Attribution of averaged spectral variation over large spatial and temporal scales to different climate variables is central to climate change fingerprinting. Using 10 years of satellite data for simulation, the authors generate a group of observation-based spectral fingerprints and a time series of monthly mean reflectance spectra over the ocean in five large latitude regions and globally. Next, these fingerprints and the interannual variation spectra are used to retrieve the interannual changes in the relevant climate variables to test the concept of using the spectral fingerprinting approach for climate change attribution. Comparing the fingerprinting retrieval of climate variable change to the actual underlying variable change, the RMS differences between the two are less than twice as large as the monthly variability for all variables in all regions. Instances where larger errors are observed correspond to those variables with large nonlinear radiative response, such as the cloud optical depth and the ice particle size. Using the linear fingerprinting approach and accounting for the nonlinear radiative error in fingerprints results in significantly higher retrieval accuracy; the RMS errors are reduced to less than the monthly variability for nearly all variables, indicating the profound impact of the nonlinear error on fingerprinting retrieval. Another important finding is that if the cloud fraction is known a priori, the retrieval accuracy in cloud optical depth would be improved substantially. Moreover, a better retrieval for the water vapor amount and aerosol optical depth can be achieved from the clear-sky data only. The test results demonstrate that climate change fingerprinting based on reflected solar benchmark spectra is possible.
The outgoing longwave and shortwave radiation spectra from Earth to space contain information about several variables relevant to changes in Earth’s climate, including cloud properties, aerosols, atmospheric trace gases, surface conditions, and atmospheric temperature profiles. Changes in climate variables can lead to separable features in the outgoing spectra at the top of the atmosphere and therefore leave unique fingerprints of individual feedbacks or climate responses in the outgoing spectra. Because of the existence of these unique spectral fingerprints for individual variables, long-term data records in the large domain-averaged spectrum (i.e., averaged over large spatial scales from thousands of kilometers to globally and time scales from months to years) may reveal trends in those important climate variables and, therefore, be used for climate change detection. With this goal in mind, a new research technique called climate change fingerprinting or climate attribution has emerged. The technique attributes the mean spectral changes between two climate states to individual variables in the climate system based on the spectral fingerprints of the variables (Goody et al. 1998; Huang et al. 2010a,b; Hasselmann 1997; Kato et al. 2014; Leroy et al. 2008). Presently, this technique has been tested only for the longwave radiation and has not been applied to the shortwave solar spectrum.
Because of the dependence on solar incidence and the strong multiple scattering by atmospheric particles, the reflected solar (RS) spectrum has much larger temporal and directional variability than thermal infrared (IR) radiation. Moreover, climate responses to changes in the atmospheric, cloud, and surface variables in the RS spectrum are very different from those in the longwave IR spectrum. Therefore, the RS spectrum provides unique and complementary information on climate changes compared to the IR spectrum. For example, the spectral fingerprints in RS radiation do not have the low cloud and surface ambiguity found with the IR, and they are not sensitive to changes in atmospheric and surface temperature. Research results in Jin et al. (2012) showed that the interannual variations in the solar spectral reflectance averaged over large spatiotemporal scales are well correlated with the corresponding variations of the averaged atmospheric and surface properties. This correlation between spectral variation and climate variable changes provides the physical foundation for attributing the spectral radiative signals of climate change to different variables of Earth’s climate system through the RS spectrum.
In this paper, we present a solar spectral fingerprinting method aimed at the future application to climate change detection and attribution from the shortwave RS spectra. Since long-term and global observational RS spectral data with climate quality are not available for now, we use observational geophysical variables as input parameters to generate the spectral fingerprints and to simulate the reflected shortwave spectra that are subsequently used to evaluate the solar fingerprinting scheme. The objective of this study is to test the concept of the climate fingerprinting attribution using the solar spectrum, estimate the attribution accuracy limit that could be achieved under the idealized conditions, and analyze the effect of the nonlinear error inherited in the spectral fingerprints on the fingerprinting retrieval.
