal D 5 K TS21K 1 GTG 21K TS21D X ( s ) s R, (17) elements of the regularization matrix, which correspond to temperature and water vapor elements, to be the with the calibration error being introduced as mean values of the corresponding diagonal elements of K TS21K the s matrix. We always check our posterior fit- D 5 K TS21K 1 GTG 21K TS21D Xcal ( s ) s Rcal . (18) ting errors in the spectral domain to ensure that they are smaller than the calibration errors. The Tikhonov matrix G is introduced here to improve With the inversion relationship defined by Eq. (14) K TS21K the matrix condition of s and in many cases is being established, we carried out a series of spectral

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FIG. 13. As in Figs. 11 and 12, but showing sample Jacobian plots for surface skin temperature (dBT/dTskin).

fingerprinting trade studies by assuming different in- edges as a result of larger instrument response un- 2 strument calibration errors. Figure 15 plots a 0.04-K certainties. We expect larger errors near 200 cm 1 be- (k 5 2) radiometric calibration error and the corre- cause of the low transmittance of the beam splitter and 2 sponding fingerprinting errors. The blue solid line in larger errors near 645, 1210, and 2000 cm 1 as a result of Fig. 15a shows the 0.04-K spectrally independent cali- the band edge effect of the MCT detector and optical bration error. The corresponding errors (k 5 2) in- filters used for each band. Considering that the pyro- troduced in temperature and water vapor vertical electric detector has sensitivity extending to the mid-IR, profiles are shown as solid blue curves in Figs. 15c,d. we can assume that there is no band edge effect to the 2 As a reference, the calibration requirements for tem- left of 645 cm 1. The red curve Fig. 15b represents a perature and water vapor that have been derived from more realistic, spectrally dependent calibration error the MERRA, ERA-Interim, and GFDL CM3 datasets curve of the CLARREO IR instrument. The corre- are plotted as dashed lines in Figs. 15c,d. The 0.04 K (k 5 2) sponding spectral fingerprinting error for temperature calibration error is marginally tolerable because the cor- and water vapor vertical profiles are shown as solid red responding fingerprint error in near-surface temperature curves in Figs. 15c,d. is approaching the calibration requirement defined by By comparing the effects of calibration errors shown MERRA and ERA-Interim data. as blue and red lines in Figs. 15c,d, we can see that the

In this study, we assume that the CLARREO IR FTS large band edge errors in the P branch of the CO2 2 (Mlynczak 2010) will use a pyroelectric detector for its spectral region (near 650 cm 1) can be tolerated because 2 far-infrared band (band 1: 200–645 cm 1) and photo- of the redundant spectral information carried by the R conductive or photovoltaic mercury cadmium tellu- branch of the CO2 spectral region. The spectral regions 2 ride (MCT) detectors for its two infrared bands (band 2: near 1210 and 2000 cm 1 contain spectral channels 2 2 645–1210 cm 1, and band 3: 1210–2000 cm 1). Usually, mainly sensitive to surface and cloud properties. Our calibration errors tend to be larger at the spectral band studies show that as long as we include the error

