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Regression Bias in using Solar Wind Measurements

Simultaneous solar wind measurements from the solar wind monitors, WIND and ACE, differ due to the spatial and temporal structure of the solar wind. Correlation studies that use these measurements as input may infer an incorrect correlation due to uncertainties arising from this spatial and temporal structure, especially at extreme and rare solar wind values. In particular, regression analysis will lead to a regression function whose slope is biased towards the mean value of the measurement parameter. This article demonstrates this regression bias by comparing simultaneous ACE and WIND solar wind measurements. A non-linear regression analysis between them leads to a perception of underestimation of extreme values of one measurement on average over the other. Using numerical experiments, we show that popular regression analysis techniques such as linear least-squares, orthogonal least-squares, and non-linear regression are not immune to this bias. Hence while using solar wind parameters as an independent variable in a correlation or regression analysis, random uncertainty in the independent variable can create unintended biases in the response of the dependent variable. More generally, the regression to the mean effect can impact both event-based, statistical studies of magnetospheric response to solar wind forcing.

magnetosphere↗

Emissions Relationships in Western Forest Fire Plumes: I. Reducing the Effect of Mixing Errors on Emission Factors

Studies of emission factors from biomass burning using aircraft data complement the results of lab studies and extend them to conditions of immense hot conflagrations. We illustrate and discuss emission relationships for 422 individual samples from many forest-fire plumes in the Western US. The samples are from two NASA investigations: ARCTAS (Arctic Research of the Composition of the Troposphere from Aircraft and Satellites) and SEAC4RS (Studies of Emissions and Atmospheric Composition, Clouds, and Climate Coupling by Regional Surveys). This work provides sample-by-sample enhancement ratios (EnRs) for 23 gases and particulate properties. Many EnRs provide candidates for emission ratios (ERs, corresponding to the EnR at the source) when the origin and degree of transformation is understood and appropriate. From these, emission factors (EFs) can be estimated when the fuel dry mass consumed is known or can be estimated using the carbon mass budget approach. This analysis requires understanding the interplay of mixing of the plume with surrounding air. Some initial examples emphasize that measured C(tot) = CO2 + CO in a fire plume does not necessarily describe the emissions of the total carbon liberated in the flames, C(burn). Rather, it represents C(tot) = C(burn) + C(bkgd), which includes possibly varying background concentrations for entrained air. Consequently, we present a simple theoretical description for plume entrainment for multiple tracers from flame to hundreds of kilometers downwind and illustrate some intrinsic linear behaviors. The analysis suggests a Mixed Effects Regression Emission Technique (MERET), which can eliminate occasional strong biases associated with the commonly used normalized excess mixing ratio (NEMR) method. MERET splits C(tot) to reveal C(burn) by exploiting the fact that C(burn) and all tracers respond linearly to dilution, while each tracer has consistent EnR behavior (slope of tracer concentration with respect to C(burn)). The two effects are separable. Two or three or preferably more emission indicators are required as a minimum; here we used ten. Limited variations in the EnRs for each tracer can be incorporated and the variations and co-variations analyzed. The percentage CO yield (or the modified combustion efficiency) plays some role. Other co-relationships involving nitrogen and organic classes are more prominent; these have strong relationships to the C(burn) to O3 emission relationship. In summary, MERET allows fine spatial resolution (EnRs for individual observations) and comparison of similar plumes distant in time and space. Alkene ratios provide us with an approximate photochemical timescale. This allows discrimination and definition, by fire situation, of ERs, allowing us to estimate emission factors.

Chatfield, Robert B.↗