2. Formulation of solar fingerprinting
Climate trends in geophysical variables might be detected through the reanalysis of long-term satellite observational data. Massive spatial and temporal data averaging over instantaneous satellite retrievals is required; thus, biases from retrieval algorithms and instrument calibration would be brought into the reanalysis in this retrieval-then-average approach for climate change detection. Climate change, however, consists of very small changes in distributions of geophysical variables, much like the small change approximations used for Taylor expansions of nonlinear mathematical equations. Therefore, biases from instantaneous retrievals would limit the ability to detect the small climate change signal. While the traditional retrieval uses the instantaneous observational spectrum, climate change spectral fingerprinting uses the averaged spectra over space and time. The concept of climate fingerprinting is to use the space and time averaged spectral difference between two climate states to directly retrieve the corresponding changes in climate variables responsible for the spectral change. Therefore, this average-then-retrieval approach provides an alternative to the reanalysis. The advantage of this new approach is to eliminate the instantaneous nonlinear retrieval step and thus circumvents the biases and/or errors in individual retrieval algorithms in the traditional retrieval-then-average analyses. Using ΔR to represent the mean spectral difference vector between two states, ΔX to represent the corresponding changes in an ensemble of climate variables, as the kernel matrix or the fingerprints, and e as the error vector, attributing the measureable spectral change to different physical variables can then be expressed as a multivariate linear regression problem:
where nw is the number of spectral channels and nx is the number of climate variables to be retrieved. The matrix (nw × nx) represents the spectral fingerprints of nx variables associated with the spectral change. A fingerprint describes the differential response of radiation to a change in a climate variable between two climate states. The fingerprints depend only on the radiative transfer algorithm and the unperturbed climate state.
To use time–space averaged spectra to fingerprint climate change, the spectral changes ΔR must be sufficiently linear with changes in geophysical variables ΔX, so that the nonlinearity error is not going to corrupt the climate signal attribution. Because the radiative response to changes in climate variables are inherently nonlinear, Eq. (1a) implies that ΔR and ΔX have to be small compared to the mean state values to maintain sufficient linearity, so that the changes can be considered perturbations from the mean state. This cannot be true for averages over small time and space scales because of the large changes in geophysical variables. However, this is indeed the case for the climate change signals and for the interannual variations in variables averaged in large climate domains. Typical decadal changes are much less than 1% and clearly are small perturbations. Based on observational data, Jin et al. (2014) demonstrated that the interannual variability in the domain-averaged solar reflectance spectrum decreases as the time and space scales used for averaging increase. When averaged over large spatiotemporal scales, the interannual difference of the solar spectral reflectance is small compared to the mean reflectance (e.g., typically a few percent for the monthly and global mean) and can also be considered as a perturbation from the mean state.
Neglecting the error, the solution of Eq. (1a) is simply
where the superscript T denotes transpose and the superscript −1 denotes a matrix inversion. This is based on the ordinary least squares estimation (LSE). Because a small error in or in ΔR could produce large error in the solution, the simple inversion as Eq. (2) may not be acceptable in some situations. Taking into account the uncertainty e in the multivariate regression, the linear fingerprinting solution of Eq. (1a) can be expressed as
This solution is the same as that obtained in the optimal detection approach (Allen and Tett 1999; Leroy et al. 2008). The in Eq. (3) is the covariance matrix of e in Eq. (1a) and = eTe. In practice, we first make the singular value decomposition (SVD) on to obtain the eigenvectors u and eigenvalues λ of ; then the −1 in Eq. (3) is calculated as u−1λuT, and only the first n (n < nw) eigenvalues and eigenvectors are used.
The formulation for fingerprinting retrieval here is similar to those used in many conventional retrieval methods applied to instantaneous satellite data. However, the fingerprinting retrieval differs from the traditional remote sensing retrieval in that it uses the average-then-retrieval approach and thus is associated with the averaged quantities over large spatiotemporal scales instead of the local or instantaneous values. In addition, the retrieval considers changes (ΔR and ΔX) between two mean climate states instead of the absolute values (R and X).
