Information-based uncertainty decomposition in dual-channel microwave remote sensing of soil moisture

The National Aeronautics and Space Administration (NASA) Soil Moisture Active-Passive (SMAP) mission characterizes global spatiotemporal patterns in surface soil moisture using dual L-band microwave retrievals of horizontal (TBh) and vertical (TBv) polarized microwave brightness temperatures through a modeled mechanistic relationship between vegetation opacity, surface scattering albedo, and soil effective temperature (Teff). Although this model has been validated against in situ soil moisture, there is a lack of systematic characterization of where and why SMAP estimates deviate from the in situ observations. Here, we assess how the information content of in situ soil moisture observations from the US Climate Reference Network contrasts with (1) the information contained within raw SMAP observations (i.e., “informational random uncertainty”) derived from TBh, TBv, and Teff themselves and with (2) the information contained in SMAP's dual-channel algorithm (DCA) soil moisture estimates (i.e., “informational model uncertainty”) derived from the model's inherent structure and parameterizations. The results show that, on average, 80 % of the information in the in situ soil moisture is unexplained by SMAP DCA soil moisture estimates. Loss of information in the DCA modeling process contributes 35 % of the unexplained information, while the remainder is induced by a lack of additional explanatory power within TBh, TBv, and Teff. Overall, retrieval quality of SMAP DCA soil moisture, denoted as the Pearson correlation coefficient between SMAP DCA soil moisture and in situ soil moisture, is negatively correlated with the informational uncertainties, with slight differences across different land covers. The informational model uncertainty (Pearson correlation of −0.59) was found to be more influential than the informational random uncertainty (Pearson correlation of −0.34), suggesting that the poor performance of SMAP DCA at some locations is driven by model parameterization and/or structure and not underlying satellite measurements of TBh and TBv. A decomposition of mutual information between TBh, TBv, and DCA soil moisture shows that on average 58 % of information provided by TBh and TBv to DCA estimates is redundant. The amount of information redundantly and synergistically provided by TBh and TBv was found to be closely related (Pearson correlations of 0.79 and −0.82, respectively) to the retrieval quality of SMAP DCA. TBh and TBv tend to contribute large redundant information to DCA estimates under surfaces or conditions where DCA makes better retrievals. This study provides a baseline approach that can also be applied to evaluate other remote sensing models and understand informational loss as satellite retrievals are translated to end-user products.

Uncertainties in eddy covariance air–sea CO₂ flux measurements and implications for gas transfer velocity parameterisations

Air–sea carbon dioxide (CO2) flux is often indirectly estimated by the bulk method using the air–sea difference in CO2 fugacity (ΔfCO2) and a parameterisation of the gas transfer velocity (K). Direct flux measurements by eddy covariance (EC) provide an independent reference for bulk flux estimates and are often used to study processes that drive K. However, inherent uncertainties in EC air–sea CO2 flux measurements from ships have not been well quantified and may confound analyses of K. This paper evaluates the uncertainties in EC CO2 fluxes from four cruises. Fluxes were measured with two state-of-the-art closed-path CO2 analysers on two ships. The mean bias in the EC CO2 flux is low, but the random error is relatively large over short timescales. The uncertainty (1 standard deviation) in hourly averaged EC air–sea CO2 fluxes (cruise mean) ranges from 1.4 to 3.2 mmolm-2d-1. This corresponds to a relative uncertainty of ∼ 20 % during two Arctic cruises that observed large CO2 flux magnitude. The relative uncertainty was greater (∼ 50 %) when the CO2 flux magnitude was small during two Atlantic cruises. Random uncertainty in the EC CO2 flux is mostly caused by sampling error. Instrument noise is relatively unimportant. Random uncertainty in EC CO2 fluxes can be reduced by averaging for longer. However, averaging for too long will result in the inclusion of more natural variability. Auto-covariance analysis of CO2 fluxes suggests that the optimal timescale for averaging EC CO2 flux measurements ranges from 1 to 3 h, which increases the mean signal-to-noise ratio of the four cruises to higher than 3. Applying an appropriate averaging timescale and suitable ΔfCO2 threshold (20 µatm) to EC flux data enables an optimal analysis of K.

