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Improving two-temperature method retrievals based on a nonlinear optimization approach

机译：基于非线性优化方法的双温方法检索的改进

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摘要

The two-temperature method (TTM) is known to be sensitive to noise, and therefore, land-surface temperature (LST) and emissivity (LSE) retrievals based on TTM are in general not reliable when obtained by algebraic procedures. Accordingly, the added value of using TTM together with a nonlinear mathematical optimization approach is investigated, focusing on the effect that an increase in the temperature difference as well as in the number of observations might have on LST and LSE retrievals. TTM has provided values of LST and LSE with a bias (root mean square error) ranging from 0.1-0.4 K (2.1-2.8 K) and from 0.005-0.010 (0.040-0.055), respectively. Obtained results were almost the same for both well-determined and overdetermined cases, as well as for the considered temperature differences, suggesting that increasing the number of observations and the temperature difference does not lead to significant improvements on the results. On the other hand, it was found out that a greater temperature difference between the first and the last observation acts like a natural constraint by restricting the solutions to a narrower region. In this case, the estimated LST and LSE values do not strongly depend upon the initial guess, and therefore, the use of several initial guess vectors may be avoided, turning TTM computationally more efficient.
机译：众所周知，双温法（TTM）对噪声敏感，因此，当通过代数程序获得时，基于TTM的地表温度（LST）和发射率（LSE）检索通常不可靠。因此，研究了将TTM与非线性数学优化方法一起使用所带来的附加价值，重点研究了温度差以及观测次数增加对LST和LSE检索的影响。 TTM提供的LST和LSE值的偏差（均方根误差）分别为0.1-0.4 K（2.1-2.8 K）和0.005-0.010（0.040-0.055）。对于确定的情况和确定的情况以及考虑的温度差异，获得的结果几乎相同，这表明增加观测次数和温度差异不会导致结果的显着改善。另一方面，发现通过将解限制在较窄的区域，第一次观察和最后一次观察之间的较大温差表现为自然约束。在这种情况下，估计的LST和LSE值在很大程度上不取决于初始猜测，因此，可以避免使用多个初始猜测向量，从而使TTM的计算效率更高。

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