Quality control and error assessment of the Aeolus L2B wind results from the Joint Aeolus Tropical Atlantic Campaign

Since the start of the European Space Agency's Aeolus mission in 2018, various studies were dedicated to the evaluation of its wind data quality and particularly to the determination of the systematic and random errors in the Rayleigh-clear and Mie-cloudy wind results provided in the Aeolus Level-2B (L2B) product. The quality control (QC) schemes applied in the analyses mostly rely on the estimated error (EE), reported in the L2B data, using different and often subjectively chosen thresholds for rejecting data outliers, thus hampering the comparability of different validation studies. This work gives insight into the calculation of the EE for the two receiver channels and reveals its limitations as a measure of the actual wind error due to its spatial and temporal variability. It is demonstrated that a precise error assessment of the Aeolus winds necessitates a careful statistical analysis, including a rigorous screening for gross errors to be compliant with the error definitions formulated in the Aeolus mission requirements. To this end, the modified Z score and normal quantile plots are shown to be useful statistical tools for effectively eliminating gross errors and for evaluating the normality of the wind error distribution in dependence on the applied QC scheme, respectively. The influence of different QC approaches and thresholds on key statistical parameters is discussed in the context of the Joint Aeolus Tropical Atlantic Campaign (JATAC), which was conducted in Cabo Verde in September 2021. Aeolus winds are compared against model background data from the European Centre for Medium-Range Weather Forecasts (ECMWF) before the assimilation of Aeolus winds and against wind data measured with the 2 µm heterodyne detection Doppler wind lidar (DWL) aboard the Falcon aircraft. The two studies make evident that the error distribution of the Mie-cloudy winds is strongly skewed with a preponderance of positively biased wind results distorting the statistics if not filtered out properly. Effective outlier removal is accomplished by applying a two-step QC based on the EE and the modified Z score, thereby ensuring an error distribution with a high degree of normality while retaining a large portion of wind results from the original dataset. After the utilization of the described QC approach, the systematic errors in the L2B Rayleigh-clear and Mie-cloudy winds are determined to be below 0.3 m s−1 with respect to both the ECMWF model background and the 2 µm DWL. Differences in the random errors relative to the two reference datasets (Mie vs. model is 5.3 m s−1, Mie vs. DWL is 4.1 m s−1, Rayleigh vs. model is 7.8 m s−1, and Rayleigh vs. DWL is 8.2 m s−1) are elaborated in the text.</p

Chance‐constrained optimal inflow control in hyperbolic supply systems with uncertain demand

In this paper, we address the task of setting up an optimal production plan taking into account an uncertain demand. The energy system is represented by a system of hyperbolic partial differential equations (PDEs) and the uncertain demand stream is captured by an Ornstein-Uhlenbeck process. We determine the optimal inflow depending on the producer's risk preferences. The resulting output is intended to optimally match the stochastic demand for the given risk criteria. We use uncertainty quantification for an adaptation to different levels of risk aversion. More precisely, we use two types of chance constraints to formulate the requirement of demand satisfaction at a prescribed probability level. In a numerical analysis, we analyze the chance-constrained optimization problem for the Telegrapher's equation and a real-world coupled gas-to-power network

Airborne temperature profiling in the troposphere during daytime by lidar utilizing Rayleigh–Brillouin scattering

The airborne measurement of a temperature profile from 10.5 km down towards ground (about 1.4 km above sea level) during daytime by means of a lidar utilizing Rayleigh-Brillouin (RB) scattering is demonstrated for the first time, to our knowledge. The spectra of the scattered light were measured by tuning the laser (Lambda=354.9 nm) over a 11 GHz frequency range with a step size of 250 MHz while using a Fabry Perot interferometer as a spectral filter. The measurement took 14 min and was conducted over a remote area in Iceland with the ALADIN Airborne Demonstrator on-board the DLR Falcon aircraft. The temperature profile was derived by applying an analytical RB line shape model to the backscatter spectra, which were measured at different altitudes with a vertical resolution of 630 m. A comparison with temperature profiles from radiosonde observations and model temperatures shows reasonable agreement with biases of less than +/-2K. Based on Poisson statistics, the random error of the derived temperatures is estimated to vary between 0.1 K and 0.4 K. The work provides insight into the possible realization of airborne lidar temperature profilers based on RB scattering

Verification of different Fizeau fringe analysis algorithms based on airborne wind lidar data in support of ESA's Aeolus mission