3. Data simulation
As shown in Eqs. (1)–(3), the spectral fingerprint and the domain-averaged spectrum R are two important variables required to obtain the fingerprinting solution ΔX. When fingerprinting is applied to actual data, ΔR represents long-term anomalies or trends in the observed reflected solar spectrum. In a “true model” study such as this one, however, it represents long-term anomalies or trends in a simulation of observed data. We apply linear spectral fingerprinting to estimate various atmospheric properties from the simulated data and compare to the true-model atmospheric properties to evaluate the usefulness of spectral fingerprinting of reflected solar data. We use 10 years (2001–10) of Clouds and the Earth’s Radiant Energy System (CERES) single scanner footprint (SSF) data product (Geier et al. 2003) from NASA’s Terra satellite measurements for radiative transfer (RT) simulation. The variables from the SSF product include the aerosol and cloud properties (i.e., optical depth, particle size, phase, and height) retrieved from MODIS measurements (Justice et al. 1998), and the column water vapor and the surface wind data from GEOS-5–MERRA reanalysis (Rienecker et al. 2011). We also use the ozone data from the Stratosphere Monitoring Ozone Blended Analysis (SMOBA) (Yang et al. 2000) and the ocean chlorophyll concentration from the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) (O’Reilly et al. 1998). It is too computationally expensive to simulate mean spectral reflectance over large climate domains using instantaneous satellite data for explicit RT computations at the CERES footprint scale. To circumvent this problem, we recently developed a computation scheme based on the cloud probability distribution function (PDF) (Jin et al. 2013). This PDF approach statistically accounts for the wide variation of cloud properties in different satellite footprints in the domain considered. This novel method essentially organizes the large number of satellite instantaneous measurements according to the cloud optical depth τ distribution, so that those footprints with similar τ and other atmospheric and/or surface properties are treated once, rather than footprint by footprint repetitively, in the RT modeling. Therefore, the computation time to obtain the mean radiance in large time–space scales is reduced significantly compared with the computation footprint by footprint, and the method is particularly suitable for simulating the mean spectral radiance and/or reflectance from a large volume of instantaneous satellite data.
Using the observational data for CERES footprints within a 10° zone at nadir, we calculate the monthly mean solar spectral reflectance at nadir at the top of the atmosphere for the mean solar angle of the nadir views for different latitude regions. The Coupled Ocean–Atmosphere Radiative Transfer (COART) model (Jin et al. 2006) is used to do the computations. COART is combined with MODTRAN to share the atmospheric absorption database and the advanced features in MODTRAN (Berk et al. 2008). While the ocean surface bidirectional reflectance distribution function (BRDF) is incorporated within COART, there is a lack of complete land surface BRDF data for various surface types required for RT modeling over the land. Compared to the highly varying land surface reflection, the ocean surface reflectance at nadir is generally low across all solar spectra and has little variation in space and time, unless it is in the sun-glint region. However, at nadir views under Terra orbit, the sun glint is minimal. To focus on the fingerprinting retrieval of atmospheric properties and on the testing of fingerprinting concept, we use the data over ocean areas only in this study, and thus the complex surface effect is avoided. We also assume a constant chlorophyll concentration of 0.1 mg m−3 in the simulation, which is approximately the global-mean value, but the chlorophyll in ocean has little effect on the reflectance at the top of atmosphere. The radiance is calculated from 320 to 2300 nm with spectral resolution of 4 nm, consistent with the spectral coverage and the spectral sampling resolution, respectively, for the proposed Climate Absolute Radiance and Refractivity Observatory (CLARREO) solar instrument (Wielicki et al. 2013; Wu et al. 2015).
Climate spectral fingerprinting is intended to infer small atmospheric changes from small observation spectral anomalies, thus requiring massive averaging in space and time. Soden et al. (2008) showed that only very large spatial scales of 2000 km and larger are driving sensitivity of the climate system to anthropogenic forcing, and thus the fingerprinting study is pertinent to large scales. We average and convert the calculated nadir radiances to the mean nadir reflectance in the five large latitude regions: the north polar region (NP; 60°–90°N), the northern midlatitude region (NML; 30°–60°N), the southern midlatitude region (SML; 30°–60°S), the tropical region (TRO; 30°S–30°N), and the entire globe (GLB). The southern polar region is excluded because the Antarctic continent occupies most of it. Figure 1 is an example that shows the global-mean and monthly reflectance anomalies over the 10-yr period. Each panel is for a different month and in each panel a different color is for a different year. The global-mean reflectance anomalies are within ±0.08, approximately ±3% of the mean reflectance.
