Status: this preprint is open for discussion and under review for Atmospheric Measurement Techniques (AMT).
Optimizing the precision of infrared measurements using the Eppley Laboratory, Inc. model PIR pyrgeometer
Joseph J. Michalsky,John A. Augustine,Emiel Hall,and Benjamin R. Sheffer
Abstract. The Eppley Model PIR is widely used for thermal infrared wavelength (3.5–50 μm) measurements of the downwelling and upwelling radiation from the atmosphere and surface, respectively. The field of view of the instrument is 2π steradians with a receiver that has an approximate cosine response. In this paper we examine four equations in the literature that have been used to transfer calibration from standards to field units that are used for network operations. After the introduction we discuss various equations used to convert the resistance of the YSI 44031 thermistors used in PIRs for temperature measurements of the body, aka case, and dome that are used in the derivation of incoming irradiance. We then use the four related, but distinct, equations for the transfer of the calibration from standards to field instruments. A clear choice for the preferred equation to use for calibration and transfer of calibration to field PIRs emerges from this study.
Received: 04 Aug 2025 – Discussion started: 05 Sep 2025
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“Optimizing the precision of infrared measurements using the Eppley Laboratory, Inc. model PIR pyrgeometer” by Michalsky et al. evaluates existing approaches for transferring calibrations from PIR standards to sensors used for field operations. The authors conduct a careful and transparent analysis that provides useful results for long term networks with a historical investment in the PIR sensor. The study is a good fit for AMT. I have some comments that should be addressed in a revision before publication.
General comments:
(1) What equation is used to produce calibrated fluxes in the WISG sensors? If the WISG also uses eq (3), then wouldn’t the results shown here be interpreted firstly as an indication of consistency, but not necessarily an indication of accuracy?
(2) Figure 7: Some additional analysis here is warranted. The most obvious candidate for explaining the difference between the first and second half of the cal period is the cloud fraction (the repeatability of pyrgeometer measurements is much worse under clear skies than stratiform clouds; e.g., https://doi.org/10.5194/amt-14-1205-2021), but perhaps mean temperature or precipitable water vapor could also explain it. Figures 6 and 7 could mean that the small differences reported earlier (from any equation) are overly optimistic compensation between opposing errors given fortuitous proportions of conditions within the cal period.
(3) It would be good to apply t-tests to determine which means are different from one another, or from zero, where appropriate. The analyzed differences are small enough that they may not be significant.
(4) L320-322: Regarding conclusions, what about the fact that the differences amongst transfer equations is so much smaller than either the WISG uncertainty or (speculatively, see 2 above) the uncertainty caused by the sampling of conditions during outdoor calibrations?
Specific comments:
L14: For clarity, “broadband thermal IR…”
L40: Maybe clarify that the dome is designed to partly transmit only in the range of 3.5-50 um.
Figure 1: A few suggestions to improve the communication in this figure: (a) Label “dome” in the picture as you have done with the thermopile so that it is not interpreted as schematic of example paths in the sky (as I did at first). (b) In the caption after the word “rays” clarify that these are the numbered vectors in the picture. (c) Tb is not actually at the base of the thermopile, but is potted in the bronze casing nearby, so it would be helpful to depict the upper part of the case to show that Tb and Tr are not measuring the same thing. (d) Label Td and Tb as being thermistor measurements to distinguish from Tr, which is estimated (see also my comment at L92, which could also refer back to this figure).
L88: Since it is not clear from this text what Reda et al.’s justification was for including k0, it is also not clear what the present study’s justification is for dropping it.
L90: I think this paragraph would benefit from a leading statement expressing the problem this paper is solving. That statement might be supported by another that explains the reason prior studies modified the original Albrecht and Cox approach. As is, the text presumes too much insider knowledge on the historical context and current gap in understanding.
L92: The fact that YSI44031s are used to measure the temperature, and which temperatures are measured this way, should be included in Figure 1.
