SCIENCE CHINA Earth Sciences • RESEARCH PAPER •

doi: 10.1007/s11430-013-4707-1

Analysis of XCO2 retrieval sensitivity using simulated Chinese Carbon Satellite (TanSat) measurements CAI ZhaoNan, LIU Yi* & YANG DongXu Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China Received May 17, 2013; accepted November 1, 2013

We present a study on the retrieval sensitivity of the column-averaged dry-air mole fraction of CO2 (XCO2) for the Chinese carbon dioxide observation satellite (TanSat) with a full physical forward model and the optimal estimation technique. The forward model is based on the vector linearized discrete ordinate radiative transfer model (VLIDORT) and considers surface reflectance, gas absorption, and the scattering of air molecules, aerosol particles, and cloud particles. XCO2 retrieval errors from synthetic TanSat measurements show solar zenith angle (SZA), albedo dependence with values varying from 0.3 to 1 ppm for bright land surface in nadir mode and 2 to 8 ppm for dark surfaces like snow. The use of glint mode over dark oceans significantly improves the CO2 information retrieved. The aerosol type and profile are more important than the aerosol optical depth, and underestimation of aerosol plume height will introduce a bias of 1.5 ppm in XCO2. The systematic errors due to radiometric calibration are also estimated using a forward model simulation approach. TanSat, retrieval sensitivity, retrieval error, simulation, XCO2 Citation:

Cai Z N, Liu Y, Yang D X. 2014. Analysis of XCO2 retrieval sensitivity using simulated Chinese Carbon Satellite (TanSat) measurements. Science China: Earth Sciences, doi: 10.1007/s11430-013-4707-1

Atmospheric carbon dioxide (CO2) is an efficient greenhouse gas (IPCC, 2007), which traps the thermal radiation emitted from the Earth’s surface. The concentration of carbon dioxide in the global atmosphere is increasing rapidly from 370 parts per million by volume (ppm) at the start of the 1970s to almost 390 ppm by 2010, with an increase rate of 1 to 2 ppm per year. Fossil fuel combustion and other human activities are currently emitting more than 30 billion tons of CO2 into the atmosphere every year. To understand the sources and sinks of CO2 generated by human and natural activities more accurately, several types of space-based spectrometers have been proposed to monitor CO2 concentration. The Greenhouse gases Observing SATellite (GOSAT), a Fourier transform spectrometer, was

*Corresponding author (email: [email protected])

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

launched into orbit in 2009. GOSAT observes infrared radiance that is backscattered and directly emitted from the Earth’s surface and the atmosphere. GOSAT has been providing XCO2 data globally since 2009 (Kuze et al., 2009; Yokota et al., 2009). Orbiting Carbon Observatory (OCO)-2 will be NASA’s first dedicated Earth remote sensing satellite to study atmospheric carbon dioxide from space. NASA’s second Orbiting Carbon Observatory (OCO-2) will be launched in 2014 (Crisp et al., 2004). The Observatory will fly with a series of other Earth orbiting satellites, known as the Earth Observing System Afternoon Constellation or the A-train. The TanSat is the first Ministry of Science and Technology (MOST) mission dedicated to monitoring CO2 from space, and aims to retrieve the column-averaged CO2 dryair mole fraction, XCO2 with a precision of 1−4 ppm. TanSat, planned for launch in 2015, will fly in a Sunearth.scichina.com