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FIG. 14. (top) Water and (bottom) ice cloud emissivity in the CLARREO IR measurement band as functions of cloud visible optical depth t (at 500-nm wavelength). estimation for these spectral regions in the error co- requirement to 0.06 K (k 5 2) means 15.1 yr are needed to 21 variance matrix Ss, the surface skin temperature and reach the 0.1 K decade trend detection uncertainty, fur- cloud property retrievals are not impacted by them, ther delaying the trend detection time by another 1.4 yr. again because of the redundant information from other Graphs like those in Fig. 16 are useful in studying the surface and cloud-sensitive channels. The spectral- synergistic usage of the CLARREO IR instrument and dependent red curve shown in Fig. 15b is a stringent operational sounders. The current hyperspectral IR calibration accuracy requirement that can ensure that sounders have provided valuable data for improving CLARREO’s observation accuracy for climate trend numerical weather prediction (NWP) forecasts for many detection falls within 20% of the accuracy of a perfect years, and the data records will continue for many de- system. The observation accuracy for lower-tropospheric cades. However, since these sounders were designed for temperature will be better than 0.04 K (k 5 2) and that for weather applications, the radiometric calibration speci- the stratospheric temperature should be 0.08 K (k 5 2). ﬁcations of these instruments are less accurate as com- The water vapor observation error near the surface will be pared to the CLARREO IR instrument. As referenced 2 smaller than 0.03 g kg 1 (k 5 2). in Wielicki et al. (2013), the absolute accuracy of the The value of a CLARREO-like observation system operational sounders such as CrIS, AIRS, and IASI with a 0.04-K (k 5 2) calibration accuracy in climate ranges from 0.2 to 0.4 K (k 5 2). Wang et al. (2015) have trend detection can be illustrated by plotting the compared the radiometric consistency of the CrIS, the dependence of lower-tropospheric temperature (at IASI-A and IASI-B on Meteorological Operational 975 hPa) trend detection uncertainty on instrument cali- satellites, and the AIRS using one year (2013) of si- bration accuracy (shown in Fig. 16). The curves are cal- multaneous nadir overpass data. They concluded that culated using a 0.25-K (k 5 2) temperature variance and a the radiometric consistency between CrIS and IASI is 3-month autocorrelation time, which are obtained from on the order of 0.1–0.2 K (68% conﬁdence level; k 5 1) the ERA-Interim data (plotted as a dashed green curve in for the longwave IR (LWIR) band and midwave IR Fig. 5). Using values obtained from MERRA data will (MWIR) band. For CrIS and AIRS, the LWIR and give similar results. We can see from Fig. 16 that a perfect MWIR differences are around 0.1 K (k 5 1) for most of observation system needs about 12.3 yr in order to reach a the spectrally averaged regions they have studied. For 2 trend detection uncertainty of 0.1 K decade 1,whilea some spectral regions in LWIR and MWIR, the differ- system with a 0.04-K calibration accuracy requires 13.7 yr, ences are in the range of 0.15–0.21 K (k 5 1). The ra- lagging 1.4 yr behind. Changing the calibration accuracy diometric differences between these four instruments in

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FIG. 15. The calibration errors and the corresponding errors introduced in temperature and water vapor observation. Spectral calibration error in BT: (a) 0.04-K (k 5 2) baseline error (blue solid curve) and (b) potential calibration error based on a 0.04-K (k 5 2) baseline with detection band edge errors added (red solid curve). Corresponding calibration-introduced (c) temperature and (d) water vapor ﬁngerprinting errors (solid lines in matching colors). Calibration requirements for temperature and water vapor based on natural variability es-

timation results (dashed lines) in (c),(d) as references: scal ECMWF derived from ERA-Interim data, scal MERRA derived from MERRA data, and scal GFDL derived from GFDL CM3 data. These calibration requirements are also plotted in Figs. 6 and 10.

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FIG. 16. Illustration of the dependence of the time to detect the lower-tropospheric temperature trend on the observation systems’ absolute calibration accuracy (95% conﬁdence). The relationships calculated using the temperature natural variability values obtained when QBO and ENSO contributions are excluded from the natural

