Level-1.1: Self-heating correction
Level 1.1 applies only to the open-path LI-7500 (IRGA75). Its corrected fluxes are in progress for FP2026.2 and are not part of FP2026.1. The fluxes of FP2026.1 come from the enclosed-path LI-7200 (IRGA72), which needs no self-heating correction.
- 31_SelfHeatingCorrection_ScalingFactors_NEE: scaling factors from the parallel measurements of 2016-2017.
- 41_SelfHeatingCorrection_Application_IRGA75_NEE_2004-2019: the correction applied to the
IRGA75record.
The correction refines the self-heating correction for open-path analysers of earlier studies (Burba et al., 2006; Järvi et al., 2009; Kittler et al., 2017). It is implemented in the Python library diive and applies to the CO2 flux only. It has three steps: an unscaled flux correction term \(\text{FCT}_{\text{unsc}}\) from physical relations, a scaling factor \(\text{SF}\) derived against the enclosed-path analyser, and the application of the scaled term to the flux.
Physical basis
In sun, the sensor head of the open-path analyser heats up and warms the air in its sampling path. The open-path analyser measures the CO2 molar density (\(q_c\), mol m-3), so the warmer, less dense air lowers the measured concentration. The result is a negative flux bias, an apparent CO2 uptake.
1. Unscaled flux correction term
The correction term is calculated from the heat transfer between the instrument surface and the air. Three methods are available: Järvi et al. (2009) (JAR09), Burba et al. (2006) (BUR06) and the multi-surface approach of Burba et al. (2008) (BUR08). For JAR09 and BUR06:
\[\text{FCT}_{\text{unsc}} = \frac{(T_s - T_a) q_c}{r_a T_a K} \left(1 + 1.6077 \frac{\rho_v}{\rho_d}\right)\]
- \(T_s\), \(T_a\): instrument surface and ambient air temperature. \(T_s\) is estimated from \(T_a\) with the parameterisation of the chosen method.
- \(q_c\): CO2 molar density (µmol m-3).
- \(r_a\): aerodynamic resistance to heat transfer (s m-1), from wind speed \(u\) and friction velocity \(u_*\).
- \(T_a K\): ambient air temperature in kelvin.
- \(1 + 1.6077 \rho_v/\rho_d\): water vapour correction factor, analogous to the WPL correction.
Gaps in \(\text{FCT}_{\text{unsc}}\), where an auxiliary variable is missing, are filled with a machine-learning model (a random forest in the existing notebooks), so that the correction can be applied to every flux.
2. Scaling factor
The physical term has to be tuned to the instrument and the site. The enclosed-path LI-7200 is not affected by self-heating and measured in parallel with the LI-7500 from January 2016 to December 2017, so its flux serves as the reference. The scaling factor \(\xi\) minimises the L1 norm of the difference between the cumulative sums of the corrected open-path flux and of the reference flux, taken at every time step:
\[\text{Minimize} \sum \left| \sum \left( \text{Flux}_{\text{OP, raw}} + \text{FCT}_{\text{unsc}} \cdot \xi \right) - \sum \text{Flux}_{\text{CP, ref}} \right|\]
Matching the cumulative sums makes the long-term CO2 budgets of the two analysers agree. The optimisation is done separately for daytime and nighttime and for classes of a variable such as \(u_*\), because self-heating depends on radiation and turbulence. Circular block bootstrapping resamples the time series while preserving its autocorrelation, and gives a median scaling factor with confidence intervals for each class.
3. Application
Each half-hour receives the median scaling factor of its class and of day or night. The corrected flux is:
\[\text{FCT} = \text{FCT}_{\text{unsc\_gf}} \cdot \text{SF}\]
\[\text{Flux}_{\text{OP, corr}} = \text{Flux}_{\text{OP, raw}} + \text{FCT}\]