Evaluation of calibration strategies for accurate <i>δ</i>¹³CH₄ measurements in dry and humid air

<p>Accurate determination of the methane isotopic composition (<span class="inline-formula"><i>δ</i>¹³</span>CH<span class="inline-formula">₄</span>) is essential for attributing emission sources of methane (CH<span class="inline-formula">₄</span>). However, for measurements with optical instruments, spectral interference from water vapor and instrumental drift often introduce substantial biases in <span class="inline-formula"><i>δ</i>¹³</span>CH<span class="inline-formula">₄</span> measurements, particularly for humid air measurements. Although multiple calibration strategies exist, a systematic evaluation of their performance under diverse field conditions remains lacking. Here, we evaluate two calibration strategies for a cavity ring-down spectrometer: a delta-based calibration for <span class="inline-formula"><i>δ</i>¹³</span>CH<span class="inline-formula">₄</span> and an isotopologue-specific calibration for <span class="inline-formula">¹²</span>CH<span class="inline-formula">₄</span> and <span class="inline-formula">¹³</span>CH<span class="inline-formula">₄</span>. We performed laboratory experiments over a water vapor range of 0.15 %–4.0 % to establish empirical correction functions, quadratic for <span class="inline-formula">¹²</span>CH<span class="inline-formula">₄</span> and <span class="inline-formula">¹³</span>CH<span class="inline-formula">₄</span>, and linear for <span class="inline-formula"><i>δ</i>¹³</span>CH<span class="inline-formula">₄</span>, to remove humidity-induced biases. These correction functions were then applied to field measurements in both dried air at the SORPES stie and humid air at the Jurong site. At the SORPES site where air samples were dried using a Nafion™ dryer, the mean difference in <span class="inline-formula"><i>δ</i>¹³</span>CH<span class="inline-formula">₄</span> between the two strategies was <span class="inline-formula">∼0.29</span> ‰. In contrast, for humid air at the Jurong site, significant inter-method difference (<span class="inline-formula">Δ<i>δ</i>¹³</span>CH<span class="inline-formula">₄</span>) was observed, with which exhibiting a strong correlation with <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M27" display="inline" overflow="scroll" dspmath="mathml"><mrow><mn mathvariant="normal">1</mn><mo>/</mo><msub><mrow class="chem"><mi mathvariant="normal">CH</mi></mrow><mn mathvariant="normal">4</mn></msub></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="35pt" height="14pt" class="svg-formula" dspmath="mathimg" md5hash="a724ef11153dc67aba6eb50abd0cee99"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-19-1763-2026-ie00001.svg" width="35pt" height="14pt" src="amt-19-1763-2026-ie00001.png"/></svg:svg></span></span>, indicating non-linear spectral effects are most pronounced at lower CH<span class="inline-formula">₄</span> concentrations and compromise the performance of delta-based calibration. Notably, only the isotopologue-specific calibration, coupled with an explicit water vapor correction, delivered stable and accurate <span class="inline-formula"><i>δ</i>¹³</span>CH<span class="inline-formula">₄</span> measurements across all conditions. This work underscores the need for robust calibration strategies to minimize bias in CH<span class="inline-formula">₄</span> isotopic composition measurements.</p>