MODIS Retrieval Errors Of Cirrus Cloud Optical Thickness And Effective Diameter And Error-correction Methods

Cirrus optical thickness(COT)and effective diameter(De)are two important parameters to climatological studies.The Moderate Resolution Imaging Spectrometer(MODIS)is among the most popular spaceborne passive sensors for acquiring COT and De on a global scale.MODIS Collection 6(C6)cloud products are constructed based on three basic assumptions: the optical and microphysical properties of cirrus clouds within an arbitrary MODIS pixel is assumed constant(Plane-Parallel Assumption,PPA),the radiative transferring processes are assumed to be idependent between adjacent pixels(Independent Pixel Assumption,IPA),and every cirrus cloud is assumed to have the same type of ice crystals(Single Habit Assumption,SHA).The retrieved De could deviate from the whole-layer true value of De due to the absorption of photons by ice particles at the MODIS shortwave infrared band(Photon Absorption Effects,PAE).The retrieval errors due to the PPA,IPA,and PAE are unique to inhomogeneous cirrus clouds,and are therefore collectively termed cloud inhomogeneity(CIN)-induced errors.Currently,cirrus parameters(COT and De)provided by the MODIS C6 level 2 cloud products are associated with errors due to SHA and CIN,which motivates the need to carry out this study.An arbitrary inhomogeneous cirrs cloud was constructed by combining the three-dimensional(3D)Ice Water Content(IWC)structure generated by the Cloudgen model,De structure(1D,2D,and 3D),the Severely Roughened Aggregates of Solid Columns(SRAC)ice cloud model and regional(midlattdue and tropical)ice cloud models.Three main topics were investigated:(i)The CIN-induced errors were quantified based on SHDOM radiative trsnsfer simulations.(ii)An improved errors analysis method was proposed,and the PPA,IPA,PAE,and SHA errors were analyzed separately.(iii)A climatology of cirrus cloud mean free path(MFP)was derived from CloudSat and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation(CALIPSO)Ice Cloud Property Product(2C-ICE)and the Atmospheric Radiation Measurement(ARM)program data in 2010 over midlatitude and tropical regions.The climatology revealed that the MFP was larger than the MODIS horizontal resolution.Such a finding lays the foundation to correct the IPA-induced errors for the COT retrievals by the Richardson-Lucy method.Four main findings were reached:(1)The CIN-induced retrieval biases(the domain-averaged errors).The CIN-induced under-and overestimations of COT(De)were within-15.1% ~ 13.5%(-3.1% ~ 16.4%).The CIN-induced biases of COT and De could be parameterized by retrieved COT and De by linear functions.PPA,IPA,and PAE errors were analyzed separately,and three main findings were reached:(i)PPA underestimated COT and overestimated De.(ii)The IPA-induced errors were determined by the sun-viewing angles,CIN,the domain-avareged COT,and etc.For small sun and viewing zenith angles,COT was underestimated by IPA.For bumpy cirrus clouds,the dependence of IPA errors was determined by the spatial distribution of cirrus clouds.(iii)For optically thick cirrus clouds,the retrieved De was only representitative of the upper-layer De due to the PAE.The PAE-induced biases were mainly determined by the De structures in the vertical direction and the optical thickness of the selected cirrus cases.(2)The SHA-induced retrieval biases.The SHA-induced biases of COT(De)were within-13.8% ~ 75.9%(-37.3% ~ 0%).For small solar and viewing zenith angles,COT was overestimated by SHA on the domain average.In addition,the SHA-induced COT biases showed distinct variation characteristics with scattering angles.Furthermore,De was consistently underestimated by SHA on the domain average.The influences of SHA on the retrieval uncertainties were negligible.(3)The relative magnitudes of the CIN-and SHA-induced errors.For opically thin cirrus clouds with small sun and viewing zenith angles,the SHA-induced biases were larger than CIN-induced errors for the COT retrievals.Similar results were also found for the De retrievals over the midlatitude region.For the tropical region,the SHA-induced biases were consistently larger than the CIN-induced biases for the De retrievals,implying that SHA was the dominant error source in such situations.(4)Correction of the IPA-induced biases for the COT retrievals.The Richardson-Lucy method was tested with a MODIS image.The results indicated that the method decreased the domain-averaged retrieval error of COT but at a sacrifice of increasing uncertainty,mainly due to the stringent limitations of the sun-viewing geometries for the sensors onboard the sun-synchronous orbit satellites like Aqua.Nevertheless,such limitations of the sun-viewing geometries could be relaxed for sensors onboard airplane and geostationary satellites.Therefore,the finding could be potentially useful for correcting the IPA errors in the COT retrievals for optically thick cirrus cloud from sensors onboard airplane and geostationary satellites.