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synchronous polar orbit at 700 km altitude with an equator-crossing time (descending node) of 13:30 am local time. TanSat carries two instruments: Carbon Dioxide Sensor (CDS) and Cloud and Aerosol Polarization Imager (CAPI). The CDS incorporates three high resolution grating spectrometers optimized for the O2-A band at 0.76 μm and the CO2 bands at 1.6 and 2.06 μm. These spectrometers will measure sunlight that is reflected and backscattered off the Earth’s surface on top of the atmosphere. In nadir mode, the instrument views the ground directly below the spacecraft. In glint mode, the instrument tracks near the location where sunlight is directly reflected on the Earth’s surface. Glint mode enhances the instrument’s ability to acquire highly accurate measurements, particularly over the ocean. In target mode, the instrument views a specified surface target continuously as the satellite passes overhead. Target mode has the capacity to collect a large number of measurements over sites where alternative ground-based and airborneinstruments also measure atmospheric CO2. In this paper, we present the results of a retrieval sensitivity study for XCO2 from synthetic TanSat measurements and give a first estimation of the error budget with contributions due to uncertainties in instrument calibration and characterization. In general, linear error analysis allows a rapid evaluation of information content, quantification of errors affected by measurements (i.e., signal-to-noise ratio (SNR), spectral resolution, and fitting windows), forward model parameters (i.e., parameters that are not retrieved or crosstalk between CO2 and parameters that are retrieved) or atmospheric variability. The linear estimate is a good approximation of the non-linear retrieval. Kuang et al., (2002) found that linear covariance analysis agrees well with non-linear retrieval where there is a low aerosol/cloud loading. Although the basic approach for studying sensitivity study has been performed for OCO/OCO-2 and GOSAT (Connor et al., 2008; Boesch et al., 2011; O’Dell et al., 2012), this paper focuses on the results acquired for TanSat, because the spectrometer characteristics are instrument specific and the forward model physics are built in very different ways. The retrieval algorithm is being developed at IAP. In this study we considered the inverse method to better understand error propagation during instruments calibration and the forward model parameters used to the retrieve XCO2 by simulating the TanSat spectra in a set of atmospheres and surfaces to assess the information content and estimated errors. Table 1

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1

Instrument model

The spectral coverage, uncertainty, spectral resolution and spectral sampling (interval) are critical to the design of the instrument. The retrieval sensitivity of CO2 depends on these parameters (Table 1) (Liu et al., 2011). 1.1 Spectral range, resolution and sampling interval The spectral regions used here, which are based on the instrument design set by the TanSat project, are as follows: “CO2 weak band”, from 1594 to 1624 nm, “CO2 strong band”, from 2042 to 2082 nm, and “O2-A”, from 758 to 778 nm. For simplicity, we assume Gaussian slit functions as the instrument line shapes (ILS) for three bands. The full width at half maximum (FWHM) describes the spectral resolution with values of 0.044, 0.081 and 0.103 nm for the O2-A, and CO2 weak and strong bands, respectively. The slit functions are used to convolve the spectra and weighting functions are calculated in very fine spectral resolution to the instrument spectral resolution. 1.2

Signal to noise ratio

For the linear error analysis we consider the random noise error of the measurement. Systematic errors of the measured spectra arise mainly from the pre-flight or in-flight calibration (e.g., errors in the Muller matrix, stray light correction and dark current correction), and characterizations of these errors are not available until the instrument is fully tested and calibrated. The capabilities of analyzing instrument calibration error propagation will be implemented when these data are set, and we give preliminary discussion about it in section 4.2. The SNRs of the three bands are set using instrument specification requirements at several specific energy levels, as shown in Table 1. We calculate the SNR for each wavelength as follows: SNR  (R  Fsol ) / I ref  SNR ref , (1) where R is the normalized radiance modeled by the vector linearized discrete ordinate radiative transfer model (VLIDORT), Fsol is the solar reference spectra, Iref is the reference intensity and SNRref is the SNR at Iref. This reflects that, for example, the SNR is 360 for a top-of-atmosphere

TANSAT preliminary instrument configuration

Configuration

Band coverage (nm)

Resolving power

Spectral resolution (nm)

Spectral interval (nm)

Number of pixels

SNR (photons s−1 cm−2 sr−1 nm−1)

