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  • View in gallery

    Flow diagrams describing the procedures used in sections 2 and 3.

  • View in gallery

    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).

  • View in gallery

    As in Fig. 2, but for global air temperature anomaly at 975 hPa.

  • View in gallery

    As in Fig. 2, but for the global surface skin temperature anomaly.

  • View in gallery

    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 τvar calculated using the AR(1) model. The legend for the curves in (right) is as in that shown in (left).

  • View in gallery

    Calibration requirement associated with the temperature variance and the autocorrelation time shown in Fig. 5, given a trend accuracy uncertainty factor Ua of 1.2 and an instrument-defined autocorrelation time τcal of 5 yr.

  • View in gallery

    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.

  • View in gallery

    As in Fig. 7, but for the global water vapor anomaly at 1000 hPa.

  • View in gallery

    (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.

  • View in gallery

    Calibration requirement associated with the water vapor variance and the autocorrelation time shown in Fig. 9, given a trend accuracy uncertainty factor Ua of 1.2 and an instrument-defined autocorrelation time τcal of 5 yr.

  • View in gallery

    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.

  • View in gallery

    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.

  • View in gallery

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

  • View in gallery

    (top) Water and (bottom) ice cloud emissivity in the CLARREO IR measurement band as functions of cloud visible optical depth τ (at 500-nm wavelength).

  • View in gallery

    The calibration errors and the corresponding errors introduced in temperature and water vapor observation. Spectral calibration error in BT: (a) 0.04-K (k = 2) baseline error (blue solid curve) and (b) potential calibration error based on a 0.04-K (k = 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 estimation results (dashed lines) in (c),(d) as references: σcal ECMWF derived from ERA-Interim data, σcal MERRA derived from MERRA data, and σcal GFDL derived from GFDL CM3 data. These calibration requirements are also plotted in Figs. 6 and 10.

  • View in gallery

    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: σvar = 0.25 K and τvar = 3.0 months (95% confidence).

  • View in gallery

    Illustration of the dependence of the time to detect the stratospheric temperature [at 70 hPa with σvar = 0.48 K and τvar = 5.6 months (95% confidence)] cooling trend on the observation systems’ calibration accuracy (95% confidence).

  • View in gallery

    Illustration of the dependence of the time to detect the surface specific humidity [at 1000 hPa with σvar = 0.17 g kg−1 and τvar = 9.6 months (95% confidence)] trend on the observation systems’ calibration accuracy (95% confidence).

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Spectrally Dependent CLARREO Infrared Spectrometer Calibration Requirement for Climate Change Detection

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  • 1 NASA Langley Research Center, Hampton, Virginia
  • | 2 Science Systems and Applications, Inc., Hampton, Virginia
  • | 3 Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, Michigan
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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 Observatory (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 Applications (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 = 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 = 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.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Xu Liu, xu.liu-1@nasa.gov

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 Observatory (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 Applications (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 = 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 = 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.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author e-mail: Xu Liu, xu.liu-1@nasa.gov

1. Introduction

The CLARREO mission has been proposed to provide the essential observations for climate change on decadal time scales with high accuracy that are traceable to International System of Units (SI) standards. The demand for high absolute calibration accuracy of the Climate Absolute Radiance and Refractivity Observatory (CLARREO) instrument is driven by the need to accurately determine the climate trend with minimum time delay relative to a perfect observation system (Wielicki et al. 2013) and by the need to accurately calibrate other satellite instruments so that data such as those from operational weather sounders and from the Earth energy budget instruments can be used to improve climate change detection.

To detect an accurate trend for a geophysical parameter, the observation system has to be able to separate the natural variability from anthropogenic climate changes. Therefore, even for a perfect observation system, one has to make sufficiently long observations to minimize the contribution from the natural variability. For a perfect observation system, the trend uncertainty for a selected geophysical parameter is statistically determined by its variability σvar and autocorrelation time τvar as has been explained by both Weatherhead et al. (1998) and Leroy et al. (2008a). How the measurement uncertainty affects the trend detection uncertainty is quantified by the accuracy uncertainty factor Ua (Wielicki et al. 2013), where Ua is given as
e1
The variable Ua defines the ratio of the trend detection uncertainty of a real system over that of a perfect system. The measurement uncertainty includes the calibration σcal, instrument noise σinstru, and orbit sampling error σorbit uncertainties, with their associated autocorrelation times τcal, τinstru, and τorbit. We can derive the calibration requirement as follows:
e2
In this paper, we assume that calibration uncertainty is the dominant factor of the total measurement uncertainty. Other factors such as the uncertainty due to instrument random noise can be minimized by performing spatial and temporal averaging of the observed spectra. Wielicki et al. (2013) have concluded that the orbital sampling error is small compared to natural variability even with just one 90° orbit. Equation (2) can be further simplified as
e3
where σcal is the observation accuracy for a geophysical parameter that can be achieved assuming some value for the trend detection uncertainty factor Ua. It should be noted here that the calibration requirement σcal defined in Eqs. (2) and (3) is not the direct spectral calibration requirement imposed on the instrument. It is the observation accuracy uncertainty of geophysical parameters that are essential to climate change study. To obtain the spectral calibration requirement for the Fourier-transform-based IR instrument of CLARREO, the inverse relationship between the spectral calibration error and the associated error for the geophysical variables needs to be established. The attribution of the change in the measured IR spectra to climate change signals (i.e., changes in temperature, water vapor, cloud property, and surface property) has been studied using spectral fingerprinting methods (Leroy et al. 2008b; Huang et al. 2010; Kato et al. 2011). We use a similar method to perform the inversion of radiance change to the geophysical parameter change. Our goal is to characterize a spectrally dependent instrument calibration requirement so that we can accurately detect the atmospheric temperature and moisture profile changes within the uncertainties defined by σcal.

