Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

Optical properties of Saharan dust aerosol and contribution from the coarse mode as measured during the Fennec 2011 aircraft campaign

New in-situ aircraft measurements of Saharan dust originating from Mali, Mauritania and Algeria taken during the Fennec 2011 aircraft campaign over a remote part of the Sahara Desert are presented. Size distributions extending to 300 μm are shown, representing measurements extending further into the coarse mode than previously published for airborne Saharan dust. A significant coarse mode was present in the size distribution measurements with effective diameter (deff) from 2.3 to 19.4 μm and coarse mode volume median diameter (dvc) from 5.8 to 45.3 μm. The mean size distribution had a larger relative proportion of coarse mode particles than previous aircraft measurements. The largest particles (with deff >12 μm, or dvc >25 μm) were only encountered within 1 km of the ground. Number concentration, mass loading and extinction coefficient showed inverse relationships to dust age since uplift. Dust particle size showed a weak exponential relationship to dust age. Two cases of freshly uplifted dust showed quite different characteristics of size distribution and number concentration. Single Scattering Albed (SSA) values at 550 nm calculated from the measured size distributions revealed high absorption ranging from 0.70 to 0.97 depending on the refractive index. SSA was found to be strongly related to deff. New instrumentation revealed that direct measurements, behind Rosemount inlets, overestimate SSA by up to 0.11 when deff is greater than 2 μm. This is caused by aircraft inlet inefficiencies and sampling losses. Previous measurements of SSA from aircraft measurements may also have been overestimates for this reason. Radiative transfer calculations indicate that the range of SSAs during Fennec 2011 can lead to underestimates in shortwave atmospheric heating rates by 2.0 to 3.0 times if the coarse mode is neglected. This will have an impact on Saharan atmospheric dynamics and circulation,which should be taken into account by numerical weather prediction and climate models.

A study on the sensitivities of simulated aerosol optical properties to composition and size distribution using airborne measurements

We present a flexible framework to calculate the optical properties of atmospheric aerosols at a given relative humidity based on their composition and size distribution. The similarity of this framework to climate model parameterisations allows rapid and extensive sensitivity tests of the impact of uncertainties in data or of new measurements on climate relevant aerosol properties. The data collected by the FAAM BAe-146 aircraft during the EUCAARI-LONGREX and VOCALS-REx campaigns have been used in a closure study to analyse the agreement between calculated and measured aerosol optical properties for two very different aerosol types. The agreement achieved for the EUCAARI-LONGREX flights is within the measurement uncertainties for both scattering and absorption. However, there is poor agreement between the calculated and the measured scattering for the VOCALS-REx flights. The high concentration of sulphate, which is a scattering aerosol with no absorption in the visible spectrum, made the absorption measurements during VOCALS-REx unreliable, and thus no closure study was possible for the absorption. The calculated hygroscopic scattering growth factor overestimates the measured values during EUCAARI-LONGREX and VOCALS-REx by ∼30% and ∼20%, respectively. We have also tested the sensitivity of the calculated aerosol optical properties to the uncertainties in the refractive indices, the hygroscopic growth factors and the aerosol size distribution. The largest source of uncertainty in the calculated scattering is the aerosol size distribution (∼35%), followed by the assumed hygroscopic growth factor for organic aerosol (∼15%), while the predominant source of uncertainty in the calculated absorption is the refractive index of organic aerosol (28–60%), although we would expect the refractive index of black carbon to be important for aerosol with a higher black carbon fraction.