Version 4 CALIPSO Imaging Infrared Radiometer ice and liquid water cloud microphysical properties – Part II: Results over oceans

Following the release of the version 4 Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, a new version 4 (V4) of the CALIPSO Imaging Infrared Radiometer (IIR) Level 2 data products has been developed. The IIR Level 2 data products include cloud effective emissivities and cloud microphysical properties such as effective diameter (De) and water path estimates for ice and liquid clouds. This paper (Part II) shows retrievals over ocean and describes the improvements made with respect to version 3 (V3) as a result of the significant changes implemented in the V4 algorithms, which are presented in a companion paper (Part I). The analysis of the three-channel IIR observations (08.65, 10.6, and 12.05 µm) is informed by the scene classification provided in the V4 CALIOP 5 km cloud layer and aerosol layer products. Thanks to the reduction of inter-channel effective emissivity biases in semi-transparent (ST) clouds when the oceanic background radiance is derived from model computations, the number of unbiased emissivity retrievals is increased by a factor of 3 in V4. In V3, these biases caused inconsistencies between the effective diameters retrieved from the 12/10 (βeff12/10 = τa,12/τa,10) and 12/08 (βeff12/08 = τa,12/τa,08) pairs of channels at emissivities smaller than 0.5. In V4, microphysical retrievals in ST ice clouds are possible in more than 80 % of the pixels down to effective emissivities of 0.05 (or visible optical depth ∼0.1). For the month of January 2008, which was chosen to illustrate the results, median ice De and ice water path (IWP) are, respectively, 38 µm and 3 g m−2 in ST clouds, with random uncertainty estimates of 50 %. The relationship between the V4 IIR 12/10 and 12/08 microphysical indices is in better agreement with the “severely roughened single column” ice habit model than with the “severely roughened eight-element aggregate” model for 80 % of the pixels in the coldest clouds (<210 K) and 60 % in the warmest clouds (>230 K). Retrievals in opaque ice clouds are improved in V4, especially at night and for 12/10 pair of channels, due to corrections of the V3 radiative temperature estimates derived from CALIOP geometric altitudes. Median ice De and IWP are 58 µm and 97 g m−2 at night in opaque clouds, with again random uncertainty estimates of 50 %. Comparisons of ice retrievals with Moderate Resolution Imaging Spectroradiometer (MODIS)/Aqua in the tropics show a better agreement of IIR De with MODIS visible–3.7 µm than with MODIS visible–2.1 µm in the coldest ST clouds and the opposite for opaque clouds. In prevailingly supercooled liquid water clouds with centroid altitudes above 4 km, retrieved median De and liquid water path are 13 µm and 3.4 g m−2 in ST clouds, with estimated random uncertainties of 45 % and 35 %, respectively. In opaque liquid clouds, these values are 18 µm and 31 g m−2 at night, with estimated uncertainties of 50 %. IIR De in opaque liquid clouds is smaller than MODIS visible–2.1 µm and visible–3.7 µm by 8 and 3 µm, respectively.

The Risk Priority Number Evaluation of FMEA Analysis Based on Random Uncertainty and Fuzzy Uncertainty

The risk priority number (RPN) calculation method is one of the critical subjects of failure mode and effects analysis (FMEA) research. Recently, RPN research under a fuzzy uncertainty environment has become a hot topic. Accordingly, increasing studies have ignored the important impact of the random sampling uncertainty in the FMEA assessment. In this study, a fuzzy beta-binomial RPN evaluation method is proposed by integrating fuzzy theory, Bayesian statistical inference, and the beta-binomial distribution. This model can effectively realize real-time, dynamic, and long-term evaluation of RPN under the condition of continuous knowledge accumulation. The major contribution of the proposed model is to use the random uncertainty and fuzzy uncertainty in an integrated model and provide a Markov Chain Monte Carlo (MCMC) method to solve the complex integrated model. The study presented a case study, which presented how to apply this model in practice and indicated the significant influence on the measurement error caused by ignoring the random uncertainty caused by expert evaluation in RPN calculations.