The nominal design of the IR spectrometer of CLARREO has a 0.5-cm−1 spectral resolution with a spectral coverage from 200 to 2000 cm−1. The additional spectral coverage of the far IR from 200 to 645 cm−1, which is not currently included in hyperspectral sounders such as the Cross-Track Infrared Sounder (CrIS), the Atmospheric Infrared Sounder (AIRS), and the Infrared Atmospheric Sounding Interferometer (IASI), will allow the CLARREO instrument to measure nearly half of the outgoing longwave radiation currently unobserved by current sounders and will provide additional information on cirrus clouds and upper-tropospheric water vapor. The CO2 atmospheric emission lines with various transmittances will provide vertical temperature profile information. The H2O emission lines will provide water vapor vertical profile information. The window spectral regions will provide information on surface skin temperature and surface emissivity. The broad spectral coverage will enable the CLARREO instrument to characterize cloud-top height, cloud phase, cloud amount, and cloud particle size.

Because of the hyperspectral nature of the IR instrument, information from one channel may be highly correlated with others. For example, the CO2 ν2 perpendicular vibrational band near 15 μm has P, Q, and R branches. The R branch, which is located on the shorter-wavelength side of the Q branch, has similar information content as the P branch, which is on the longer-wavelength side of the Q branch. We can tolerate larger calibration errors for those channels in the CO2 P branch as long as we can accurately calibrate the spectral region that covers the R branch (or vice versa). Based on this rationale, we may be able to relax the calibration requirement for spectral regions where the transmittances of the Fourier transform spectrometer (FTS) optics or the detector sensitivities are low (e.g., at spectral band edges).

The details of this study are contained in sections 2 and 3. Section 2 of this paper describes the efforts to derive natural variability values using deseasonalized MERRA (Rienecker et al. 2011) and ECMWF interim reanalysis (ERA-Interim; Dee et al. 2011) data, which include the information from multiple decades of satellite data. Our approach follows the trend analysis methodology of Weatherhead et al. (1998) and Leroy et al. (2008a). Both methods assume the representation of climate anomalies in a time series using a linear trend model with noise processes (natural variability) embedded and correlated among successive measurements. Climate anomalies here can be viewed as a linear combination of the climate trends [a0 in Eq. (4)], the climate variations associated with known climate forcing factors, and the natural variability:
e4
where Y is the climate anomalies as a function of time t, C is the contribution of climate forcing factors, and ε is 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 feasibility 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 anomalies in order to derive the magnitude of natural variability 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 other reanalysis dataset (e.g., ERA-Interim).

In addition to the comparison study between results from the MERRA data and those from ERA-Interim data, we further compare the reanalysis results with those from a general circulation model (GCM) simulation made by the NOAA/Geophysical Fluid Dynamics Laboratory (GFDL) for phase 5 of the Coupled Model Intercomparison Project (CMIP5). Natural variability for the vertical profile of temperature and moisture and the surface skin temperature are calculated and presented. Our goal is to derive reliable natural variability values σvar that can be used to define the calibration requirement σcal.

Section 3 discusses the simulation study to establish the baseline for the spectral calibration requirement and how the requirements for specific channels are modified to accommodate the instrumentation concerns. We summarize the information content difference between channels in various wavelength regions and illustrate how σcal changes in correspondence to the change in spectral calibration errors. Limiting factors that determine the calibration requirement are discussed. We then present feasible spectral calibration requirement solutions that take potential engineering concerns into consideration. In section 3, we also discuss the impact of calibration errors on the time to detect climate trends and how the CLARREO IR can be used in synergy with current and future operational sounders to decrease the time needed to detect the temperature climate trends accurately. Fig. 1 shows flowcharts summarizing the procedures used in sections 2 and 3 to derive the instrument calibration requirement.

Fig. 1.
Fig. 1.

Flow diagrams describing the procedures used in sections 2 and 3.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Finally, we present our conclusions on the methodology developed in this study and how we can improve the work in future studies.

2. Natural variability study

Continuous time series for temperature, water vapor, and surface skin temperature are obtained from MERRA and ERA-Interim data. Both time series datasets consist of monthly mean results of the satellite observation era (from January 1979 to December 2013). The MERRA data are obtained from Goddard Earth Sciences Data and Information Service Center as daily means for 1.25° × 1.25° latitude–longitude grid boxes. The monthly mean values are derived from the daily means. The ERA-Interim data are available as monthly means for 3° × 3° latitude–longitude grid boxes. Global mean or zonal mean values are calculated as the weighted average of all the nonmissing gridbox values. The weights used are the cosines of the central latitudes of each grid box. Anomalies are calculated using the deseasonalized global mean time series data by subtracting the monthly mean data in all years from each individual monthly data value. Both temperature and water vapor data of MERRA and ERA-Interim are collected as vertical profile layer quantities on pressure grids extending from 1000 to 1 hPa. Both pressure grids are divided into 37 levels, although their pressure level values are not identical. Atmospheric temperature and water vapor variability are obtained by applying trend analyses on the time series anomalies for each layer and estimating the standard errors.

