arXiv subjects

Peter T. Gallagher

Publications and source records attributed to Peter T. Gallagher.

At least 37 records · Page 2Linked to original sources

arXiv2021

Quasi-Periodic Particle Acceleration in a Solar Flare

A common feature of electromagnetic emission from solar flares is the presence of intensity pulsations that vary as a function of time. Known as quasi-periodic pulsations (QPPs), these variations in flux appear to include periodic components and characteristic time-scales. Here, we analyse a GOES M3.7 class flare exhibiting pronounced QPPs across a broad band of wavelengths using imaging and time-series analysis. We identify QPPs in the timeseries of X-ray, low frequency radio and EUV wavelengths using wavelet analysis, and localise the region of the flare site from which the QPPs originate via X-ray and EUV imaging. It was found that the pulsations within the 171 Ȧ, 1600 Ȧ, soft X-ray (SXR), and hard X-ray (HXR) light curves yielded similar periods of $\sim$122 s, $\sim$131s, $\sim$123 s, and $\sim$137 s, respectively, indicating a common progenitor. The low frequency radio emission at 2.5 MHz contained a longer period of $\sim$231 s. Imaging analysis indicates that the location of the X-ray and EUV pulsations originates from a HXR footpoint linked to a system of nearby open magnetic field lines. Our results suggest that intermittent particle acceleration, likely due to 'bursty' magnetic reconnection, is responsible for the QPPs. The precipitating electrons accelerated towards the chromosphere produce the X-ray and EUV pulsations, while the escaping electrons result in low frequency radio pulses in the form of type III radio bursts. The modulation of the reconnection process, resulting in episodic particle acceleration, explains the presence of these QPPs across the entire spatial range of flaring emission.

astro-ph.SR↗

arXiv2021

LOFAR observations of a jet-driven piston shock in the low solar corona

The Sun produces highly dynamic and eruptive events that can drive shocks through the corona. These shocks can accelerate electrons, which result in plasma emission in the form of a type II radio burst. Despite the large number of type II radio bursts observations, the precise origin of coronal shocks is still subject to investigation. Here we present a well observed solar eruptive event that occurred on 16 October 2015, focusing on a jet observed in the extreme ultraviolet (EUV) by the Atmospheric Imaging Assembly (SDO/AIA), a streamer observed in white-light by the Large Angle and Spectrometric Coronagraph (SOHO/LASCO), and a metric type II radio burst observed by the LOw Frequency Array (LOFAR). LOFAR interferometrically imaged the fundamental and harmonic sources of a type II radio burst and revealed that the sources did not appear to be co-spatial, as would be expected from the plasma emission mechanism. We correct for the separation between the fundamental and harmonic using a model which accounts for scattering of radio waves by electron density fluctuations in a turbulent plasma. This allows us to show the type II radio sources were located $\sim$0.5 R$_\odot$ above the jet and propagated at a speed of $\sim$1000 kms$^{-1}$, which was significantly faster than the jet speed of $\sim$200 kms$^{-1}$. This suggests that the type II burst was generated by a piston shock driven by the jet in the low corona.

astro-ph.SR↗

arXiv2020

LOFAR observations of radio burst source sizes and scattering in the solar corona

Low frequency radio wave scattering and refraction can have a dramatic effect on the observed size and position of radio sources in the solar corona. The scattering and refraction is thought to be due to fluctuations in electron density caused by turbulence. Hence, determining the true radio source size can provide information on the turbulence in coronal plasma. However, the lack of high spatial resolution radio interferometric observations at low frequencies, such as with the LOw Frequency ARray (LOFAR), has made it difficult to determine the true radio source size and level of radio wave scattering. Here we directly fit the visibilities of a LOFAR observation of a Type IIIb radio burst with an elliptical Gaussian to determine its source size and position. This circumvents the need to image the source and then de-convolve LOFAR's point spread function, which can introduce spurious effects to the source size and shape. For a burst at 34.76 MHz, we find full width at half maximum (FWHM) heights along the major and minor axes to be $18.8^\prime$ $\pm~0.1^\prime$ and $10.2^\prime$ $\pm~0.1^\prime$, respectively, at a plane of sky heliocentric distance of 1.75 R$_\odot$. Our results suggest that the level of density fluctuations in the solar corona is the main cause of the scattering of radio waves, resulting in large source sizes. However, the magnitude of $\varepsilon$ may be smaller than what has been previously derived in observations of radio wave scattering in tied-array images.

astro-ph.SR↗

arXiv2020

Ensemble Forecasting of Major Solar Flares: Methods for Combining Models

One essential component of operational space weather forecasting is the prediction of solar flares. With a multitude of flare forecasting methods now available online it is still unclear which of these methods performs best, and none are substantially better than climatological forecasts. Space weather researchers are increasingly looking towards methods used by the terrestrial weather community to improve current forecasting techniques. Ensemble forecasting has been used in numerical weather prediction for many years as a way to combine different predictions in order to obtain a more accurate result. Here we construct ensemble forecasts for major solar flares by linearly combining the full-disk probabilistic forecasts from a group of operational forecasting methods (ASAP, ASSA, MAG4, MOSWOC, NOAA, and MCSTAT). Forecasts from each method are weighted by a factor that accounts for the method's ability to predict previous events, and several performance metrics (both probabilistic and categorical) are considered. It is found that most ensembles achieve a better skill metric (between 5\% and 15\%) than any of the members alone. Moreover, over 90\% of ensembles perform better (as measured by forecast attributes) than a simple equal-weights average. Finally, ensemble uncertainties are highly dependent on the internal metric being optimized and they are estimated to be less than 20\% for probabilities greater than 0.2. This simple multi-model, linear ensemble technique can provide operational space weather centres with the basis for constructing a versatile ensemble forecasting system -- an improved starting point to their forecasts that can be tailored to different end-user needs.