Uncertainties in eddy covariance air-sea CO₂ flux measurements and implications for gas transfer velocity parameterisations

Air-sea carbon dioxide (CO2) flux is often indirectly estimated by the bulk method using the air-sea difference in CO2 fugacity (ΔfCO2) and a parameterisation of the gas transfer velocity (K). Direct flux measurements by eddy covariance (EC) provide an independent reference for bulk flux estimates and are often used to study processes that drive K. However, inherent uncertainties in EC air-sea CO2 flux measurements from ships have not been well quantified and may confound analyses of K. This paper evaluates the uncertainties in EC CO2 fluxes from four cruises. Fluxes were measured with two state-of-the-art closed-path CO2 analysers on two ships. The mean bias in the EC CO2 flux is low but the random error is relatively large over short time scales. The uncertainty (1 standard deviation) in hourly averaged EC air-sea CO2 fluxes (cruise-mean) ranges from 1.4 to 3.2 mmol m−2 day−1. This corresponds to a relative uncertainty of ~20 % during two Arctic cruises that observed large CO2 flux magnitude. The relative uncertainty was greater (~50 %) when the CO2 flux magnitude was small during two Atlantic cruises. Random uncertainty in the EC CO2 flux is mostly caused by sampling error. Instrument noise is relatively unimportant. Random uncertainty in EC CO2 fluxes can be reduced by averaging for longer. However, averaging for too long will result in the inclusion of more natural variability. Auto-covariance analysis of CO2 fluxes suggests that the optimal timescale for averaging EC CO2 flux measurements ranges from 1–3 hours, which increases the mean signal-to-noise ratio of the four cruises to higher than 3. Applying an appropriate averaging timescale and suitable ΔfCO2 threshold (20 µatm) to EC flux data enables an optimal analysis of K.

Version 4 CALIPSO IIR ice and liquid water cloud microphysical properties, Part II: results over oceans

Following the release of the Version 4 Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data products from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission, a new version 4 (V4) of the CALIPSO Imaging Infrared Radiometer (IIR) Level 2 data products has been developed. The IIR Level 2 data products include cloud effective emissivities and cloud microphysical properties such as effective diameter (De) and ice or liquid water path estimates. This paper (Part II) shows retrievals over ocean and describes the improvements made with respect to version (V3) as a result of the significant changes implemented in the V4 algorithms, which are presented in a companion paper (Part I). The analysis of the three-channel IIR observations (08.65 μm, 10.6 μm, and 12.05 μm) is informed by the scene classification provided in the V4 CALIOP 5-km cloud layer and aerosol layer products. Thanks to the reduction of inter-channel effective emissivity biases in semi-transparent (ST) clouds when the oceanic background radiance is derived from model computations, the number of unbiased emissivity retrievals is increased by a factor 3 in V4. In V3, these biases caused inconsistencies between the effective diameters retrieved from the 12/10 and 12/08 pairs of channels at emissivities smaller than 0.5. In V4, microphysical retrievals in ST ice clouds are possible in more than 80 % of the pixels down to effective emissivities of 0.05 (or visible optical depth ~ 0.1). For the month of January 2008 chosen to illustrate the results, median ice De and ice water path (IWP) are, respectively, 38 µm and 3 g⋅m−2 in ST clouds, with random uncertainty estimates of 50 %. The relationship between the V4 IIR 12/10 and 12/08 microphysical indices is in better agreement with the severely roughened single column ice crystal model than with the severely roughened 8-element aggregate model for 80 % of the pixels in the coldest clouds ( 230 K). Retrievals in opaque ice clouds are improved in V4, especially at night and for 12/10 pair of channels, owing to corrections of the V3 radiative temperature estimates derived from CALIOP geometric altitudes. Median ice De and IWP are 58 µm and 97 g⋅m−2 at night in opaque clouds, with again random uncertainty estimates of 50 %. Comparisons of ice retrievals with Aqua/Moderate Resolution Imaging Spectroradiometer (MODIS) in the tropics show a better agreement of IIR De with MODIS visible/3.7 µm than with MODIS visible/2.1 µm in the coldest ST clouds and the opposite for opaque clouds. In prevailingly supercooled liquid water clouds with centroid altitudes above 4 km, retrieved median De and liquid water path are 13 µm and 3.4 g.m−2 in ST clouds, with estimated random uncertainties of 45 % and 35 % respectively. In opaque liquid clouds, these values are 18 µm and 31 g.m−2 at night, with estimated uncertainties of 50 %. IIR De in opaque liquid clouds is smaller than MODIS visible/2.1 and visible/3.7 by 8 µm and 3 µm, respectively.