O2-A

758−778

17454

0.044

0.022

910

[email protected]×1012

CO2-weak

1594−1624

19864

0.081

0.081

371

[email protected]×1012

CO2-strong

2042−2082

20019

0.103

0.103

389

[email protected]×1012

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(TOA) radiance of 5.8×1012 photons s−1 cm−2 sr−1 nm−1. This equation assumes that the SNR varies linearly with the energy entering the instrument. However, for a real instrument, it only reflects the readout noise and not the shot noise, which is determined by the detector array and varies with the square root of energy. 1.3 Polarization correction To reduce the polarization sensitivity of the spectrometer, the entrance slit of the TanSat instrument is designed to be perpendicular to the principal plane, because the CDS is only sensitive to light polarized in the direction parallel to the orientation of the long axis of the spectrometer slits. The principal plane is defined by the target, the Sun and satellite. The radiance at the TOA that is calculated by the radiative transfer model is described by the Stokes vector I {I, Q, U, V}. Vector I is defined with respect to the local meridian plane, which is in turn defined by the line-of-sight and local zenith. To model the polarized radiance that is measured by the instrument, a polarization correction (i.e. reference plane conversion) must be performed externally. This is quite straight forward in principal (Chandrasekhar, 1950), and the measured radiance can be written as: I p  0.5  (I  cos 2  Q  sin 2  U) ,

(2)

where I, Q, and U are the VLIDORT outputs, Ip is the polarization corrected radiance that is measured by the spectrometer, and φ is the angle between the norm vector of two planes. The weighting functions with respect to all the considered parameters are corrected in the same way.

2 Forward model 2.1

Radiative transfer model and inputs

CDS is a polarizing spectrometer, for which the vector radiative transfer is an essential forward modeling component

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of the retrieval algorithm. The simulated spectra are calculated using VLIDORT version 2.5 (Spurr, 2006), a fully linearized multiple scattering multi-layer radiative transfer model that can simulate the full Stokes vector I, Q (0°/90° polarization), U (±45° polarization), and V (circular polarization), and their analytic Jacobians with respect to any atmospheric or surface parameter. In the atmosphere, V is quite small and can be neglected. The model also gives provision for Lambertion surface as well as a set of different Bidirectional Reflectance Distribution Functions (BRDF) subroutines allowing the modeling of different anisotropic surfaces. VLIDORT is used to model the upwelling radiance for a set of atmospheric settings at the TOA and the sensitivity to several atmospheric variables, i.e., weighting function: temperature, surface pressure, CO2, O2 and H2O, aerosol/ cloud optical depth, and surface parameters (Lambertian albedo or wind speed on the sea surface). The reference solar spectrum is taken from Kurucz (http://kurucz.harvard. edu/sun.html), which was developed for GOSAT. We simulate TANSAT measurements in nadir mode and glint mode. For land, we select four types of Lambertian surfaces: vegetation, sand, snow, and soil. Wavelengthdependent surface reflectance data are taken from the ASTER spectral library (Baldridge et al., 2009). For sea surfaces, TanSat mainly uses the glint mode over the dark ocean water surface to improve the measurement signal. We model the BRDF by the Cox and Munk kernel at a windspeed of 5 m/s. The aerosol extinction profiles are modeled by an exponentially-decreasing distribution function. We select three types of aerosol: mineral dust, sulfate, and black carbon. The ice cloud (e.g., cirrus clouds) extinction profile is modeled using a Gaussian distribution function with a peak at 10 km and a half width of 0.5 km. The aerosol/cloud spectra extinction, absorption coefficients, and scattering matrix are calculated using Mie scattering code (Mishchenko et al., 2002). Figure 1 shows synthetic TanSat spectra for different surface albedos of 0.05, 0.1, 0.2, ice cloud with and optical

Figure 1 Simulated TanSat normalized radiance in O2-A, CO2 1.6 μm and CO2 2.06 μm bands for clear sky conditions with Lambertian surface albedos of 0.05, 0.1, 0.2, dust, sulfate, back carbon and ice cloud.