The preindustrial control run (piControl) from the GFDL CM3 (Donner et al. 2011) is also used in this study. Global mean values are again calculated as the weighted average of all the gridbox values with a 2° × 1.5° latitude–longitude spatial resolution and a 23-layer pressure grid (1–1000 hPa). We apply a similar procedure as mentioned in the previous paragraph to deseasonalize the time series data and extract trend and natural variability out of the deseasonalized data.

a. Temperature

Major climate forcing factors that have been taken into consideration for the global temperature trend study generally consist of “external forcings,” which include short-term volcanic eruption and solar variability, and “internal variability,” which includes ENSO and QBO. The relative influence of each climate forcing factor can be estimated by performing multiple regression of temperature against their proxy data. By removing contributions from these factors, a linear trend, which represents the climate change due to anthropogenic factors, can then be derived. Previous climate trend studies have focused on the impact of the above known factors on temperature variations in different atmospheric regions. Effects of ENSO and volcanoes on the global surface temperature trend were illustrated in various papers (Wigley 2000; Lean and Rind 2008; Foster and Rahmstorf 2011). Angell (2000) studied the influence of ENSO in tropospheric temperature variations. Santer et al. (2001) accounted for the effects of both volcanoes and ENSO in tropospheric temperature trends. The influence of solar activity on surface temperature was addressed by both Lean and Rind (2008) and Foster and Rahmstorf (2011). Crooks and Gray (2005) used an ECMWF dataset for the period 1979–2001 to study the influence of the 11-yr solar cycle on atmospheric temperature and zonal winds with volcanic, ENSO, and QBO signatures being extracted as part of the multivariate regression analysis. Chiodo et al. (2014) investigated the relative role of volcanic eruptions, ENSO, and QBO in the quasi-decadal signal in the tropical stratosphere with regard to temperature and ozone attributed to the 11-yr solar cycle. Although the QBO’s signature in the lower-troposphere to surface region has been neglected in the papers as mentioned above, Powell and Xu (2013) showed the globally distributed response of tropospheric temperature to the QBO and that most of the statistically significant area was over the mid-to-high latitudes.

ENSO is usually characterized by the Southern Oscillation index (SOI) (Wigley 2000; Santer et al. 2001), the multivariate ENSO index (MEI) (Lean and Rind 2008; Foster and Rahmstorf 2011), or sea surface temperatures for the Niño-3 and Niño-3.4 regions (Angell 2000; Santer et al. 2001). Solar influence can be characterized using monthly sunspot numbers (Foster and Rahmstorf 2011), the solar 10.7-cm radio flux (Crooks and Gray 2005; Powell and Xu 2013), ultraviolet solar radiation flux integrated in the Hartley band (240–270 nm) (Chiodo et al. 2014), or total solar irradiance (Lean and Rind 2008; Foster and Rahmstorf 2011). The choice of QBO proxy indices include zonal wind time series at 30 and 10 hPa (Chiodo et al. 2014; Powell and Xu 2013) or principal components of averaged stratospheric zonal wind indices (Crooks and Gray 2005). The volcanic aerosol effect has been estimated using global stratospheric aerosol optical depth (AOD) (Foster and Rahmstorf 2011; Powell and Xu 2013; Crooks and Gray 2005). Our multiple-regression experiments show that the choice of characteristic proxy for climate forcing factors in general is believed to have an insignificant effect on the trend analysis, and the uncertainty of a certain climate forcing signal as a result of the inaccuracy of the proxy indices has negligible impact on the analysis for other climate forcing signals.

We choose MEI (Wolter and Timlin 2011) to characterize ENSO. The multivariate ENSO index, which is derived from sea level pressure, sea surface wind, sea surface temperature, air temperature, and cloud fraction, provides a more complete and flexible description of the nature of the coupled ocean–atmosphere system and is less vulnerable to occasional data glitches in the monthly update cycles and thus more suitable for the global ENSO impact study. We use the zonal average of the 30-hPa zonal wind at the equator (NOAA/NCEP 2016) as the QBO index, and monthly sunspot numbers (SILSO 2015) are used as a proxy for solar activity. We characterize volcanic influence by the AOD data from a global stratospheric aerosol optical thicknesses database (GISS 2016), which are derived from optical extinction data (Sato et al. 1993).

Considering the delayed response of temperature anomaly to the climate forcing factors, the multiple regression analysis is carried out with optimally lagged climate forcing signals, and the naturally occurring temperature ε is given as follows:
e5
where T(t) is the temperature anomaly, and E(t), Q(t), S(t), and V(t) are MEI, QBO index, sunspot number, and AOD in time series, respectively. We carry out the lag-correlation analysis using values from 0 to 24 months for each of the four factors and then select the lag values (τ1, τ2, τ3, and τ4) that correspond to the best fit. Once the lag values are obtained a multiple regression is performed to obtain the ε(t) with climate trend a0 and other factors removed. Figures 2 and 3 are examples that demonstrate the influence of climate forcing factors on global temperature data from MERRA and ERA-Interim at 70 and 975 hPa. Figures 2 and 3 clearly illustrate the difference between the climate forcing signature in the stratosphere and that in the troposphere. Generally speaking, volcanic aerosol induces strong heating in the stratosphere and cooling in the troposphere. Solar activity influence is much stronger in the stratosphere as compared with its influence in the troposphere, while ENSO influence is stronger in the troposphere. Figure 4 illustrates the influence of different forcing factors on the global surface skin temperature trend. The multiple regression analysis gives similar results for both MERRA and ERA-Interim temperature records. Both results demonstrate a cooling temperature trend at 70 hPa and a warming trend in lower-tropospheric and surface temperature. With the attribution of different climate forcings fully accounted for, naturally occurring variations of temperature at specific altitudes can then be estimated and validated with the climate model simulation results.
Fig. 2.
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).

