Adding method of delta-four-stream spherical harmonic expansion approximation for infrared radiative transfer parameterization
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The adding method for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-four-stream spherical harmonic expansion approximation (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4SDA) is obtained.

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The accuracy of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4SDA is superior than that of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-two-stream discrete-ordinates method (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-2DDA), especially for the cloudy sky.

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class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4SDA is more accurate than class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-four-stream discrete-ordinates method (class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4DDA) in ice cloud cases.

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class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4SDA is slightly less accurate than class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4DDA under water cloud conditions.

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The computational efficiency of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4SDA is higher than that of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1350449516302961&_mathId=si3.gif&_user=111111111&_pii=S1350449516302961&_rdoc=1&_issn=13504495&md5=d0cf526c70b126d5e826fd81c17a4f26" title="Click to view the MathML source">δclass="mathContainer hidden">class="mathCode">w="scroll">w>δw>-4DDA.

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