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depth of 0.5 at 10 km and aerosol with an optical depth of 0.3 (at 550 nm), for a solar zenith angle (SZA) of 30°, viewing zenith angle of 0.1°, and relative azimuth angle of 90°. VLIDORT requires the derivatives of layer optical thickness, single scattering albedo, and the scattering matrix with respect to atmospheric parameters as input for the weighting function calculations. The derivatives with respect to gases and aerosol/cloud are straight forward. The temperature dependency is more complex. We consider the temperature dependency of the gas absorption cross-section and air column density. We assume that all the optical thicknesses depend linearly on surface pressure and that the single scattering albedo and scattering matrix do not change. We calculate the spectra and weighting function at a step size of 0.002 nm and then convolve them to the TanSat resolution using the assumed ILS. 2.2

Absorption coefficients

The CO2, O2 and H2O line parameters and isotopic abundances are taken from the High Resolution Transmission (HITRAN) 2008 database (Rothman et al., 2009). The absorption coefficients are calculated using a line-by-line model (Kelly Chance, personal contact) from these parameters. For simplicity, we do not consider the line mixing (LM) and collision induced absorption (CIA) in the simulation. This is not considered to affect the results because the lines in simulated measurements and the retrieval process are from the same spectroscopy database. However, it has been shown that for real spectra fitting, including LM in the CO2 spectroscopic data can reduce the fitting residual in the 2.1 μm band significantly, and it can also reduce the dependence on air mass and improve the consistency between the 1.6 and 2.1 μm bands (Hartmann et al., 2009). LM and CIA in the O2-A band are essential for accurate retrieval of surface pressure. We implement both processes in our retrieval algorithm (SAtellite Inversion Lab for CO2 Research) for real spectra.

3 Inverse model 3.1 Introduction to the optimal estimation and error analysis tools Atmospheric inverse problems are usually non-linear and lead to ill-posed problems. An optimal solution is normally derived by minimizing the cost function which describes a balance of the a- priori information and measurements associated with their uncertainties. The retrieved state can be regarded as the average of a priori information xa (a priori state) and measurements x (true state) weighted by the averaging kernel (AK) matrix A (Rodgers, 2000): xˆ = Ax + (I  A)x a ,

(3)

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where the AK matrix is given by A=

xˆ = GK = (K T S y1K + S a1 ) 1 K T S y1K , x

(4)

where Sa is the a priori covariance matrix, Sy is the measurement error covariance matrix, K is the weighting function matrix or Jacobins of the forward model with respect to the state vector, and G is the contribution function matrix. For the iteration process, the cost function χ2 can be written: 1

2

1

2

 2  S y 2 K i (Xi 1  Xi )   Y  F(Xi )  S a 2 (Xi 1  Xa ) , 

2



2

(5) where Xi+1 and Xi are the current and previous state vectors, Y is the measurement vector, and F is the forward model. The posterior solution is: X i 1  X i  (K iT S y1K i )1  K iT S y1  Y  F(X i )  S a1 (Xi  X a ) . (6) There are several interpretation tools for evaluating the characteristics of retrievals. The AK matrix A describes the sensitivity of the retrieved state to the real state, in which a row of A at a given layer indicates the sensitivities of retrieval at that layer to the variations at all layers. The diagonal elements of A provide a description of the number of independent pieces of information from measurements at each layer (i.e., degree of freedom for signal, DFS). The trace of A is the total DFS, whereas the sum of CO2 diagonal elements of A gives the CO2 DFS. The column averaging kernel (CAK) is derived by summing all the rows of A. Retrieval error is another measure used for characterizing the retrievals. It consists of random noise error S n = GS y G T, systematic errors in the instrument calibration, the forward model and forward model parameters S b = GK b S b K Tb G T (Sb and Kb are the ensemble covariance and jacobian for parameter b), and the smoothing error S m = (A  I)S c (A  I)T (Sc is the ensemble covariance for CO2), respectively. The linear estimate is a good and fast approximation of the non-linear retrieval. It allows a fast assessment of the retrieval characteristics and an understanding of the errors propagating from the instrument, forward model and atmospheric variability to the retrieved XCO2. The linear estimate technique assumes that the measurements can be correctly modeled by the forward model and the retrieval of the first iteration has converged to the right answer. This technique has been widely used in the development of the retrieval algorithm as well as the instrument design (Connor et al., 2008; Boesch et al., 2011; O’Dell et al., 2012).