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 3.
Fig. 3.

As in Fig. 2, but for global air temperature anomaly at 975 hPa.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 4.
Fig. 4.

As in Fig. 2, but for the global surface skin temperature anomaly.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Figure 5 compares the temperature variability from reanalysis data with that from the 35-yr-long GFDL CM3 piControl output. The CMIP5 piControl experiment with GFDL CM3 imposes nonevolving, preindustrial conditions that do not include volcanic eruption influences and assumes constant solar forcing (Taylor et al. 2009). The difference between tropospheric temperature variation from MERRA, ERA-Interim, and the GFDL CM3 is smaller than 0.05 K after we subtract those two external forcing influences from the reanalysis temperature anomaly data. The discrepancy among the three sets of results is much larger at high altitude, starting from the tropopause (located at 100–200 hPa) and extending into the stratosphere. Errors embedded in the multiple regression analysis, uncertainties associated with the reanalysis data, and the inaccuracies of the climate model can all affect the accuracies of the derived temperature variance. But the consistency among the tropospheric temperature variance from both reanalysis and climate model results gives us confidence to establish a solid standard error estimation baseline for temperature variance that is key to set the calibration requirement of CLARREO.

Fig. 5.
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 τvar calculated using the AR(1) model. The legend for the curves in (right) is as in that shown in (left).

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Figure 5 also demonstrates that although ENSO and QBO make trivial contribution to the temperature variation in the stratosphere, their contribution below 100 hPa can be as large as 0.1 K. It should be noted that ENSO plays a much more dominant role than QBO in the troposphere as illustrated in Fig. 3. The σvar value shown in Fig. 5 (left) is the standard deviation of the temperature residual after we subtract the linear trends and prescribed forcing effects from the time series data. The proper estimation of natural temperature variation also requires the autoregressive analysis to estimate the autocorrelation time τvar. Leroy et al. (2008a) presented a theoretical way to define an accurate way to calculate autocorrelation time, which requires the calculation of autocorrelation coefficients at all lags. A method by Weatherhead et al. (1998) has been widely used for the climate trend detection. Phojanamongkolkij et al. (2014) compared the two methods and concluded that the choice of the method depends on the autocorrelation characteristics of the data. For simplicity, we follow the method used by Weatherhead et al. (1998) and treat the residual as a first-order autoregressive [AR(1)] process. Different autocorrelation time values are plotted in Fig. 5 (right).

We use Eq. (3) to establish different CLARREO calibration requirements defined by σvar and τvar in Fig. 5. Figure 6 shows the calculated σcal, given a trend accuracy uncertainty factor Ua of 1.2 and an instrument-defined autocorrelation time τcal of 5 yr. The value of Ua and τcal are chosen to be consistent with those used by Leroy et al. (2008a) and Wielicki et al. (2013). The most stringent calibration requirement comes from the observation requirement for lower-tropospheric temperature. Depending on whether we include the internal climate forcing (QBO and ENSO) as natural variability or not, the σcal ranges from 0.033 to 0.055 K (k = 2; 95% confidence). This means that a CLARREO-like satellite system needs to achieve an observation accuracy of 0.033–0.055 K (k = 2) for lower-tropospheric temperature to ensure the desired climate trend detection ability. The observation requirement for surface skin temperature trend detection is approximately 0.045 K (k = 2) (see Table 1) when QBO and ENSO contributions are excluded from the natural variability.

Fig. 6.
Fig. 6.

Calibration requirement associated with the temperature variance and the autocorrelation time shown in Fig. 5, given a trend accuracy uncertainty factor Ua of 1.2 and an instrument-defined autocorrelation time τcal of 5 yr.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Table 1.

Statistics of surface skin temperature variability (Ua = 1.2 and τcal = 5 yr).

Table 1.

b. Water vapor

Similar to the analysis applied to temperature, we 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 factors to the global water vapor variations. The naturally occurring water vapor variations can thus be given by subtracting the linear trend and associated climate forcing contributions from the globally distributed water vapor anomaly data:
e6
Our studies show that the dominant climate forcing factor that affects the water vapor variations in the troposphere region is the ENSO. Including volcanic contribution in Eq. (6) produces insignificant difference. Li and Sharma (2013) concluded that although CMIP3 data show strong negative correlation between volcanic aerosol optical depth and water vapor, the reanalysis data only show weak correlation on a global scale, which is consistent with our finding. Figures 7 and 8 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 models agree well since they correlate more strongly with short-term fluctuations than the long-term trend. The standard deviation plots demonstrated in Fig. 9 also show much better agreement between water vapor variations than the comparison between trends from the two reanalysis models. We apply a similar analysis as has been applied to the temperature anomalies in section 2a to establish the observation requirements for the global water vapor trend study. The requirements are plotted in Fig. 10. Although there is a large discrepancy between the trend derived from ERA-Interim water vapor anomaly and that from MERRA, the ENSO signals extracted from both water vapor datasets are similar in scale. The magnitudes of the long-term water vapor natural variations obtained by subtracting the linear trend and the ENSO signals are in reasonable agreement.
Fig. 7.
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.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 8.
Fig. 8.

As in Fig. 7, but for the global water vapor anomaly at 1000 hPa.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 9.
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.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 10.
Fig. 10.