As described in Jin et al. (2011), the spectral fingerprints are calculated for each 10° latitude zone based on the modified partial radiative perturbation (PRP) method (Wetherald and Manabe 1988), but the zonal mean radiances in the mean state and the perturbed state are calculated based on the PDF approach. The mean state is defined as the average across the 10 years from 2001 to 2010. In each zone and each month, we generate a total of 11 fingerprints corresponding to 11 climate variables: the total column precipitable water (PW), the aerosol optical depth (AOD), the column ozone amount (O3), and the cloud fraction (Fc), cloud-top height (Ht), cloud particle size (Re or De), and cloud τ for the water and ice phases, respectively. These variables determine the RS spectrum at the top of atmosphere. The fingerprints over larger regions are obtained from the area weighted and incident energy weighted average of the zonal mean fingerprints (Jin et al. 2011). Figure 2 shows the 11 fingerprints averaged over global ocean for the month of January; those for all other months (not shown) are very similar to this result. Each panel is for a different variable and the abscissa is for wavelength. For easy comparison, each fingerprint is normalized by its own integral over the entire spectral range from 320 to 2300 nm. The fingerprints for different variables show different spectral characteristics. Particularly, the sensitive spectral regions in the fingerprint of ozone are well separated from those for all other variables. However, the fingerprints for cloud fraction and cloud optical depth have similar spectral shape for both ice and water clouds. We use the averaged fingerprints in the five large latitude regions as shown here and the spectral reflectance differences (anomalies) as shown in Fig. 1 for the fingerprinting test.
4. Fingerprinting retrieval
The utility of a climate fingerprinting scheme relies on whether the mean climate variable changes between two climate states can be attributed from the spectral signal—the corresponding domain-averaged spectral difference. If this attribution is successful, a long time series of the interannual variations in climate variables can be retrieved from the observed climate benchmark spectra and subsequently be used for the detection of climate trends.
We apply the spectral fingerprinting to retrieve the interannual variations of the 11 climate variables from the simulated spectra. The atmospheric properties used for the true-model simulation are the truth to be used to examine the fingerprinting accuracy. Using the monthly mean reflectance spectra, Fig. 3 compares the retrieved global-mean results with the truth, in which each panel represents a different variable. There are a total of 120 retrievals in each panel representing the anomalies in all months in the 10 years. In each month and each region, the anomaly for a year is calculated as the difference between the monthly mean in that year and the mean across all 10 years in the same month. The number at the lower right in each panel is the root-mean-square (RMS) difference of the retrieval from the truth. The ozone amount has the best retrieval accuracy, likely due to its distinctive spectral fingerprint as shown in Fig. 2 and its high stratospheric location in the actual atmosphere where its radiative interaction with other tropospheric atmospheric components is small.
The retrieval in Fig. 3 is based on the LSE approach as expressed by Eq. (2), which represents the attribution without any error consideration. Although the reflectance spectra used here are from model simulation data and thus are error-free, the nonlinearity errors exist in the spatiotemporal averaged spectral fingerprints due to large second-order terms in reflectance R as a function of the atmospheric variables X (Jin et al. 2011; Huang et al. 2010b). In a true-model test such as this, nonlinearity errors can be exactly evaluated. We now examine the nonlinearity error due to the two important and inherent nonlinear radiative processes in the fingerprints:
The nonlinear radiative response to a variable change, that is, .
The radiative interactions among different variables, which result in that the simple sum of the responses to individual variable changes differs from the total response that is obtained with all variables changed simultaneously, that is, .
Studies in Jin et al. (2011) showed that this nonlinearity error varies with a number of factors, for example, the variation range of variable, the atmospheric conditions, the sun-view geometry, and the wavelength. To test the nonlinearity effect on fingerprinting retrieval, Fig. 4 shows the retrieval results same as in Fig. 3 but the nonlinearity error described here is taken into account by using the linear fingerprinting as expressed by Eq. (3). Comparing Fig. 4 with Fig. 3, it is clear that the retrieval accuracy is generally improved, especially for the cloud properties.