3.2

State vector and a priori covariance

The state vector contains CO2 partial column density (mol-

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ecules/cm2) in 24 layers. In addition to the CO2 variables, the state vector also includes scaling factor of H2O column density, zero- and first- order surface albedo for each band, surface pressure, temperature offset and aerosol/cloud optical depths. Table 2 lists the a priori value and a priori error of each element. The a priori CO2 profile is taken from the chemical transport model (GEOS-Chem) output. The temperature profile, water vapor profile and surface pressure used in the forward model are taken from European Centre for Medium-Range Weather Forecasts (ECMWF) database. In the retrieval model, we fit a scaling factor of water vapor profile and an offset of temperature profile. Following the approach proposed by (O’Dell et al., 2012), we estimated prior values of the zero order albedo from the continuum in the spectrum of each band. In the retrieval model, we fit a first order polynomial to estimate wavelength dependent surface albedo, and here they are mean albedo and slope of each band. For retrievals over the ocean, the albedo terms are replaced by the wind-speed. The CO2 dry-air mixing ratio (XCO2) is given by N

XCO 2 

 xˆ i 1 N

i

 ci

 h T xˆ ,

(7)

i 1

where c is the column density of dry air, and x denotes the retrieved CO2 partial column density. The subscripts indicate the layers. We define the air column vector h, similarly to ACOS algorithm (O’Dell et al., 2012), but with differences in its construction, to relate the retrieved CO2 partial column density in the discrete pressure layers to the profile weighted XCO2. The error variance of XCO2 is  2XCO2  h T Sh . The CO2 a priori covariance is based on an ad-hoc constraint with a correlation length of 1 km. For this linear error analysis study, only the a priori error of the state vector is required.

4 Discussion and results 4.1

Sensitivity to the forward model physics

We calculate the radiance and weighting functions for clear Table 2

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and cloud/aerosol-contaminated scenarios. Measurement noise is calculated using the noise model described in section 2.2. We use the optimal estimation technique to calculate the AK and post-covariance matrix from the a priori covariance matrix, measurement noise and weighting functions for each simulation. The surface albedo significantly contributes to the TanSat measured radiances under clear-sky conditions as shown in Figure 1, which compares simulations for surface albedos of 0.05, 0.1, and 0.2. In the simulated TanSat measurements we use the ASTER reflectance database while in the retrieval process, we use a first-order polynomial (i.e., an offset and slope) to model the wavelengthdependent albedo. The differences between the retrieved and actual albedos are sufficiently small, and the errors in the retrieved albedo typically contribute <0.04 ppm (for the worst case: 0.05 albedo and 85° SZA) error to XCO2 retrievals. It is valuable to estimate retrieval error under the “best” case scenario in order to understand how well the proposed instrument characterization will perform. Figure 2 shows the DFSs and retrieval errors as a function of SZA under clear-sky conditions for six surface types: ocean (nadir mode), ocean (glint mode), snow, desert, soil and vegetation. The DFSs and retrieval errors are due primarily to the SNR of the measurements, which vary with surface albedo and SZA. In the nadir mode, the DFS is highest for bright surfaces such as soil, desert, and vegetation, with values ranging from 2.2 to 1.5 and decreasing with decreasing surface albedo. The DFSs for dark surfaces, such as snow and ocean, are much smaller. The retrieval error is a combination of random noise error and smoothing error, although it is dominated by the random noise error. For bright surfaces, the retrieval error for a single sounding is less than 0.5 ppm for SZA<75° and increases up to 1 ppm for higher SZA values. For dark surfaces such as snow, which is very bright in the O2-A band and quite dark in the CO2 bands, the retrieval errors increase substantially with values of 2 ppm for small SZA values and up to 8 ppm when SZA=85°. The retrieval errors for ocean (nadir mode) are 1 ppm for smaller SZA values and reach 4 ppm when SZA=85°. TanSat will operate mainly in glint mode over the dark ocean surfaces, which will significantly increase the signal level. Owing to the increasing reflectivity with the increasing SZA, the