L112: Eq. 7 is odd. Can you write “c” instead of 0 in the equation to be more consistent with the Section 2 analysis/figure and then clarify in the text that in the classical form, S-H set c = 0?
L119: I’m confused about the use of the quadratic term. It looks like c = 0 for all lines in Figure 2. Where in the figure is the full cubic found? If it is the dashed blue line, it seems to be defined differently, as there is a minus sign in both the legend and the y-axis (Is the dashed blue line actually comparable to the other lines?) Also, what is c when it isn’t 0, and when it is not 0, are a, b, and d the same or do they also change?
L120: “Interestingly…” I don’t understand this statement. It seems like it would be much more surprising that changing the units yields a different result. The paper is not very long. Perhaps the appendix can be returned to the main text.
Figure 2: An error of 0.01 C in the thermistor will produce an error < 0.05 Wm2 at 0 C, which is negligible compared to other uncertainties (similar, in fact, to the error produced by the conventional, though incorrect, assumption that sigma is 5.6700e-8). Isn’t it true that the most relevant problem attributable to the YSI44031 is not the calibration method, but instead either the representativeness of its placement in the sensor in the case or the variance amongst individual thermistors in conforming to the calibration coefficients? So, I’m left not being entirely sure what the purpose of this exercise is. Is the take-away message that the YSI calibration isn’t the problem with the flux calibration? If so, make that clear. [Returning to this point after reading the conclusion, I appreciate the point you made at L299-304, though it might be worth commenting on the other issues with the thermistor in the conclusion. At very least, I suggest making the purpose of the thermistor section clearer in Section 2.]
L164: When you say “using these standards”, do you mean that the average of the standards was used for the calibration?
L247, 266: I think Figures 6 and 7, which show larger differences than Figures 3 and 4, suggest that the conditions under which outdoor calibrations (clarify somewhere that these are indeed outdoor?) are carried out are responsible for larger calibration uncertainty than the choice of equation. Yet, I think the community has historically been more focused on methodology. Maybe a recommendation to be made there?
L313: “…are small.” Specifically, the differences are an order of magnitude smaller in the transfer of relative calibrations than the reported uncertainty of the WISG.
L360, 364: Are these equation references supposed to be to A#?
We examine four equations for calculating infrared radiation (3–50 mm) measured with a Eppley PIR pyrgeometer. These equations are used to transfer calibrations from the World Infrared Standard Group at the World Radiation Center in Davos, Switzerland, to the three PIR pyrgeometers we use as standards. A clear choice in terms of the most precise method to follow emerges from this study. Furthermore, we evaluate the stability of the Eppley PIR, necessary for long-term trend analysis.
We examine four equations for calculating infrared radiation (3–50 mm) measured with a Eppley...
“Optimizing the precision of infrared measurements using the Eppley Laboratory, Inc. model PIR pyrgeometer” by Michalsky et al. evaluates existing approaches for transferring calibrations from PIR standards to sensors used for field operations. The authors conduct a careful and transparent analysis that provides useful results for long term networks with a historical investment in the PIR sensor. The study is a good fit for AMT. I have some comments that should be addressed in a revision before publication.
General comments:
(1) What equation is used to produce calibrated fluxes in the WISG sensors? If the WISG also uses eq (3), then wouldn’t the results shown here be interpreted firstly as an indication of consistency, but not necessarily an indication of accuracy?
(2) Figure 7: Some additional analysis here is warranted. The most obvious candidate for explaining the difference between the first and second half of the cal period is the cloud fraction (the repeatability of pyrgeometer measurements is much worse under clear skies than stratiform clouds; e.g., https://doi.org/10.5194/amt-14-1205-2021), but perhaps mean temperature or precipitable water vapor could also explain it. Figures 6 and 7 could mean that the small differences reported earlier (from any equation) are overly optimistic compensation between opposing errors given fortuitous proportions of conditions within the cal period.