We have applied the fingerprinting retrieval with and without the nonlinear error for all the five climate regions defined. Instead of showing the detailed comparison as in Figs. 3 and 4, Fig. 5 only shows the RMS errors in all regions for all 11 variables retrieved. Each panel in Fig. 5 is for a different region. The red and black bars represent the RMS errors with and without the nonlinearity accounted, respectively. It is hard to directly compare the absolute RMS for all variables because they have different dimensions and vary greatly in different regions. To make the RMS comparable across variables and regions, the RMS error is normalized by the intermonthly variability σ for each region and variable. This intercomparison shows that
without consideration of the nonlinearity, the RMS errors of fingerprinting retrieval for all variables in all regions are less than twice as large as monthly variability, except ice cloud optical depth in the tropics where RMS error can exceed twice monthly variability and
with the nonlinearity considered, the RMS errors are mostly reduced, especially for the cloud properties. All of the RMS errors are less than the monthly variability, except for the global-mean ice cloud optical depth, which has the RMS error slightly higher than monthly variability.
In addition to the nonlinear error, another important error exists in the large domain-averaged fingerprints and it is resulted from the averaging process from local fingerprints to the mean regional fingerprint. The regional fingerprint is the weighted average of local or zonal fingerprints (i.e., ). Here wj and kj represent the weight and local fingerprint, respectively, in zone j. Unless the local fingerprint kj does not change, the regional radiative response based on the mean fingerprint and the mean variable change differs from the sum of the local responses, that is
This averaging error causes spectral shape uncertainty in the mean fingerprint, and it depends on the variation range of the local fingerprints in the region. The larger the region, the larger the fingerprint uncertainty, because the fingerprint variation in magnitude and spectral shape usually increases as the regional size increases. Figure 6 shows the same retrieval as in Fig. 3 but the spectral shape uncertainty in the mean fingerprint is taken into account in the retrieval. Compared to the results shown in Fig. 3, the RMS error is reduced for most of the variables, but the improvement is limited for those cloud variables with large nonlinear radiative response such as the cloud optical depth and cloud height. It should be noted that this example is for the global mean in which the spectral shape uncertainty is largest. Figure 7 summarizes the RMS errors in all the five regions after the fingerprint shape uncertainty is taken into account in the retrieval (the red bars). The RMS errors from the LSE approach (the black bars) are plotted for comparison. Different from the nonlinear error, which reduces the retrieval accuracy generally in all regions for all variables, the spectral shape uncertainty has different impact on different variables and in different regions. In smaller regions, such as the polar ocean and the north midlatitude ocean, the averaging error has smaller effect, because the fingerprint spectral shape does not change much and the nonlinearity error is dominant in these regions. In these cases, if the shape error biases to the opposite direction of the nonlinearity error and thus has compensating effect in the total error, the RMS retrieval error with shape uncertainty considered could be larger than that from the LSE approach in which no any error is accounted. The shape uncertainty becomes important for the large tropic region and globe.
To permit evaluation of climate forcing and feedbacks, certain accuracies are required for various climate variable datasets. Based on models of long-term climate change, Ohring et al. (2005) analyzed the anticipated climate signal in terms of expected change per decade and determined the accuracies of climate variables needed to permit detection of the signal. Table 1 compares the fingerprinting RMS errors with the accuracies required for the climate detection for all the 11 climate variables in global average. The RMS errors listed in the table are from the retrievals by the LSE, the fingerprinting with nonlinear error (E_nl) considered, and the fingerprinting with the shape uncertainty (E_sp) considered, respectively. The accuracy value for some of the variables in Ohring et al. (2005) is in percentage and those are converted to the same unit as the retrieved variables. To relate the fingerprinting error to larger issues of climate change uncertainty and climate model performance, it is useful to compare the fingerprinting errors to the spread in climate model predictions. Based on the doubled-CO2 simulations from an ensemble of 11 climate models, Zelinka et al. (2012) derived the ensemble mean change in cloud fraction, height, and optical depth in response to surface and air temperature change. Combining those numbers with the climate sensitivity from the latest generation of global climate models (GCMs), which ranges from 2.1 to 4.7 K (Forster et al. 2013), we can derive the spread in climate model projected changes in response to CO2 doubling in the three cloud variables analyzed by Zelinka et al. (2012). For example, using the global-mean cloud fraction change of 0.44% K−1 in Zelinka et al., we can calculate the spread of cloud fraction change corresponding to the GCM predicted temperature change from 2.1 to 4.7 K, which is from 0.009 to 0.021 (in fractional units, not percentage). To compare with the fingerprinting error, the calculated variation range in the three cloud properties based on the GCM projection in response to CO2 doubling is listed in the bottom row in Table 1. Nevertheless, this comparison is approximate, because the global-mean sensitivity values given in Zelinka et al. have no distinction between ocean and land and between ice and water clouds as we have in fingerprinting. The results in Table 1 show that the fingerprinting errors are well below the accuracy required for climate detection for all variables and below the climate model projected variations in response to CO2 doubling. However, it should be noted that the fingerprinting in this study is conducted under idealized conditions; there is no error in the spectral data and it is limited to ocean area only.
