“Tau-Omega”- and Two-Stream Emission Models Used for Passive L-Band Retrievals: Application to Close-Range Measurements over a Forest

• Main Authors: Mike Schwank, Reza Naderpour, Christian Mätzler
• Format: Article
• Language: English
• Published: MDPI AG 2018-11-01
• Series: Remote Sensing
• Subjects: passive microwave radiometry; L-band; soil moisture; vegetation optical depth; emission model; retrieval; SMOS; SMAP
• Online Access: https://www.mdpi.com/2072-4292/10/12/1868

Microwave Emission Models (EM) are used in retrieval algorithms to estimate geophysical state parameters such as soil Water Content (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>W</mi> <mi>C</mi> </mrow> </semantics> </math> </inline-formula>) and vegetation optical depth (<inline-formula> <math display="inline"> <semantics> <mi>&#964;</mi> </semantics> </math> </inline-formula>), from brightness temperatures <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>T</mi> <mi mathvariant="normal">B</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>&#952;</mi> </mrow> </msubsup> </mrow> </semantics> </math> </inline-formula> measured at nadir angles <inline-formula> <math display="inline"> <semantics> <mi>&#952;</mi> </semantics> </math> </inline-formula> at Horizontal and Vertical polarizations <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mi mathvariant="normal">H</mi> <mo>,</mo> <mi mathvariant="normal">V</mi> </mrow> <mo>}</mo> </mrow> </mrow> </semantics> </math> </inline-formula>. An EM adequate for implementation in a retrieval algorithm must capture the responses of <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>T</mi> <mi mathvariant="normal">B</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>&#952;</mi> </mrow> </msubsup> </mrow> </semantics> </math> </inline-formula> to the retrieval parameters, and the EM parameters must be experimentally accessible and representative of the measurement footprint. The objective of this study is to explore the benefits of the multiple-scattering Two-Stream (2S) EM over the &#8220;Tau-Omega&#8222; (TO) EM considered as the &#8220;reference&#8222; to retrieve <inline-formula> <math display="inline"> <semantics> <mrow> <mi>W</mi> <mi>C</mi> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mi>&#964;</mi> </semantics> </math> </inline-formula> from L-band <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>T</mi> <mi mathvariant="normal">B</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>&#952;</mi> </mrow> </msubsup> </mrow> </semantics> </math> </inline-formula>. For sparse and low-scattering vegetation <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>T</mi> <mrow> <mi mathvariant="normal">B</mi> <mo>,</mo> <mi>E</mi> <mi>M</mi> </mrow> <mrow> <mi>p</mi> <mo>,</mo> <mi>&#952;</mi> </mrow> </msubsup> </mrow> </semantics> </math> </inline-formula> simulated with <inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mi>M</mi> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mi>TO</mi> <mo>,</mo> <mtext>&nbsp;</mtext> <mn>2</mn> <mi mathvariant="normal">S</mi> </mrow> <mo>}</mo> </mrow> </mrow> </semantics> </math> </inline-formula> converge. This is not the case for dense and strongly scattering vegetation. Two-Parameter (2P) retrievals <inline-formula> <math display="inline"> <semantics> <mrow> <mn mathvariant="bold">2</mn> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>P</mi> </mstyle> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <mrow> <mi>W</mi> <msub> <mi>C</mi> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&#964;</mi> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> are computed from elevation scans <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>T</mi> <mi mathvariant="normal">B</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&#952;</mi> <mi>j</mi> </msub> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>T</mi> <mrow> <mi mathvariant="normal">B</mi> <mo>,</mo> <mi>TO</mi> </mrow> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&#952;</mi> <mi>j</mi> </msub> </mrow> </msubsup> </mrow> </semantics> </math> </inline-formula> synthesized with TO EM and from <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>T</mi> <mi mathvariant="normal">B</mi> <mrow> <mi>p</mi> <mo>,</mo> <msub> <mi>&#952;</mi> <mi>j</mi> </msub> </mrow> </msubsup> </mrow> </semantics> </math> </inline-formula> measured from a tower within a deciduous forest. Retrieval Configurations (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </semantics> </math> </inline-formula>) employ either <inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mi>M</mi> <mo>=</mo> <mi>TO</mi> </mrow> </semantics> </math> </inline-formula> or <inline-formula> <math display="inline"> <semantics> <mrow> <mi>E</mi> <mi>M</mi> <mo>=</mo> <mn>2</mn> <mi mathvariant="normal">S</mi> </mrow> </semantics> </math> </inline-formula> and assume fixed scattering albedos. <inline-formula> <math display="inline"> <semantics> <mrow> <mi>W</mi> <msub> <mi>C</mi> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> achieved with the 2S <i>RC</i> is marginally lower (<inline-formula> <math display="inline"> <semantics> <mrow> <mo>~</mo> <mn>1</mn> <msup> <mrow> <mrow> <mtext>&nbsp;</mtext> <mi mathvariant="normal">m</mi> </mrow> </mrow> <mn>3</mn> </msup> <msup> <mi mathvariant="normal">m</mi> <mrow> <mo>&#8722;</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics> </math> </inline-formula>) than if achieved with the &#8220;reference&#8222; TO <i>RC</i>, while <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>&#964;</mi> <mrow> <mi>R</mi> <mi>C</mi> </mrow> </msub> </mrow> </semantics> </math> </inline-formula> is reduced considerably when using 2S EM instead of TO EM. Our study outlines a number of advantages of the 2S EM over the TO EM currently implemented in the operational SMOS and SMAP retrieval algorithms.