Characterization of errors in satellite-based HCHO ∕ NO ₂ tropospheric column ratios with respect to chemistry, column-to-PBL translation, spatial representation, and retrieval uncertainties

Abstract. The availability of formaldehyde (HCHO) (a proxy for volatile organic compound reactivity) and nitrogen dioxide (NO2) (a proxy for nitrogen oxides) tropospheric columns from ultraviolet–visible (UV–Vis) satellites has motivated many to use their ratios to gain some insights into the near-surface ozone sensitivity. Strong emphasis has been placed on the challenges that come with transforming what is being observed in the tropospheric column to what is actually in the planetary boundary layer (PBL) and near the surface; however, little attention has been paid to other sources of error such as chemistry, spatial representation, and retrieval uncertainties. Here we leverage a wide spectrum of tools and data to quantify those errors carefully. Concerning the chemistry error, a well-characterized box model constrained by more than 500 h of aircraft data from NASA's air quality campaigns is used to simulate the ratio of the chemical loss of HO2 + RO2 (LROx) to the chemical loss of NOx (LNOx). Subsequently, we challenge the predictive power of HCHO/NO2 ratios (FNRs), which are commonly applied in current research, in detecting the underlying ozone regimes by comparing them to LROx/LNOx. FNRs show a strongly linear (R2=0.94) relationship with LROx/LNOx, but only on the logarithmic scale. Following the baseline (i.e., ln(LROx/LNOx) = −1.0 ± 0.2) with the model and mechanism (CB06, r2) used for segregating NOx-sensitive from VOC-sensitive regimes, we observe a broad range of FNR thresholds ranging from 1 to 4. The transitioning ratios strictly follow a Gaussian distribution with a mean and standard deviation of 1.8 and 0.4, respectively. This implies that the FNR has an inherent 20 % standard error (1σ) resulting from not accurately describing the ROx–HOx cycle. We calculate high ozone production rates (PO3) dominated by large HCHO × NO2 concentration levels, a new proxy for the abundance of ozone precursors. The relationship between PO3 and HCHO × NO2 becomes more pronounced when moving towards NOx-sensitive regions due to nonlinear chemistry; our results indicate that there is fruitful information in the HCHO × NO2 metric that has not been utilized in ozone studies. The vast amount of vertical information on HCHO and NO2 concentrations from the air quality campaigns enables us to parameterize the vertical shapes of FNRs using a second-order rational function permitting an analytical solution for an altitude adjustment factor to partition the tropospheric columns into the PBL region. We propose a mathematical solution to the spatial representation error based on modeling isotropic semivariograms. Based on summertime-averaged data, the Ozone Monitoring Instrument (OMI) loses 12 % of its spatial information at its native resolution with respect to a high-resolution sensor like the TROPOspheric Monitoring Instrument (TROPOMI) (> 5.5 × 3.5 km2). A pixel with a grid size of 216 km2 fails at capturing ∼ 65 % of the spatial information in FNRs at a 50 km length scale comparable to the size of a large urban center (e.g., Los Angeles). We ultimately leverage a large suite of in situ and ground-based remote sensing measurements to draw the error distributions of daily TROPOMI and OMI tropospheric NO2 and HCHO columns. At a 68 % confidence interval (1σ), errors pertaining to daily TROPOMI observations, either HCHO or tropospheric NO2 columns, should be above 1.2–1.5 × 1016 molec. cm−2 to attain a 20 %–30 % standard error in the ratio. This level of error is almost non-achievable with the OMI given its large error in HCHO. The satellite column retrieval error is the largest contributor to the total error (40 %–90 %) in the FNRs. Due to a stronger signal in cities, the total relative error (< 50 %) tends to be mild, whereas areas with low vegetation and anthropogenic sources (e.g., the Rocky Mountains) are markedly uncertain (> 100 %). Our study suggests that continuing development in the retrieval algorithm and sensor design and calibration is essential to be able to advance the application of FNRs beyond a qualitative metric.