Cloud variables, especially the optical depth, have retrieval error that is considered large for linear fingerprinting. Although the spectral fingerprints are generally unique, the spectral fingerprint for cloud amount is similar to that for the cloud optical depth for both ice and liquid water clouds. Figure 8 shows the spectral fingerprints for cloud optical depth and cloud fraction in a tropic zone for water and ice clouds. The results clearly show the similarity in spectral shape for the two fingerprints for both cloud phases. This similarity implies that it may be hard to distinguish the cloud optical depth effect from the cloud amount effect in the solar spectral reflectance and thus results in ambiguity in the fingerprinting attribution. This ambiguity in fingerprints could have adversely affected the retrieval accuracy in cloud optical depth. To examine this hypothesis, we make the same fingerprinting attribution with the assumption that the cloud fraction is known a priori, and thus the total number of variables to be retrieved is reduced from 11 to 9. Figure 9 is an example to compare the retrieved cloud optical depth with (right panels) and without (left panels) the cloud fraction known a priori. The upper panels are for water clouds and the lower panels are for ice clouds. The results confirm the hypothesis above on the attribution ambiguity. The RMS errors in the retrieved cloud optical depth are reduced substantially when the cloud fraction is known a priori as the observed value. We made the same retrieval tests for all five regions and Fig. 10 compares the RMS errors in these regions. The retrieval accuracy in cloud τ is improved in all regions when the cloud fraction is known a priori, but the effects on retrieval in other variables are mixed and minor (not shown).
In practice, a separate measure of cloud fraction from CLARREO-like or other instruments [e.g., Visible Infrared Imaging Radiometer Suite (VIIRS) and MODIS] to unscramble cloud fraction and optical depth is possible. An additional benefit of knowing the cloud fraction a priori is that the atmospheric properties (PW, AOD, and ozone) can be retrieved separately from the clear-sky spectra only. Figure 11 is an example to compare the all-sky retrieval (left panels) and the clear-sky retrieval (right panels) for the three atmospheric properties. The RMS errors for the PW and AOD are much smaller from the clear-sky retrieval than those from the all-sky data, but the retrieval accuracy for ozone does not change much. Test results show that these are true for all other cases. Figure 12 compares the RMS errors between all-sky and clear-sky retrievals for the three atmospheric variables in the five regions. The accuracy improvement in PW and AOD from using clear-sky data is significant. The clear-sky effect on ozone retrieval is mixed and small, but the retrieval accuracy is highest in ozone for either the clear-sky or all-sky cases.
5. Discussion and conclusions
The objective of spectral climate change fingerprinting is to attribute the large spatiotemporal averaged spectral variation to different climate variables. Climate fingerprinting based on actual observational spectrum needs long-term highly accurate spectral measurement over global scale. Such observational data are lacking for now but will be provided by future climate observation missions such as CLARREO. CLARREO’s accuracy is required to be a factor of 5–10 times better than current operational satellite measurements in the RS spectrum. Those CLARREO-like data will be used to establish the benchmark climate records for climate change detection. To evaluate the feasibility of climate change detection using the solar benchmark spectra, a climate fingerprinting method pertinent to the solar spectrum needs to be developed.