The Aeolus mission by the European Space Agency was launched in August 2018 and stopped operations in April 2023. Aeolus carried the direct-detection Atmospheric LAser Doppler INstrument (ALADIN). To support the preparation of Aeolus, the ALADIN Airborne Demonstrator (A2D) instrument was developed and applied in several field campaigns. Both ALADIN and A2D consist of so-called Rayleigh and Mie channels used to measure wind from both molecular and particulate backscatter signals. The Mie channel is based on the fringe-imaging technique, which relies on determining the spatial location of a linear interference pattern (fringe) that originated from multiple interference in a Fizeauspectrometer.The accuracy of the retrieved winds is among others depending on the analytic algorithm used for determining the fringe location on the detector. In this paper, the performance of two algorithms using Lorentzian and Voigt fit functions is investigated by applying them to A2D data that were acquired during the AVATAR-I airborne campaign. For performance validation, the data of a highly accurate heterodyne detection wind lidar (2-µm DWL) that was flown in parallel are used as a reference. In addition, a fast and non-fit-based algorithm based on a four-pixel intensity ratio approach (R4) is developed. It is revealed that the Voigt-fit-based algorithm provides 50% more data points than the Lorentzian-based algorithm while applying a quality control that yields a similar random error of about 1.5 m/s. The R4 algorithm is shown to deliver a similar accuracy as the Voigt-fit-based algorithms, with the advantage of a one to two orders of magnitude faster computation time. Principally, the R4 algorithm can be adapted to other spectroscopic applications where sub-pixel knowledge of the location of measured peak profiles is needed

Validation of the Aeolus L2B wind product: A new, very fast algorithm for the Fizeau fringe analysis based on pixel intensity ratios

The measurement of Aeolus Mie-cloudy winds is based on the fringe-imaging technique. It relies on determining the spatial location of a linear interference pattern (fringe) that is originated from multiple interference in a Fizeau spectrometer and vertically imaged onto the Mie-channel detector. The accuracy of Mie-cloudy winds thus depends on several pre- and post-detection factors. These include the optical quality of the Fizeau interferometer, its manner of illumination and any spurious background light, as well as the number of detector pixels and the analytic algorithm used for determining the fringe location on the detector. In the Aeolus Level 1 B (L1B) processor, the centroid location and the width of the Fizeau fringes are usually analyzed by the Mie-core 2 algorithm, which applies a downhill simplex fit routine of a Lorentzian peak function to the measurement data. Although this algorithm works accurately and reliably, recent investigations based on atmospheric ground return signals demonstrated, that the Mie fringe profile is better described by a Voigt profile and, thus, the application of a Voigt fit improves the frequency measurement and the accuracy of the retrieved scattering ratio. The Voigt-fit was implemented in the L1B processor in 2022 and will be tested in the future for Mie fringe centroid computation. Against this background, an alternative algorithm based on an intensity ratio of the inner 4 pixels was developed (R4) which is insensitive to uniform background illumination. Simulations also demonstrated that the R4 algorithm is rather insensitive to the spectral shape of the fringe profile and that it is potentially one to two orders of magnitude faster than the fit-based approaches. Besides simulations, the R4 algorithm was applied to data of the Aladin Airborne Demonstrator (A2D) and the results were compared to both, the Lorentzian and the Voigt fit analysis. In particular, the data set from the AVATAR-I (Aeolus VAlidation Through Airborne LidaRs in Iceland) campaign was used for this study. In this contribution, we introduce the R4 algorithm in detail and investigate differences to the existing Mie-core algorithms (Lorentzian and Voigt fits) based on A2D data acquired during the AVATAR-I campaign in Iceland in 2019

Overview of Instrument Response Calibrations

The Instrument Response Calibration (IRC) constitutes a fundamental part of the Aeolus processing chain and the basis for accurate and precise wind information provided to the global user community. The IRC is a crucial instrument mode for the wind measurement and has, hence, been extensively investigated with the ALADIN Airborne Demonstrator already before launch of the Aeolus satellite. IRCs are used to determine the relationship between the Doppler frequency shift on the backscattered light, i.e. the wind speed, and the frequency response of the Rayleigh and Mie spectrometers. This is achieved by sampling a frequency range of 1 GHz in steps of 25 MHz around the nominal laser frequency for the wind measurement. Whereas Aeolus wind measurements (WVM) are obtained under an off-nadir viewing angle of 35°, IRCs are performed in nadir viewing mode, thereby trying to avoid the atmospheric horizontal wind component along the line-of-sight as well as the component of the satellite velocity. The special importance of the IRC mode has changed with time caused by the experiences gained after the launch of Aeolus

RAYLEIGH WIND RETRIEVAL FOR THE ALADIN AIRBORNE DEMONSTRATOR OF THE AEOLUS MISSION USING SIMULATED RESPONSE CALIBRATION

Aeolus, launched on 22 August 2018, is the first ever satellite to directly observe wind information from space on a global scale. An airborne prototype called ALADIN Airborne Demonstrator (A2D) was developed at the German Aerospace Center (DLR) for validating the Aeolus measurement principle based on realistic atmospheric signals. However, atmospheric and instrumental variability currently limit the reliability and repeatability of the A2D instrument response calibration. In this study, a simulated Rayleigh response calibration (SRRC) is presented for resolving the limitations of A2D instrument response calibration