(3) It would be good to apply t-tests to determine which means are different from one another, or from zero, where appropriate. The analyzed differences are small enough that they may not be significant.
(4) L320-322: Regarding conclusions, what about the fact that the differences amongst transfer equations is so much smaller than either the WISG uncertainty or (speculatively, see 2 above) the uncertainty caused by the sampling of conditions during outdoor calibrations?
Specific comments:
L14: For clarity, “broadband thermal IR…”
L40: Maybe clarify that the dome is designed to partly transmit only in the range of 3.5-50 um.
Figure 1: A few suggestions to improve the communication in this figure: (a) Label “dome” in the picture as you have done with the thermopile so that it is not interpreted as schematic of example paths in the sky (as I did at first). (b) In the caption after the word “rays” clarify that these are the numbered vectors in the picture. (c) Tb is not actually at the base of the thermopile, but is potted in the bronze casing nearby, so it would be helpful to depict the upper part of the case to show that Tb and Tr are not measuring the same thing. (d) Label Td and Tb as being thermistor measurements to distinguish from Tr, which is estimated (see also my comment at L92, which could also refer back to this figure).
L88: Since it is not clear from this text what Reda et al.’s justification was for including k0, it is also not clear what the present study’s justification is for dropping it.
L90: I think this paragraph would benefit from a leading statement expressing the problem this paper is solving. That statement might be supported by another that explains the reason prior studies modified the original Albrecht and Cox approach. As is, the text presumes too much insider knowledge on the historical context and current gap in understanding.
L92: The fact that YSI44031s are used to measure the temperature, and which temperatures are measured this way, should be included in Figure 1.
L112: Eq. 7 is odd. Can you write “c” instead of 0 in the equation to be more consistent with the Section 2 analysis/figure and then clarify in the text that in the classical form, S-H set c = 0?
L119: I’m confused about the use of the quadratic term. It looks like c = 0 for all lines in Figure 2. Where in the figure is the full cubic found? If it is the dashed blue line, it seems to be defined differently, as there is a minus sign in both the legend and the y-axis (Is the dashed blue line actually comparable to the other lines?) Also, what is c when it isn’t 0, and when it is not 0, are a, b, and d the same or do they also change?
L120: “Interestingly…” I don’t understand this statement. It seems like it would be much more surprising that changing the units yields a different result. The paper is not very long. Perhaps the appendix can be returned to the main text.
Figure 2: An error of 0.01 C in the thermistor will produce an error < 0.05 Wm2 at 0 C, which is negligible compared to other uncertainties (similar, in fact, to the error produced by the conventional, though incorrect, assumption that sigma is 5.6700e-8). Isn’t it true that the most relevant problem attributable to the YSI44031 is not the calibration method, but instead either the representativeness of its placement in the sensor in the case or the variance amongst individual thermistors in conforming to the calibration coefficients? So, I’m left not being entirely sure what the purpose of this exercise is. Is the take-away message that the YSI calibration isn’t the problem with the flux calibration? If so, make that clear. [Returning to this point after reading the conclusion, I appreciate the point you made at L299-304, though it might be worth commenting on the other issues with the thermistor in the conclusion. At very least, I suggest making the purpose of the thermistor section clearer in Section 2.]
L164: When you say “using these standards”, do you mean that the average of the standards was used for the calibration?
L247, 266: I think Figures 6 and 7, which show larger differences than Figures 3 and 4, suggest that the conditions under which outdoor calibrations (clarify somewhere that these are indeed outdoor?) are carried out are responsible for larger calibration uncertainty than the choice of equation. Yet, I think the community has historically been more focused on methodology. Maybe a recommendation to be made there?
L313: “…are small.” Specifically, the differences are an order of magnitude smaller in the transfer of relative calibrations than the reported uncertainty of the WISG.
L360, 364: Are these equation references supposed to be to A#?
L417: Is this Grobner (2025) from the main text?