Variables’ name, a priori value, a priori error and index Variables CO2 H2O column scaling factor mean albedo for each band Slope for each band Surface pressure Temperature offset Aerosol optical depth

A priori GEOS-Chem model 1.0 Estimated from continuum spectra 0.0 ECMWF 0 (K) 0.1

A priori error O’Dell et al. (2012) 0.2 0.05 0.0025 20 hPa 5K 0.5

Index 1–24 25 26, 28, 30 27, 29, 31 32 33 34

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° Figure 2 XCO2 degree of freedom for signal (a) and XCO2 retrieval error for all surfaces as a function of SZA under clear sky condition (single sounding) (b).

Figure 3

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retrieval error will decrease from 0.4 ppm at lower levels of solar radiation to less than 0.1 ppm at higher levels of solar radiation. For the source and sink study, the single measurement precision requirement is therefore not very meaningful and must be combined with the number of data in a given spatio-temporal interval. The random error will decrease in the order of the square root of the number of “good” retrievals. Figure 3 shows the corresponding CAK for different surfaces. In the absence of aerosol and cloud contamination, CAKs are unity in the boundary layer for most cases, except for those that have a very dark snow surface, where the sensitivity to the boundary layer decreases substantially with increasing SZA. For bright surfaces, the sensitivity in the middle and upper troposphere (200−800 hPa) decreases with increasing SZA, whereas the sensitivity to the boundary layer is slightly enhanced at larger SZA values. In the glint mode, CAKs increase towards unity with increasing SZA. The information retrieved is contained mainly in the troposphere (>200 hPa), and up to half of one piece of CO2 information in the boundary layer (>800 hPa) could be

Column averaging kernels for all surfaces for different solar zenith angles under clear sky conditions.

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detected and retrieved by TanSat. Several studies have shown that the uncertainty resulting from scattering by aerosol particles or optical thin cloud is the main source of error in XCO2 retrievals from GOSAT, and current CO2 retrievals are limited to nearly clear-sky conditions with low aerosol loadings (Butz et al., 2009; Yoshida et al., 2011; O’Dell et al., 2012). Aerosol/cloud scattering can affect the measurement signal and modify the light path for absorption by gases (Yang et al., 2013). Measurements in the O2-A and CO2 strong band show distinguished spectra signatures for different scatters, as shown in Figure 1. Figure 4 shows the XCO2 retrieval error for different types of aerosol (AOD=0.3) at 0−2 km in the boundary layer. For bright surfaces (soil, sand and vegetation, α>0.2) and for different aerosol types and cloud, the errors are typically less than 1 ppm for both low and high SZA values. The retrieval errors are slightly larger than for clear-sky conditions because these scatters reduce the CO2 information. The small errors in XCO2 arise because the optical depth itself can be retrieved from the O2-A and near-infrared CO2 bands at very high precision, which can satisfy the requirement proposed by (Aben et al., 2007) for which the correct scattering properties and profiles are known. Figures 5 and 6 show the corresponding CAKs for two aerosol types: black carbon (BC) and mineral dust (DU), and two types of aerosol profiles with plume peaks at 0 and 5 km. For BC, the CAKs are not sensitive to plume height, because of the low sensitivity in the near-infrared CO2 bands. For DU, CAKs show little sensitivity to plume

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XCO2

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Figure 4 XCO2 retrieval error for nadir simulations of four surfaces for AOD of 0.3 with aerosol plume peak at 1 and 5 km and for ice cloud optical depth of 0.3 at 10 km, at SZA 30° and 75°.