Calibration requirement associated with the water vapor variance and the autocorrelation time shown in Fig. 9, given a trend accuracy uncertainty factor Ua of 1.2 and an instrument-defined autocorrelation time τcal of 5 yr.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

3. IR instrument calibration requirement trade study

The CLARREO IR instrument is designed to have sufficient spectral resolution, spectral coverage, and global spatial sampling so that the space–time-averaged spectra can be used to “fingerprint” climate change signals. The radiometric calibration requirement for the CLARREO IR instrument is based on the consideration that the errors in the attributed climate signals introduced by the radiometric calibration inaccuracy should be less than the natural variability measurement requirements. The natural variability measurement requirements, predominantly driven by the requirements for temperature and the water vapor observations, are established in sections 2a and 2b. We first derive the inverse relationship to quantify the attribution of the spectral radiance change to temperature and moisture and then carry out a simulation study by using synthetic spectral errors that resemble realistic CLARREO instrument characteristics. A practical calibration requirement can thus be established by considering possible calibration errors resulting from low detector sensitivity and low optical transmittance near band edges and by checking the corresponding error introduced in temperature and moisture, using the natural variability measurement requirements as the reference.

The spectral dependent relationship between the outgoing IR radiation change and the temperature and water vapor fingerprints can be characterized as
e7
where ΔR represents the IR spectral fingerprints, is the spectral signature (fingerprint) matrix, 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 . The least squares solution (Hasselmann 1997) is given as
e8
where Σ is the covariance of the residual r.
In this study, we take into account the instrument calibration error in the inversion process explicitly. Our goal is to find out how much calibration error we can tolerate in order to detect a climate variable change to a required accuracy. The spectral calibration error ΔRcal will introduce errors in the geophysical variables such as atmospheric temperature and moisture profiles:
e9
To have a direct illustration of the effect that spectral calibration errors may impose on the temperature and water vapor retrieval, spectral signatures of various climate forcing factors can be decomposed into the linear combination of the radiance change resulting from the change of geophysical parameters associated with each corresponding climate forcing factor:
e10
Equation (7) can thus be rewritten as
e11
where is the space–time-averaged radiance change, and is the Jacobian (dR/dX) for instantaneous observation and defines the spectral shape and magnitude of the response of radiance to the change of atmospheric parameters. The term ΔX represents the change of atmospheric parameters at a certain geographical location after a certain observation time interval. The residual term is the nonlinear residual [R(X + ΔX) − R(X)] − ΔX. Equation (11) can be further expanded as follows:
e12
The residual in Eq. (13) includes two parts: the space–time-averaged radiance signal uncertainty due to the natural variability of atmospheric parameters and the space–time-averaged nonlinearity errors. The optimal detection method can be used to give the solution:
e13
where Σs is the covariance matrix that accounts for both postfit residuals in Eq. (13). Hence, the effect of calibration error ΔRcal on the retrieved atmospheric parameters can be established as follows:
e14
How ΔXcal is affected by ΔRcal can be partially illustrated by the spectral characteristics of the Jacobian . Figures 11, 12, and 13 are sample plots of air temperature T, water vapor (H2O), and skin temperature (Tskin) Jacobians, respectively. We can see from Fig. 11 that the spectral change in the narrow CO2 absorption band (600–800 cm−1) can be attributed to the change in the vertical atmospheric temperature. Figures 11 and 12 together show that observational errors of temperature and water vapor profiles in the lower troposphere (about 200–900 hPa) can be ascribed to radiance errors in the 200–600- and 1210–2000-cm−1 wavenumber regions. The hyperspectral feature of CLARREO allows the vertical profiling of atmospheric properties with high vertical resolution. We also expect that a CLARREO-like instrument can, under a wide range of cloudy sky conditions, provide atmospheric information from below clouds as long as the cloud optical depth is not too high. Figure 14 plots the effective emissivity of water and ice clouds as a function of cloud optical depth. Even with cloud optical depth as high as 4, the effective cloud emissivity is less than 0.9 in most spectral regions (non-opaque). This conclusion is further supported by the nonzero values of the temperature, water vapor, and surface skin temperature Jacobians below clouds as shown in Figs. 11, 12 and 13. It should be noted that the cloud optical depth values are in reference to a visible wavelength at 550 nm. The infrared cloud optical depths can be estimated from the visible cloud optical depth according to the following formula:
e15
where τ is the optical thickness and Qe is the cloud extinction coefficient, υ represents the infrared channel frequency, and vis represents the visible wavelength (550 nm). The infrared cloud optical depths are usually smaller than those at 550 nm because Qe(vis) is usually 2 and Qe in the IR spectral region is usually smaller than 2. The Jacobians are shown as the change of top-of-atmosphere (TOA) brightness temperature (BT) to the change of the geophysical parameters. The top-left panels of Figs. 11, 12, and 13 illustrate a case with a cloud visible optical depth as thick as 3.95. The spectral signature of water vapor absorption from below the clouds is still clear (Fig. 12, top left), and the contribution of surface emission to TOA radiance is nonnegligible (Fig. 13, top left), indicating non-opaqueness of the cloud.
Fig. 11.
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.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 12.
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.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 13.
Fig. 13.

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

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Fig. 14.
Fig. 14.

(top) Water and (bottom) ice cloud emissivity in the CLARREO IR measurement band as functions of cloud visible optical depth τ (at 500-nm wavelength).