Impact of atmospheric transport on the evolution of microphysical and optical properties of Saharan dust

Saharan dust affects the climate by altering the radiation balance and by depositing minerals to the Atlantic Ocean. Both are dependent on particle size. We present aircraft measurements comprising 42 profiles of size distribution (0.1–300 µm), representing freshly uplifted dust, regional aged dust, and dust in the Saharan Air Layer (SAL) over the Canary Islands. The mean effective diameter of dust in SAL profiles is 4.5 µm smaller than that in freshly uplifted dust, while the vertical structure changes from a low shallow layer (0–1.5 km) to a well-mixed deep Saharan dust layer (0–5 km). Size distributions show a loss of 60 to 90% of particles larger than 30 µm 12 h after uplift. The single scattering albedo (SSA) increases from 0.92 to 0.94 to 0.95 between fresh, aged, and SAL profiles: this is enough to alter heating rates by 26%. Some fresh dust close to the surface shows SSA as low as 0.85

Infrared optical coatings for the EarthCARE Multispectral Imager

The Earth Cloud, Aerosol and Radiation Explorer mission (EarthCARE) Multispectral Imager (MSI) is a radiometric instrument designed to provide the imaging of the atmospheric cloud cover and the cloud top surface temperature from a sun-synchronous low Earth orbit. The MSI forms part of a suite of four instruments destined to support the European Space Agency Living Planet mission on-board the EarthCARE satellite payload to be launched in 2016, whose synergy will be used to construct three-dimensional scenes, textures and temperatures of atmospheric clouds and aerosols. The MSI instrument contains seven channels: four solar channels to measure visible and short-wave infrared wavelengths, and three channels to measure infrared thermal emission. In this paper, we describe the optical layout of the infrared instrument channels, thin-film multilayer designs, the coating deposition method and the spectral system throughput for the bandpass interference filters, dichroic beam splitters, lenses and mirror coatings to discriminate wavelengths at 8.8, 10.8, & 12.0 µm. The rationale for the selection of thin-film materials, spectral measurement technique, and environmental testing performance are also presented.

Phase calibration of the EISCAT Svalbard Radar interferometer using optical satellite signatures

The link between natural ion-line enhancements in radar spectra and auroral activity has been the subject of recent studies but conclusions have been limited by the spatial and temporal resolution previously available. The next challenge is to use shorter sub-second integration times in combination with interferometric programmes to resolve spatial structure within the main radar beam, and so relate enhanced filaments to individual auroral rays. This paper presents initial studies of a technique, using optical and spectral satellite signatures, to calibrate the received phase of a signal with the position of the scattering source along the interferometric baseline of the EISCAT Svalbard Radar. It is shown that a consistent relationship can be found only if the satellite passage through the phase fringes is adjusted from the passage predicted by optical tracking. This required adjustment is interpreted as being due to the vector between the theoretical focusing points of the two antennae, i.e. the true radar baseline, differing from the baseline obtained by survey between the antenna foot points. A method to obtain a measurement of the true interferometric baseline using multiple satellite passes is outlined.

Simultaneous optical and radar signatures of poleward-moving auroral forms

Dayside poleward moving auroral forms (PMAFs) were detected between 06:30 and 07:00 UT on December 16, 1998, by the meridian scanning photometer and the all-sky camera at Ny Alesund, Svalbard. Simultaneous SuperDARN HF radar measurements permitted the study of the associated ionospheric velocity pattern. A good general agreement is observed between the location and movement of velocity enhancements (flow channels) and the PMAFs. Clear signatures of equatorward flow were detected in the vicinity of PMAFs. This flow is believed to be the signature of a return flow outside the reconnected Aux tube, as predicted by the Southwood model. The simulated signatures of this model reproduce globally the measured signatures, and differences with the experimental data can be explained by the simplifications of the model. Proposed schemes of the flow modification due to the presence of several flow channels and the modification of cusp and region 1 field-aligned currents at the time of sporadic reconnection events are shown to fit well with the observations.