To test the fingerprinting concept, we use 10 years of satellite observational data of the atmosphere, aerosols, and clouds to generate a group of observation-based spectral fingerprints and to simulate the mean reflectance spectra in large time and space scales. An advantage of using this “true model” simulated spectra for fingerprinting is that the nonlinear errors in fingerprints can be exactly estimated, because the observational data and the simulated reflectance spectra are considered as truth. Therefore, the impact of the nonlinearity errors on the attribution accuracy can be quantified. We use the interannual variation spectra derived from the true-model simulated spectral reflectance and the observation-based fingerprints to do the fingerprinting retrieval of the interannual variations in different climate variables in the defined five large latitude regions. The test results demonstrate that the concept of climate change fingerprinting based on climate benchmark spectra is viable.
Comparing the retrieval results from the LSE method to the observational truth, the RMS differences are basically less than twice as large as monthly variability for all variables in all regions. Large RMS error usually corresponds to those variables with large nonlinear radiative response, such as cloud optical depth and ice cloud particle size. Through the introduction of a covariance error matrix, the nonlinear error in fingerprint can be taken into account in the linear fingerprinting retrieval. Specifically, we investigated the effect from the two important nonlinear radiative processes: the nonlinear radiative response to individual variable change and the radiative interaction between different climate variables. After these nonlinear errors are accounted for in the fingerprinting, the retrieval accuracy is significantly higher, especially for those variables with large nonlinear radiative response. With the nonlinearity considered, the retrieval RMS errors are less than the monthly variability for nearly all variables in all regions, indicating the profound impact of the nonlinear error on the retrieval accuracy.
The averaging process from local fingerprints to mean regional fingerprint results in uncertainty in spectral shape of the mean fingerprint. This shape error increases as the region size increases. Different from the nonlinearity error which adversely affects the retrieval accuracy in all regions, the impact of fingerprint shape error is mixed and considering this shape uncertainty improves fingerprinting retrieval accuracy only in large regions (including globally).
The fingerprints for the cloud amount and the cloud optical depth show similar spectral shapes in many cases. Our test results prove that this fingerprint similarity causes ambiguity in the fingerprinting attribution. An important finding is that if the cloud fraction is known a priori, the retrieval accuracy in cloud optical depth would be improved substantially and generally. This finding suggests that a separate measure of cloud fraction should be done in future climate observation system to unscramble cloud fraction and optical depth variations. In fact, the proposed CLARREO measurements have high spatial resolution (500 m) and full spectral coverage, thus having the capability to measure the cloud fraction.
If the cloud fraction can be observed directly from climate benchmark measurements such as CLARREO, or indirectly from other instruments such as VIIRS and MODIS, an additional benefit is that the climate changes in some atmospheric properties such as precipitable water, aerosol optical depth, and ozone amount can be retrieved using the clear sky data only. The test results also indicate that using clear-sky data greatly improve the retrieval accuracy in PW and AOD, but the effect on ozone is small.
Ozone retrieval has the highest accuracy among all variables in all cases, likely because the radiative sensitive spectral region for ozone is well separated from those for other variables in the solar spectrum, and atmospheric ozone is located in a well-separated and higher stratospheric level from all other tropospheric climate variables, so its radiative interaction with other variables is minimum.
The climate change fingerprinting uses space and time averaged spectra to retrieve the variable changes between two climate states. This average-then-retrieval approach eliminates the instantaneous nonlinear retrieval step in the traditional retrieval-then-average approach. However, it only applies to quantities averaged over large scales when the interannual variation can be considered as a perturbation from the mean state, and therefore, it cannot replace the traditional retrieval-then-average approach but provides an alternative to reanalysis.
This study is a first step toward solar fingerprinting climate change, which has never been done before. Several processes are simplified in this initial study. The same RT model is used to generate the spectral fingerprints and to simulate the reflectance spectra, so that the spectra and the fingerprints used in the fingerprinting retrieval are consistent in physics. In addition, the true-model simulated spectra are error-free. In this sense, the fingerprinting accuracy in this study may represent the accuracy limit achievable under idealized conditions in comparison to a real-world application of the fingerprinting method. This initial study on solar fingerprinting is focused on the concept test. Further studies for more complex cases will be conducted on the basis of this research.
We thank the NASA CERES group for the SSF data, Dr. Sky Yang and Dr. Shuntai Zhou for the ozone data, and Amber Richards and Rosemary Baize for help in editing. This research is supported by the Radiation Sciences Program and the CLARREO project of NASA's Earth Science Division.