variability: svar 5 0.25 K and tvar 5 3.0 months (95% confidence). the shortwave IR band are larger as compared to the spatial sampling for climate trend detection by leverag- LWIR and MWIR bands. Using Fig. 16, we can compare ing the CLARREO intercalibrated sounder data. The detection times needed to accurately determine near- combined data will provide better characterization of surface atmospheric temperature using various satellite climate changes in different climate zones or regions, instruments. For the purpose of quantitative compari- which in turn will provide detection for global temper- son, we assume that the absolute calibration accuracy of ature and water vapor changes. the CrIS, AIRS, and IASI is about 0.24 K (k 5 2). It will Our study demonstrates that atmospheric tempera- take 30 years of operation time to achieve the temper- ture trend observations between the midtroposphere 2 ature detection uncertainty of 0.1 K decade 1. This and stratosphere region are less sensitive to instrument means that a CLARREO-like instrument with a 0.04-K calibration error than that between the surface and (k 5 2) calibration accuracy can save more than 16 years lower-troposphere region since the temperature natural as compared with existing hyperspectral IR systems. variability is larger in the upper atmosphere. Figure 17 Furthermore, if a CLARREO IR Pathfinder instrument shows the impact of instrument calibration errors on the is mounted on the International Space Station with the delay of climate trend detection in stratospheric tem- CLARREO reflected solar (RS) Pathfinder instrument perature at 70 hPa. If we assume a 0.48-K (k 5 2) natural or if a CLARREO IR instrument is mounted on a Free variability and an autocorrelation time of 5.6 months, Flyer satellite, we will be able to perform on-orbit in- which are from the GFDL CM3 simulation, a system tersatellite calibration and reduce the calibration un- with a 0.06-K (k 5 2) calibration accuracy will save more certainty of the sounder instruments. We can then take than 10 years of operational time to achieve a 2 advantage of the sounders’ long time records and more 0.1 K decade 1 (k 5 2) trend uncertainty as compared diverse temporal and spatial coverages to further improve with the current IR instruments in orbit and will only lag the accuracy of global temperature climate trend detection. behind a perfect observation system by one year. It should be noted that the CLARREO IR instrument The impact of instrument calibration accuracy on the not only has SI-traceable blackbody temperature mea- surface water vapor trend observation is illustrated in surements but also has an independent onboard verifi- Fig. 18. A significant global-scale increase in surface cation system to check absolute calibrations at various water vapor has been identified (Dai 2006; Willett et al. scene temperatures. The highly accurate hyperspectral 2007), and the reported global surface water vapor radiance spectra observed by the CLARREO IR in- anomalies are on a similar scale to the water vapor anomaly strument can be used as absolute references for inter- derived from MERRA data (shown in Fig. 8). By taking 2 2 satellite calibration and can be used to identify potential the linear trend difference (about 0.1 g kg 1 decade 1) error sources such as the blackbody temperature mea- between the MERRA result and the ERA-Interim surement and nonlinearity correction. Since the opera- result (red lines in Fig. 8) as a rough estimation for tional sounders provide swath widths larger than the surface water vapor trend uncertainty, a system 2000 km, we will have improved diurnal sampling and with a 0.06-K (k 5 2) calibration accuracy has the

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FIG. 17. Illustration of the dependence of the time to detect the stratospheric temperature [at 70 hPa with svar 5 0.48 K and tvar 5 5.6 months (95% conﬁdence)] cooling trend on the observation systems’ calibration accuracy (95% conﬁdence). potential to reduce the detection time by more than six validates the use of multiple regression to obtain reliable years relative to the current IR instruments in orbit. natural variability free of major forcing factors. Al- though the uncertainty of temperature variance in the stratosphere is large—the discrepancy between re- 4. Conclusions analysis variability and GFDL CM3 variability in the We have studied the spectrally dependent radiometric stratosphere can be larger than 100%—only a narrow calibration requirement of the CLARREO IR in- spectral region’s calibration requirement is associated strument based on the climate trend detection un- with the stratospheric temperature observation re- certainty requirement. The validity of the presented quirement. The differences in the prescriptions of water calibration requirement depends on the accuracy of the vapor variance, especially those between reanalyses and reanalysis and the climate model data from which the the GCM, introduce uncertainty in the calibration re- magnitude of naturally occurring variations are calcu- quirement for monitoring tropospheric water vapor in lated. Our analysis shows a good agreement between the the infrared spectra; however, our simulation study temperature variance derived from ERA-Interim data demonstrates that the radiometric calibration re- and that from MERRA data. Also demonstrated is the quirement imposed by the atmospheric temperature consistency between the reanalysis results and the trend observation needs will be more stringent than that GFDL CM3 results in the troposphere region, which derived from the most conservative water vapor natural

FIG. 18. Illustration of the dependence of the time to detect the surface specific humidity [at 1000 hPa with svar 5 21 0.17 g kg and tvar 5 9.6 months (95% confidence)] trend on the observation systems’ calibration accuracy (95% confidence).

Unauthenticated | Downloaded 10/06/21 02:30 PM UTC 1JUNE 2017 L I U E T A L . 3997 variability value. It is the observation requirement for Acknowledgments. This research was supported by the temperature of the troposphere and surface that the NASA CLARREO project. The effort of two co- determines the spectral calibration baseline in the IR authors, Huang and Chen, was supported by NASA measurement band. under Grant NNX15AC25G awarded to the University The 0.04-K (k 5 2; 95% confidence level) calibration of Michigan. The NASA SMD High-End Computing baseline demonstrated in Fig. 15b is established based (HEC) resources were used to support the radiative on a given uncertainty factor (Ua 5 1.2). It can be viewed transfer model (PCRTM) development. We thank as a conservative and stringent solution. 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