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

The effect of spectrally dependent radiometric calibration errors of the CLARREO IR instrument on the fingerprints of the space–time-averaged variations of temperature and water vapor vertical profiles, being mathematically expressed in Eq. (14), are estimated via simulation studies. We used a global atmospheric profile database (Borbas et al. 2005), which consists of 15 704 globally selected temperature, water vapor, and ozone profiles at 101 vertical pressure levels. We chose this database because it was carefully selected from global radiosondes, ECMWF forecast profiles, and various other data sources (Seemann et al. 2008; Martins et al. 2016). Both temperature and water vapor profiles have large dynamic ranges and representative global coverage (Martins et al. 2016). There is no cloud information in the database, so we matched these atmospheric profiles with various cloud conditions, including clear sky, thin cloud, and opaque cloud cases. The phase of the cloud is determined according to the temperatures at the cloud altitude. The cloud optical depth at 550 nm and cloud particle sizes are randomly assigned. The ranges of effective radius for water and ice clouds are 2.5–15 and 5–35 μm, respectively. We use a fast principal-component-based radiative transfer model (PCRTM) to simulate TOA radiance and generate the Jacobians associated with the temperature, water vapor, surface properties, and cloud parameters (Liu et al. 2006, 2007, 2009, 2016; Yang et al. 2016). The advantages of the PCRTM include fast computational speed and high accuracy. It takes about 0.02 s to compute one CLARREO radiance spectrum using an Intel 1.6-GHz CPU. The root-mean-square errors of the PCRTM relative to a line-by-line radiative transfer model (Clough et al. 1992) are less than 0.03 K. The fast speed of the PCRTM is achieved by compressing the CLARREO spectra into the principal component (PC) domain and by removing redundant radiative transfer calculations at numerous monochromatic frequencies (Liu et al. 2006). For the CLARREO IR instrument with 0.5-cm−1 spectral resolution, only a few hundred monochromatic radiative transfer calculations are needed to accurately represent the whole spectrum. PCRTM has been used to retrieve atmospheric and cloud properties from hyperspectral IR measurements (Liu et al. 2009) and in an atmospheric fingerprinting study (Kato et al. 2011). PCRTM provides analytical solutions of the Jacobians as direct outputs and is a well-suited tool for the calibration study presented here.

Numerically, the Jacobian is a linear approximation for radiative transfer equations. is usually ill-conditioned and regularization is needed to solve for ΔX in Eq. (14). We have applied two constraints in our spectral fingerprinting process. One is to reduce correlations between matrix elements by projecting temperature and moisture vertical profiles onto PC space as described by Liu et al. (2009). The other one is to add the Tikhonov regularization to the cost function. By converting the profiles into PC space using selected leading principal components, we can improve the conditional number of the matrix. In this study, the vertical temperature and water vapor profiles have 101 pressure levels when calculating the Jacobian matrix . After PC compressing, we only need to retain 20 temperature PC scores and 15 water vapor PC scores. The Tikhonov regularization method, if applied here to find the solution to Eq. (14), amounts to finding the solution of ΔX, which gives a least squares fit to ΔR but penalizes solutions by minimizing the cost function:
e16
The solution to Eq. (14) can be rewritten as
e17
with the calibration error being introduced as
e18
The Tikhonov matrix Γ is introduced here to improve the matrix condition of and in many cases is chosen as a multiple of the identity matrix such that Γ = λ. The damping factor λ is chosen in the way that the subspaces of the kernel matrix with smallest singular values can be dampened so that the inversion operation will not amplify the contribution of trivial features. We adopt a regularization scheme that employs different damping factors for temperature and water vapor of the kernel matrix . The scheme is based on our experience in temperature and water vapor retrievals using hyperspectral data such as IASI (Liu et al. 2009). Since the atmospheric temperature and water profiles have different units and they are compressed into the PC domain, the state vector X elements have large difference in values. To reduce the contributions from PCs with small scores, we take the diagonal elements of the regularization matrix, which correspond to temperature and water vapor elements, to be the mean values of the corresponding diagonal elements of the matrix. We always check our posterior fitting errors in the spectral domain to ensure that they are smaller than the calibration errors.

With the inversion relationship defined by Eq. (14) being established, we carried out a series of spectral fingerprinting trade studies by assuming different instrument calibration errors. Figure 15 plots a 0.04-K (k = 2) radiometric calibration error and the corresponding fingerprinting errors. The blue solid line in Fig. 15a shows the 0.04-K spectrally independent calibration error. The corresponding errors (k = 2) introduced in temperature and water vapor vertical profiles are shown as solid blue curves in Figs. 15c,d. As a reference, the calibration requirements for temperature and water vapor that have been derived from the MERRA, ERA-Interim, and GFDL CM3 datasets are plotted as dashed lines in Figs. 15c,d. The 0.04 K (k = 2) calibration error is marginally tolerable because the corresponding fingerprint error in near-surface temperature is approaching the calibration requirement defined by MERRA and ERA-Interim data.

Fig. 15.
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 = 2) baseline error (blue solid curve) and (b) potential calibration error based on a 0.04-K (k = 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 estimation results (dashed lines) in (c),(d) as references: σcal ECMWF derived from ERA-Interim data, σcal MERRA derived from MERRA data, and σcal GFDL derived from GFDL CM3 data. These calibration requirements are also plotted in Figs. 6 and 10.

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

In this study, we assume that the CLARREO IR FTS (Mlynczak 2010) will use a pyroelectric detector for its far-infrared band (band 1: 200–645 cm−1) and photoconductive or photovoltaic mercury cadmium telluride (MCT) detectors for its two infrared bands (band 2: 645–1210 cm−1, and band 3: 1210–2000 cm−1). Usually, calibration errors tend to be larger at the spectral band edges as a result of larger instrument response uncertainties. We expect larger errors near 200 cm−1 because of the low transmittance of the beam splitter and larger errors near 645, 1210, and 2000 cm−1 as a result of the band edge effect of the MCT detector and optical filters used for each band. Considering that the pyroelectric detector has sensitivity extending to the mid-IR, we can assume that there is no band edge effect to the left of 645 cm−1. The red curve Fig. 15b represents a more realistic, spectrally dependent calibration error curve of the CLARREO IR instrument. The corresponding spectral fingerprinting error for temperature and water vapor vertical profiles are shown as solid red curves in Figs. 15c,d.