Rayleigh wind retrieval for the ALADIN airborne demonstrator of the Aeolus mission using simulated response calibration

Aeolus, launched on 22 August in 2018, is the first ever satellite to directly observe wind information from the surface up to 30 km on a global scale. An airborne prototype instrument called ALADIN airborne demonstrator (A2D) was developed at the German Aerospace Center (DLR) for validating the Aeolus measurement principle based on realistic atmospheric signals. To obtain accurate wind retrievals, the A2D uses a measured Rayleigh response calibration (MRRC) to calibrate its Rayleigh channel signals. However, differences exist between the respective atmospheric temperature profiles that are present during the conduction of the MRRC and the actual wind measurements. These differences are an important source of wind bias since the atmospheric temperature has a direct effect on the instrument response calibration. Furthermore, some experimental limitations and requirements need to be considered carefully to achieve a reliable MRRC. The atmospheric and instrumental variability thus currently limit the reliability and repeatability of a MRRC. In this paper, a procedure for a simulated Rayleigh response calibration (SRRC) is developed and presented in order to resolve these limitations of the A2D MRRC. At first the transmission functions of the A2D Rayleigh channel double-edge Fabry-Pérot interferometers (FPIs) in the internal reference path and the atmospheric path are characterized and optimized based on measurements performed during different airborne and ground-based campaigns. The optimized FPI transmission functions are then combined with the laser reference spectrum and the temperature-dependent molecular Rayleigh backscatter spectrum to derive an accurate A2D SRRC which can finally be implemented into the wind retrieval. Using dropsonde data as a reference, a statistical analysis based on a dataset from a flight campaign in 2016 reveals a bias and a standard deviation of line-of-sight (LOS) wind speeds derived from a SRRC of only 0.05 and 2.52 m/s, respectively. Compared to the result derived from a MRRC with a bias of 0.23 m/s and a standard deviation of 2.20 m/s, the accuracy improved and the precision is considered to be at the same level. Furthermore, it is shown that the SRRC allows for the simulation of receiver responses over the whole altitude range from the aircraft down to sea level, thus overcoming limitations due to high ground elevation during the acquisition of an airborne instrument response calibration

Presentation and medical management of peripheral arterial disease in general practice: rationale, aims, design and baseline results of the PACE-PAD Study

Background: Peripheral arterial disease (PAD) is highly prevalent among individuals of higher age or those with one or more cardiovascular risk factors. Screening for PAD is recommended, since it is often linked to atherothrombotic manifestations in the coronary or carotid circulation and associated with a substantial increase in all-cause and cardiovascular mortality. We aimed to assess patients with newly diagnosed, suspected and confirmed PAD in the primary care setting with regards to clinical characteristics, diagnostic and therapeutic management (including referral to specialists), and medium-term outcomes. Methods: This was a multicentre, prospective, observational cohort study with a cross-sectional and a longitudinal part. A total of 2,781 general practitioners across Germany were cluster randomised to document five consecutive patients each in one of the strata: (1) patients with intermittent claudication (IC) or other typical PAD-related complaints (group A) or (2) patients >55 years of age with one or more risk factors (group B) for PAD (current smoking, diabetes, previous myocardial infection and/or previous stroke). Patients with confirmed PAD will be followed up for diagnostic procedures, therapy and vascular events over 18 months. Results: In group A, a total of 2,131 patients with suspected PAD (80.1% confirmed, 75.9% with referral to specialists) and in group B 9,921 patients were included (44.6% confirmed, 54.6% referral). The ankle-brachial index was calculated in 41.3% and 33.5% only. Mean age was 66.6 years (group A) and 68.4 years (group B), respectively. Vascular risk factors were prevalent in both groups, in particular smoking (group A 44.6%, group B 44.4%), hypertension (73.2 and 78.1%), hypercholesterolaemia (64.6 and 70.6%) and diabetes mellitus (41.7 and 60.6%). Concomitant atherothrombotic morbidities were frequent in both groups. In patients with the respective diseases, antihypertensive, antidiabetic, lipid-lowering and antithrombotic therapies were prescribed in group A in 96.6, 96.0, 91.1 and 89.7% and in group B in 98.3, 97.4, 94.1 and 91.2%. Conclusion: The cross-sectional part of the study indicates a substantial burden of disease in PAD patients in primary care. Treatment rates appear to have improved compared to earlier surveys. In the follow-up period, outcomes of these patients and their association with disease stages, guideline-oriented treatment or patient compliance and disease-coping strategies, among other factors, will be determined