height at small SZA values, except for snow surface. At SZA = 75°, the CAKs are strongly sensitive to the plume heights. The lower aerosol plume reduces XCO2 sensitivity to CO2 changes in the boundary layer (>800 hPa) and enhances sensitivity to CO2 changes above it. Light scattering from near-ground aerosols enhances the backscattered light and effectively acts as surface albedo with a broad-band spectral signature. The effect can be account for by fitting a polynomial from the experience of fitting ozone from ultraviolet measurements (Cai et al., 2012). For both higher and lower aerosol plumes, CAKs are enhanced at higher altitudes, with the highest value at 400 hPa. These dependencies also indicate crosstalk between the surface albedo and aerosol height, i.e., the increasing effect of plume height with decreasing surface albedo. The dependencies of plume height and aerosol type, rather than the optical depth, indicate that it is critical to model or parameterize the aerosol

Figure 5 Column averaging kernels for nadir simulations of four surfaces for black carbon with AOD of 0.3 with aerosol plume peak at 1 km and 5 km, at SZA 30° and 75°.

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Same as Figure 5 but for dust aerosol.

profile and aerosol type in the retrieval algorithm. Figure 7 shows the case of an ice cloud located at 10 km for three optical depths: 0.01, 0.3, and 1.0 at 550 nm. As with aerosol particles, ice cloud particles increase the possibility of scattering and light path modification in the upper troposphere, which increases CO2 information in those layers. The enhanced sensitivity also presents a risk of significant errors in XCO2, which will be introduced when this kind of cloud that is not account for. It is possible to retrieve ice cloud optical depth simultaneously by assuming distribution profile. A more conservative way is to remove the pixels that were contaminated by high level cloud using the pre-screen filters, such as that was proposed in (O’Dell et al., 2012). One of the most important differences between CAI/GOSAT and CAPI/TanSat is that CAPI will measure the radiance at 1.37 μm, used for high level thin cirrus detection. This is critical for CO2 observation over East Asia especially for Northwest China where there is more cirrus than the other regions, and the optical depth is about 0.4 in average for visible band (Min et al., 2011). It has been shown that the distribution as a function of altitude of the scatters other than air molecules is more critical for CO2 retrieval. Figure 8 shows the XCO2 errors due to a miss-assignment of aerosol height between the retrieval algorithm and the true value, which could be regard as the error in plume height in the forward model. For AOD=0.3, an overestimate of 3 km produces a bias of 1.5 ppm in the retrieval. The error is more sensitive to the underestimation of plume height, and the bias could reach −1.5 ppm. A first estimation of XCO2 bias due to a 5-km error in plume height can be up to 7 ppm in the case of dust aerosol and

vegetation surface at SZA=30°, and would be much higher for larger SZA and darker surfaces. The CO2 retrieval would benefit from the parameterization of aerosol/cloud profiles or a good A-priori profile from independent measurements or chemical transport models. 4.2

Sensitivity to radiometric calibration

It has been shown that satellite retrievals of XCO2 provide additional information regarding CO2 surface fluxes if a precision of 2.5 ppm can be achieved for monthly averages in regions of 8°×10° (Rayner et al., 2000 and publications thereafter). However it is critical that the measurements are free of spatially and temporally coherent biases. Errors in instrument line shape, instrument degradation, dark current level and gain coefficients as well as the non-linearity in pixel-to-pixel gain will introduce systematic error in the retrieved XCO2. It is difficult to illustrate systematic error in measurements comprehensively. Here, we focus on the radiometric calibration error in the observed spectra, which can be estimated using a simulation for three bands of the following form: y i  gFi (x)  y z ,

(8)

where g is the spectra gain coefficients; here, we assume that the readout depends linearly on the incoming energy (i.e., g does not change with the radiance) and yz is the dark current offset. Pre-flight instrument calibration will employ error analyses of these parameters in the laboratory in the near future. For this sensitivity study, g and yz are given small perturba-

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t

Figure 7

Similar to Figure 4 but for ice cloud with plume peak at 10 km.

shows little dependency (less than 0.1 ppm) on the error in g, because scaling does not change the CO2 line depth. For the real spectral fitting, most of the g effect can be removed by normalizing Earth radiance by the measured solar irradiance, and the remains can be fitted. The uncorrected dark current offset will add a constant offset to the measured radiance, which will decrease the depths of the CO2 absorption lines. Figure 9 shows systematic biases in XCO2 due to 0.2% add-on offsets in the CO2 spectrum. These biases are SZA and surface albedo dependent; that is, the XCO2 retrievals will show dependencies on geo-location and surface albedo and introduce artificial sources and sinks (Kuang et al., 2002). For TanSat, the dark current level and noise will be measured once per orbit to minimize the effect at the dark side of orbit.