Dynamic auroral structure in the vicinity of the polar cusp - multipoint observations during southward and northward IMF

The low- and high-latitude boundary layers of the earth's magnetosphere [low-latitude boundary layer (LLBL) and mantle] play important roles in transferring momentum and energy from the solar wind to the magnetosphere-ionosphere system. Particle precipitation, field-aligned current, auroral emission, ionospheric ion drift and ground magnetic perturbations are among the low-altitude parameters that show signatures of various plasma processes in the LLBL and the magnetopause current layer. Magnetic merging events, Kelvin-Helmholtz waves, and pressure pulses excited by the variable solar wind/magnetosheath plasma are examples of boundary phenomena that may be coupled to the ionosphere via field-aligned currents. Optical auroral observation, by photometry and all-sky TV cameras, is a unique technique for investigating the spatial and temporal structure of the electron precipitation associated with such phenomena. However, the distinction between the different boundary layer plasma populations cannot in general be unambiguously determined by optics alone. Additional information, such as satellite observations of particle boundaries and field-aligned currents, is needed in order to identify the plasma source(s) and the magnetosphere-ionosphere coupling mode(s). Two categories of auroral activity/structure in the vicinity of the polar cusp are discussed in this paper, based on combined ground and satellite data. In one case, the quasi-periodic sequence of auroral events at the polar cap boundary involves accelerated electrons (< 1 keV) moving poleward (< 1 km s-1) and azimuthally along the persistent cusp/cleft arc poleward boundary with velocities (< 4 km s-1), comparable to the local ionospheric ion drift during periods of southward IMF. A critical question is whether or not the optical events signify a corresponding plasma flow across the open/closed field line boundary in such cases. Near-simultaneous observations of magnetopause flux transfer events (FTEs) and such optical/ion drift events are reported. The reverse pattern of motion of discrete auroral forms is observed during positive interplanetary magnetic field (IMF) B(Z), i.e. equatorward motion into the cusp/cleft background arc from the poleward edge. Combined satellite and ground-based information for the latter cases indicate a source mechanism, poleward of the cusp at the high-latitude magnetopause or plasma mantle, giving rise to strong momentum transfer and electron precipitation structures within a approximately 200 km-wide latitudinal zone at the cusp/cleft poleward boundary. The striking similarities of auroral electrodynamics in the cleft/mantle region during northward and southward IMF indicate that a qualitatively similar solar wind-magnetosphere coupling mode is operating. It is suggested that, in both cases, the discrete auroral forms represent temporal/spatial structure of larger-scale convection over the polar magnetosphere.

Auroral bright spot sequence near 1400 MLT: Coordinated optical and ion drift observations

Optical observations of a dayside auroral brightening sequence, by means of all-sky TV cameras and meridian scanning photometers, have been combined with EISCAT ion drift observations within the same invariant latitude-MLT sector. The observations were made during a January 1989 campaign by utilizing the high F region ion densities during the maximum phase of the solar cycle. The characteristic intermittent optical events, covering ∼300 km in east-west extent, move eastward (antisunward) along the poleward boundary of the persistent background aurora at velocities of ∼1.5 km s−1 and are associated with ion flows which swing from eastward to westward, with a subsequent return to eastward, during the interval of a few minutes when there is enhanced auroral emission within the radar field of view. The breakup of discrete auroral forms occurs at the reversal (negative potential) that forms between eastward plasma flow, maximizing near the persistent arc poleward boundary, and strong transient westward flow to the south. The reported events, covering a 35 min interval around 1400 MLT, are embedded within a longer period of similar auroral activity between 0830 (1200 MLT) and 1300 UT (1600 MLT). These observations are discussed in relation to recent models of boundary layer plasma dynamics and the associated magnetosphere-ionosphere coupling. The ionospheric events may correspond to large-scale wave like motions of the low-latitude boundary layer (LLBL)/plasma sheet (PS) boundary. On the basis of this interpretation the observed spot size, speed and repetition period (∼10 min) give a wavelength (the distance between spots) of ∼900 km in the present case. The events can also be explained as ionospheric signatures of newly opened flux tubes associated with reconnection bursts at the magnetopause near 1400 MLT. We also discuss these data in relation to random, patchy reconnection (as has recently been invoked to explain the presence of the sheathlike plasma on closed field lines in the LLBL). In view of the lack of IMF data, and the existing uncertainty on the location of the open-closed field line boundary relative to the optical events, an unambiguous discrimination between the different alternatives is not easily obtained.