Importance of the Webb, Pearman, and Leuning (WPL) correction for the measurement of small CO₂ fluxes

The WPL (Webb, Pearman, and Leuning) correction is fully accepted to correct trace gas fluxes like CO2 for density fluctuations due to water vapour and temperature fluctuations for open-path gas analysers. It is known that this additive correction can be on the order of magnitude of the actual flux. However, this is hardly ever included in the analysis of data quality. An example from the Arctic shows the problems, because the size of the correction is a multiple of the actual flux. As a general result, we examined and tabulated the magnitude of the WPL correction for carbon dioxide flux as a function of sensible and latent heat flux. Furthermore, we propose a parameter to better estimate possible deficits in data quality and recommend integrating the quality flag derived with this parameter into the general study of small carbon dioxide fluxes.

Importance of the WPL correction for the measurement of small CO₂ fluxes

The WPL (Webb, Pearman, and Leuning) correction is fully accepted to correct trace gas fluxes like CO2 for density fluctuations due to water vapor and temperature fluctuations for open-path gas analysers. It is known that this additive correction can be in the order of magnitude of the actual flux. However, this is hardly ever included in the analysis of data quality. An example from the Arctic shows the problems, because the size of the correction is a multiple of the actual flux. As a general result, we examined and tabulated the magnitude of the WPL correction for carbon dioxide flux as a function of sensible and latent heat flux. Furthermore, we propose a parameter to better estimate possible deficits in data quality and recommend integrating the quality flag derived with this parameter into the general study of small carbon dioxide fluxes.

Method of Vicarious Calibration of the Kanopus-V Satellite Constellation Data Based on Long-Term Observation of RadCalNet Polygons

The article discusses a method of vicarious data calibration of the MSS sensor of the Kanopus-V spacecraft based on the observation of RadCalNet polygons in the 2018–2020 period. The technique includes the stage of processing ground-based RadCalNet measurements for the period, with the aim of analytical approximation of the time series to ensure its continuity when compared with the MSS imagery of the Kanopus-V spacecraft constellation. The second stage evaluates the multiplicative and additive correction of the absolute calibration parameters for each of the constellation sensors based on the array of MSS observations and RadCalNet measurements. At the third stage, the assessment of the comparability of measurements by the MSS radiometer of the Kanopus-V spacecraft constellation is carried out on the basis of the results of surveying of natural calibration sites. The results obtained demonstrate a significant improvement in the comparability of measurements with the MSS radiometer within the constellation: the spread of the systematic measurement error was reduced by more than 2–3 times (depending on the spectral channel).

A numerical method to improve the spatial interpolation of water vapor from numerical weather models: a case study in South and Central America

Commonly, numerical weather model (NWM) users can get the vertically integrated water vapor (IWV) value at a given location from the values at nearby grid points. In this study we used a validated and freely available global navigation satellite system (GNSS) IWV data set to analyze the very well-known effect of height differences. To this end, we studied the behavior of 67 GNSS stations in Central and South America with the prerequisite that they have a minimum of 5 years of data during the period from 2007 to 2013. The values of IWV from GNSS were compared with the respective values from ERA-Interim and MERRA-2 from the same period. Firstly, the total set of stations was compared in order to detect cases in which the geopotential difference between GNSS and NWM required correction. An additive integral correction to the IWV values from ERA-Interim was then proposed. For the calculation of this correction, the multilevel values of specific humidity and temperature given at 37 pressure levels by ERA-Interim were used. The performance of the numerical integration method was tested by accurately reproducing the IWV values at every individual grid point surrounding each of the GNSS sites under study. Finally, considering the IWVGNSS values as a reference, the improvement introduced to the IWVERA-Interim values after correction was analyzed. In general, the corrections were always recommended, but they are not advisable in marine coastal areas or on islands as at least two grid points of the model are usually in the water. In such cases, the additive correction could overestimate the IWV.

An Efficient Minibatch Acceptance Test for Metropolis-Hastings

We present a novel Metropolis-Hastings method for large datasets that uses small expected-size mini-batches of data. Previous work on reducing the cost of Metropolis-Hastings tests yields only constant factor reductions versus using the full dataset for each sample. Here we present a method that can be tuned to provide arbitrarily small batch sizes, by adjusting either proposal step size or temperature. Our test uses the noise-tolerant Barker acceptance test with a novel additive correction variable. The resulting test has similar cost to a normal SGD update. Our experiments demonstrate several order-of-magnitude speedups over previous work.

Stochastic optimal enhancement of distributed formation control using Kalman smoothers

SUMMARYBeginning with a deterministic distributed feedback control for nonholonomic vehicle formations, we develop a stochastic optimal control approach for agents to enhance their non-optimal controls with additive correction terms based on the Hamilton–Jacobi–Bellman equation, making them optimal and robust to uncertainties. In order to avoid discretization of the high-dimensional cost-to-go function, we exploit the stochasticity of the distributed nature of the problem to develop an equivalent Kalman smoothing problem in a continuous state space using a path integral representation. Our approach is illustrated by numerical examples in which agents achieve a formation with their neighbors using only local observations.

The Diameter of Sparse Random Graphs

In this paper we study the diameter of the random graph G(n, p), i.e., the largest finite distance between two vertices, for a wide range of functions p = p(n). For p = λ/n with λ > 1 constant we give a simple proof of an essentially best possible result, with an Op(1) additive correction term. Using similar techniques, we establish two-point concentration in the case that np → ∞. For p =(1 + ε)/n with ε → 0, we obtain a corresponding result that applies all the way down to the scaling window of the phase transition, with an Op(1/ε) additive correction term whose (appropriately scaled) limiting distribution we describe. Combined with earlier results, our new results complete the determination of the diameter of the random graph G(n, p) to an accuracy of the order of its standard deviation (or better), for all functions p = p(n). Throughout we use branching process methods, rather than the more common approach of separate analysis of the 2-core and the trees attached to it.