By comparing the effects of calibration errors shown as blue and red lines in Figs. 15c,d, we can see that the large band edge errors in the P branch of the CO2 spectral region (near 650 cm−1) can be tolerated because of the redundant spectral information carried by the R branch of the CO2 spectral region. The spectral regions near 1210 and 2000 cm−1 contain spectral channels mainly sensitive to surface and cloud properties. Our studies show that as long as we include the error estimation for these spectral regions in the error covariance matrix Σs, the surface skin temperature and cloud property retrievals are not impacted by them, again because of the redundant information from other surface and cloud-sensitive channels. The spectral-dependent red curve shown in Fig. 15b is a stringent calibration accuracy requirement that can ensure that CLARREO’s observation accuracy for climate trend detection falls within 20% of the accuracy of a perfect system. The observation accuracy for lower-tropospheric temperature will be better than 0.04 K (k = 2) and that for the stratospheric temperature should be 0.08 K (k = 2). The water vapor observation error near the surface will be smaller than 0.03 g kg−1 (k = 2).

The value of a CLARREO-like observation system with a 0.04-K (k = 2) calibration accuracy in climate trend detection can be illustrated by plotting the dependence of lower-tropospheric temperature (at 975 hPa) trend detection uncertainty on instrument calibration accuracy (shown in Fig. 16). The curves are calculated using a 0.25-K (k = 2) temperature variance and a 3-month autocorrelation time, which are obtained from the ERA-Interim data (plotted as a dashed green curve in Fig. 5). Using values obtained from MERRA data will give similar results. We can see from Fig. 16 that a perfect observation system needs about 12.3 yr in order to reach a trend detection uncertainty of 0.1 K decade−1, while a system with a 0.04-K calibration accuracy requires 13.7 yr, lagging 1.4 yr behind. Changing the calibration accuracy requirement to 0.06 K (k = 2) means 15.1 yr are needed to reach the 0.1 K decade−1 trend detection uncertainty, further delaying the trend detection time by another 1.4 yr.

Fig. 16.
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: σvar = 0.25 K and τvar = 3.0 months (95% confidence).

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

Graphs like those in Fig. 16 are useful in studying the synergistic usage of the CLARREO IR instrument and operational sounders. The current hyperspectral IR sounders have provided valuable data for improving numerical weather prediction (NWP) forecasts for many years, and the data records will continue for many decades. However, since these sounders were designed for weather applications, the radiometric calibration specifications of these instruments are less accurate as compared to the CLARREO IR instrument. As referenced in Wielicki et al. (2013), the absolute accuracy of the operational sounders such as CrIS, AIRS, and IASI ranges from 0.2 to 0.4 K (k = 2). Wang et al. (2015) have compared the radiometric consistency of the CrIS, the IASI-A and IASI-B on Meteorological Operational satellites, and the AIRS using one year (2013) of simultaneous nadir overpass data. They concluded that the radiometric consistency between CrIS and IASI is on the order of 0.1–0.2 K (68% confidence level; k = 1) for the longwave IR (LWIR) band and midwave IR (MWIR) band. For CrIS and AIRS, the LWIR and MWIR differences are around 0.1 K (k = 1) for most of the spectrally averaged regions they have studied. For some spectral regions in LWIR and MWIR, the differences are in the range of 0.15–0.21 K (k = 1). The radiometric differences between these four instruments in the shortwave IR band are larger as compared to the LWIR and MWIR bands. Using Fig. 16, we can compare detection times needed to accurately determine near-surface atmospheric temperature using various satellite instruments. For the purpose of quantitative comparison, we assume that the absolute calibration accuracy of the CrIS, AIRS, and IASI is about 0.24 K (k = 2). It will take 30 years of operation time to achieve the temperature detection uncertainty of 0.1 K decade−1. This means that a CLARREO-like instrument with a 0.04-K (k = 2) calibration accuracy can save more than 16 years as compared with existing hyperspectral IR systems. Furthermore, if a CLARREO IR Pathfinder instrument is mounted on the International Space Station with the CLARREO reflected solar (RS) Pathfinder instrument or if a CLARREO IR instrument is mounted on a Free Flyer satellite, we will be able to perform on-orbit intersatellite calibration and reduce the calibration uncertainty of the sounder instruments. We can then take advantage of the sounders’ long time records and more diverse temporal and spatial coverages to further improve the accuracy of global temperature climate trend detection.

It should be noted that the CLARREO IR instrument not only has SI-traceable blackbody temperature measurements but also has an independent onboard verification system to check absolute calibrations at various scene temperatures. The highly accurate hyperspectral radiance spectra observed by the CLARREO IR instrument can be used as absolute references for intersatellite calibration and can be used to identify potential error sources such as the blackbody temperature measurement and nonlinearity correction. Since the operational sounders provide swath widths larger than 2000 km, we will have improved diurnal sampling and spatial sampling for climate trend detection by leveraging the CLARREO intercalibrated sounder data. The combined data will provide better characterization of climate changes in different climate zones or regions, which in turn will provide detection for global temperature and water vapor changes.