Figure 8 XCO2 retrieval error due to the miss assignment of aerosol peak height. The AOD is 0.3 at 550 nm.

tions, namely 5% for g and 0.2% for yz. The latter is estimated from the continuum level for an albedo of 0.05 at 30° SZA with an equivalent energy of 2.6×109 photons cm−2 nm−1 s−1 sr−1 in the CO2 weak band and 9×108 photons cm−2 nm−1 s−1 sr−1 in the CO2 strong band. It should be noted that here we only consider the systematic part of the error in dark current calibration, because the random part is included in the measurement noise calculation (section 2.2). Hyper-spectral spectrometers, such as TanSat, make the CO2 lines distinguished from the lower order spectral signatures. For a linear error analysis, the XCO2 retrieval error

° Figure 9 Systematic error in the retrieved XCO2 due to the assumed dark current calibration error.

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5 Conclusions We have conducted (1) a full physical forward model to simulate TanSat measurements in the O2-A and near-infrared CO2 bands based on the prototype instrument design and (2) retrieval simulation tools to estimate the error budget due to uncertainties in instrument calibration and characterizations. This study provides the first estimation of the expected performance for the TanSat mission, which is scheduled for launch in early 2015. We analyze XCO2 retrieval sensitivity to the forward model physics from synthetic TanSat measurements and estimated the retrieval errors due to the possible uncertainty in instrument radiometric calibration. The nadir mode over different land surface and glint mode over oceans are tested. The XCO2 retrieval sensitivity analysis shows that the retrieved information of XCO2 depends on surface albedo, SZA or viewing geometries, and aerosol/cloud (optical depth, plume height and aerosol typed). The lower level aerosol will reduce sensitivity to CO2 variations in the boundary layer, and higher aerosol/cloud will modify light path in the atmosphere significantly. The imperfect knowledge of cloud and aerosol will increase the uncertainties in retrieved CO2. We then evaluate the XCO2 errors due to uncertainties in aerosol types and plume height and conclude that it is most important to account for the effect of aerosol type and profile in the retrieval algorithm. The retrieval precision of single sounding is expected to be within 1 ppm for bright land surfaces, and the systematic error due to radiometric calibration will be less than 2 ppm where the dark current offset is well measured and corrected within 0.2% of the continuum level in CO2 bands. The retrieval error also depends on surface types, geometries. For the worst cases, such as scenes over snow, the value varies from 2 to 8 ppm. Compared to random noise errors, the systematic errors that vary tempo-spatially are critical to the implementation in CO2 sources and sinks inventory. This study was supported by the Strategic Priority Research Program— Climate Change: Carbon Budget and Relevant Issues (Grant No. XDA05040200) and the National High-tech Research and Development Program of China (Grant No. 2011AA12A104). We thank Dr. R. J. D. Spurr for providing VLIDORT code. Aben I, Hasekamp O, Hartmann W. 2007. Uncertainties in the space-based measurements of CO2 columns due to scattering in the Earth’s atmosphere. J Quant Spectrosc Radiat Transf, 104: 450–459 Baldridge A M, Hook S J, Grove C I, et al. 2009. The ASTER spectral library version 2.0. Remote Sens Environ, 113: 711–715 Boesch H, Baker D, Connor B, et al. 2011. Global characterization of CO2 column retrievals from shortwave-infrared satellite observations of the Orbiting Carbon Observatory-2 mission. Remote Sens, 3: 270–304 Butz A, Hasekamp O P, Frankenberg C, et al. 2009. Retrievals of atmos-

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