| 30 Sep 2026
A log-domain method for decoupling environmental interference from hardware response in multi-filter calibration of forward-scatter visibility sensors
Abstract. Accurate calibration of forward-scatter visibility sensors remains challenging because their response depends on instrument geometry and scattering conditions, while field calibration is additionally perturbed by background atmospheric extinction. Existing indoor multi-filter protocols can characterize sensor response under controlled conditions, but their transfer to outdoor operation is hindered by environmental contamination during reference measurements. Here, we propose a log-domain calibration framework that separates a hardware-dependent calibration factor, fcal , from an environment-dependent interference term, fenv , by comparing paired darkroom and outdoor regressions of measured versus reference meteorological optical range (MOR). In this formulation, the darkroom intercept represents the hardware baseline, whereas the outdoor intercept contains both hardware and environmental contributions. The framework was evaluated using two forward-scatter sensor families, the Vaisala PWD22 and Biral SWS-200, with neutral-density filter sets and an LT31 transmissometer used to define model-specific reference meteorological optical range (MOR) values and monitor outdoor background visibility.
The PWD22 exhibited near-unit darkroom slope and stable intercept transfer, allowing modest fenv contributions to be resolved under relatively clear outdoor conditions, whereas the SWS-200 was more sensitive to slope instability and filter-seating effects. In both cases, calibration improved bias more than scatter, so the framework is best viewed as a practical field-transfer method for suitable forward-scatter sensors that does not replace transmissometer-based traceability and remains conditional on sufficiently high background visibility and stable sensor slope.
Field calibration of forward-scatter sensors, which at many sites cannot be removed for laboratory calibration, is an important and still unresolved practical problem. I noted a few points where the equations, tables and figures do not seem to agree, and I list them below in case they are helpful for the revision.
1. Eq. (6) implies that background extinction can only lower the MOR measured outdoors, and the theoretical curve in Fig. 6, fenv = 1/(1 + Vcal/Vbg), accordingly never exceeds 1. Table 4, however, gives fenv > 1 for PWD22 (1.161, 1.187) and SWS-200 Set B (1.077) and interprets these values as physical. By contrast, the SWS-200 Set E value (0.878), which is in the direction expected from Eq. (6), is described as not physically consistent with the additive-background interpretation (lines 380–382). In addition, the legend of Fig. 6 gives different values for the same four events (0.976, 1.023, 1.045 and 1.000), and the text quotes both sets: lines 289–290 describe the PWD22 values as “close to unity”, while lines 359–360 quote 1.161 and 1.187. Could the author clarify the sign convention of fenv and which values are correct?
2. According to Sect. 4.3.1 (lines 323–325), the PWD22 correction uses aln from the A01 darkroom regression (0.99 for Set B, as in the title of Fig. 8b) and Cout from the B01 outdoor sequence (0.125, Table 4). With these values, Eq. (5) gives ln Vcorr = (ln Vmeas - 0.125)/0.99, which is smaller than ln Vmeas everywhere in the observed MOR range. The Set-B correction should therefore lower all PWD22 values and make the global log-bias more negative, yet Table 5 and Fig. 8b show it changing from -0.010 to +0.020. Could the author check which parameter values were used for the Set-B correction?
3. Sect. 1.1 (lines 32–33) notes that the WMO requirement is range-dependent: 50 m below 600 m, 10 % from 600 to 1500 m, and 20 % above 1500 m. The rest of the paper, however, uses a uniform ±10 % band labelled as the WMO tolerance (Fig. 2, the caption of Fig. 6, Figs. 8–9, Table 5, Sect. 5.4 and the Conclusions). This band is stricter than the WMO requirement over most of the range, in particular for the >10 000 m bin that dominates the residuals (lines 361–362), where the requirement is 20 %. It might help to describe the band as a simplified ±10 % benchmark, or to also report compliance against the range-dependent WMO requirement.
4. In Table 3, the CIC (95 %) column appears to repeat the standard errors of the intercepts (e.g. -0.007 ± 0.014 with CI_C = 0.014). In contrast, CIaln is about t × SE (e.g. 0.002 → 0.006), and the legends of Fig. 5 also give intercept intervals of about t × SE (e.g. C = -0.01 ± 0.04 for A01 Set B Seq. 1). If so, the 95 % intercept intervals are about three times wider than listed, which would affect the statement in lines 269–270 and the uncertainty of ln fenv obtained from Eq. (4).