Our study demonstrates that atmospheric temperature trend observations between the midtroposphere and stratosphere region are less sensitive to instrument calibration error than that between the surface and lower-troposphere region since the temperature natural variability is larger in the upper atmosphere. Figure 17 shows the impact of instrument calibration errors on the delay of climate trend detection in stratospheric temperature at 70 hPa. If we assume a 0.48-K (k = 2) natural variability and an autocorrelation time of 5.6 months, which are from the GFDL CM3 simulation, a system with a 0.06-K (k = 2) calibration accuracy will save more than 10 years of operational time to achieve a 0.1 K decade−1 (k = 2) trend uncertainty as compared with the current IR instruments in orbit and will only lag behind a perfect observation system by one year.

Fig. 17.
Fig. 17.

Illustration of the dependence of the time to detect the stratospheric temperature [at 70 hPa with σvar = 0.48 K and τvar = 5.6 months (95% confidence)] cooling trend on the observation systems’ calibration accuracy (95% confidence).

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

The impact of instrument calibration accuracy on the surface water vapor trend observation is illustrated in Fig. 18. A significant global-scale increase in surface water vapor has been identified (Dai 2006; Willett et al. 2007), and the reported global surface water vapor anomalies are on a similar scale to the water vapor anomaly derived from MERRA data (shown in Fig. 8). By taking the linear trend difference (about 0.1 g kg−1 decade−1) between the MERRA result and the ERA-Interim result (red lines in Fig. 8) as a rough estimation for the surface water vapor trend uncertainty, a system with a 0.06-K (k = 2) calibration accuracy has the potential to reduce the detection time by more than six years relative to the current IR instruments in orbit.

Fig. 18.
Fig. 18.

Illustration of the dependence of the time to detect the surface specific humidity [at 1000 hPa with σvar = 0.17 g kg−1 and τvar = 9.6 months (95% confidence)] trend on the observation systems’ calibration accuracy (95% confidence).

Citation: Journal of Climate 30, 11; 10.1175/JCLI-D-16-0704.1

4. Conclusions

We have studied the spectrally dependent radiometric calibration requirement of the CLARREO IR instrument based on the climate trend detection uncertainty requirement. The validity of the presented calibration requirement depends on the accuracy of the reanalysis and the climate model data from which the magnitude of naturally occurring variations are calculated. Our analysis shows a good agreement between the temperature variance derived from ERA-Interim data and that from MERRA data. Also demonstrated is the consistency between the reanalysis results and the GFDL CM3 results in the troposphere region, which validates the use of multiple regression to obtain reliable natural variability free of major forcing factors. Although the uncertainty of temperature variance in the stratosphere is large—the discrepancy between reanalysis variability and GFDL CM3 variability in the stratosphere can be larger than 100%—only a narrow spectral region’s calibration requirement is associated with the stratospheric temperature observation requirement. The differences in the prescriptions of water vapor variance, especially those between reanalyses and the GCM, introduce uncertainty in the calibration requirement for monitoring tropospheric water vapor in the infrared spectra; however, our simulation study demonstrates that the radiometric calibration requirement imposed by the atmospheric temperature trend observation needs will be more stringent than that derived from the most conservative water vapor natural variability value. It is the observation requirement for the temperature of the troposphere and surface that determines the spectral calibration baseline in the IR measurement band.

The 0.04-K (k = 2; 95% confidence level) calibration baseline demonstrated in Fig. 15b is established based on a given uncertainty factor (Ua = 1.2). It can be viewed as a conservative and stringent solution. The natural variability values used here are obtained after subtracting the contributions of volcanic eruptions, solar cycle, ENSO, and QBO from the temperature and water vapor anomalies. Our study is based on the assumption that the climate fingerprints of ENSO and QBO can be effectively and accurately separated from the climate anomalies. If QBO and ENSO (especially ENSO, which is a key climate forcing factor contributing to the lower-tropospheric temperature variation) are included as part of the natural variability, the magnitude of the temperature variance will be larger, as can be seen from the difference between the dashed curves and the solid curves in Fig. 5. The corresponding temperature calibration requirement will be relaxed to 0.055 K (k = 2) in the troposphere region. Whether to include ENSO-caused water vapor fluctuations as a part of the naturally occurring process or not has negligent impact on calibration requirements for water vapor observations (shown in Figs. 9 and 10). Following the same inversion process described in section 3, the relaxed temperature calibration requirement will transfer into a less stringent spectral calibration requirement of 0.06 K (k = 2).

The calibration requirement study here is based on the temperature and water vapor data with statistics obtained from NWP reanalysis data and climate model simulation results. The demonstrated spectral calibration baseline is established as a “safe” estimation that can be adjusted based on the finalization of the trend observation uncertainty requirement and the potential improvement in the accuracy of natural variability values in the future. The calibration trade study methodology presented in section 3 can be used for any future calibration requirement study based on the observation requirement for other key climate change parameters such as clouds and CO2. The current study mainly focused on the spectral fingerprinting, and we used global mean anomalies to derive atmospheric temperature and water vapor natural variabilities. It should be noted that a lot of information is available in the spatial patterns of the climate signals. In the future, we will perform observing system simulation experiments (OSSEs) using either ERA-Interim or MERRA to detect climate trends in different climate regions and to study the longwave radiative feedbacks using CLARREO IR spectra.

Acknowledgments

This research was supported by the NASA CLARREO project. The effort of two coauthors, Huang and Chen, was supported by NASA under Grant NNX15AC25G awarded to the University of Michigan. The NASA SMD High-End Computing (HEC) resources were used to support the radiative transfer model (PCRTM) development. We thank Ms. Amber Richards for proofreading the manuscript.

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