physics.space-ph↗

arXiv2020

Statistical Study of GOES X-ray Quasi-Periodic Pulsations in Solar Flares

Small amplitude quasi-periodic pulsations (QPPs) detected in soft X-ray emission are commonplace in many flares. To date, the underpinning processes resulting in the QPPs are unknown. In this paper, we attempt to constrain the prevalence of \textit{stationary} QPPs in the largest statistical study to date, including a study of the relationship of QPP periods to the properties of the flaring active region, flare ribbons, and CME affiliation. We build upon the work of \cite{inglis2016} and use a model comparison test to search for significant power in the Fourier spectra of lightcurves of the GOES 1--8~Å channel. We analyze all X-, M- and C- class flares of the past solar cycle, a total of 5519 flares, and search for periodicity in the 6-300~s timescale range. Approximately 46\% of X-class, 29\% of M-class and 7\% of C-class flares show evidence of stationary QPPs, with periods that follow a log-normal distribution peaked at 20~s. The QPP periods were found to be independent of flare magnitude, however a positive correlation was found between QPP period and flare duration. No dependence of the QPP periods to the global active region properties was identified. A positive correlation was found between QPPs and ribbon properties including unsigned magnetic flux, ribbon area and ribbon separation distance. We found that both flares with and without an associated CME can host QPPs. Furthermore, we demonstrate that for X- and M- class flares, decay phase QPPs have statistically longer periods than impulsive phase QPPs.

astro-ph.SR↗

arXiv2020

A new facility for airborne solar astronomy: NASA's WB-57 at the 2017 total solar eclipse

NASA's WB-57 High Altitude Research Program provides a deployable, mobile, stratospheric platform for scientific research. Airborne platforms are of particular value for making coronal observations during total solar eclipses because of their ability both to follow the Moon's shadow and to get above most of the atmospheric airmass that can interfere with astronomical observations. We used the 2017 Aug 21 eclipse as a pathfinding mission for high-altitude airborne solar astronomy, using the existing high-speed visible-light and near-/mid-wave infrared imaging suite mounted in the WB-57 nose cone. In this paper, we describe the aircraft, the instrument, and the 2017 mission; operations and data acquisition; and preliminary analysis of data quality from the existing instrument suite. We describe benefits and technical limitations of this platform for solar and other astronomical observations. We present a preliminary analysis of the visible-light data quality and discuss the limiting factors that must be overcome with future instrumentation. We conclude with a discussion of lessons learned from this pathfinding mission and prospects for future research at upcoming eclipses, as well as an evaluation of the capabilities of the WB-57 platform for future solar astronomy and general astronomical observation.

astro-ph.IM↗

arXiv2020

A Comparison of Flare Forecasting Methods. IV. Evaluating Consecutive-Day Forecasting Patterns

A crucial challenge to successful flare prediction is forecasting periods that transition between "flare-quiet" and "flare-active". Building on earlier studies in this series (Barnes et al. 2016; Leka et al. 2019a,b) in which we describe methodology, details, and results of flare forecasting comparison efforts, we focus here on patterns of forecast outcomes (success and failure) over multi-day periods. A novel analysis is developed to evaluate forecasting success in the context of catching the first event of flare-active periods, and conversely, of correctly predicting declining flare activity. We demonstrate these evaluation methods graphically and quantitatively as they provide both quick comparative evaluations and options for detailed analysis. For the testing interval 2016-2017, we determine the relative frequency distribution of two-day dichotomous forecast outcomes for three different event histories (i.e., event/event, no-event/event and event/no-event), and use it to highlight performance differences between forecasting methods. A trend is identified across all forecasting methods that a high/low forecast probability on day-1 remains high/low on day-2 even though flaring activity is transitioning. For M-class and larger flares, we find that explicitly including persistence or prior flare history in computing forecasts helps to improve overall forecast performance. It is also found that using magnetic/modern data leads to improvement in catching the first-event/first-no-event transitions. Finally, 15% of major (i.e., M-class or above) flare days over the testing interval were effectively missed due to a lack of observations from instruments away from the Earth-Sun line.

astro-ph.SR↗

arXiv2019

Evolution of the Alfvén Mach number associated with a coronal mass ejection shock

The Sun regularly produces large-scale eruptive events, such as coronal mass ejections (CMEs) that can drive shock waves through the solar corona. Such shocks can result in electron acceleration and subsequent radio emission in the form of a type II radio burst. However, the early-phase evolution of shock properties and its relationship to type II burst evolution is still subject to investigation. Here we study the evolution of a CME-driven shock by comparing three commonly used methods of calculating the Alfvén Mach number ($M_A$), namely: shock geometry, a comparison of CME speed to a model of the coronal Alfvén speed, and the type II band-splitting method. We applied the three methods to the 2017 September 2 event, focusing on the shock wave observed in extreme ultraviolet (EUV) by the Solar Ultraviolet Imager (SUVI) on board GOES-16, in white-light by the Large Angle and Spectrometric Coronagraph (LASCO) on board SOHO, and the type II radio burst observed by the Irish Low Frequency Array (I-LOFAR). We show that the three different methods of estimating shock $M_A$ yield consistent results and provide a means of relating shock property evolution to the type II emission duration. The type II radio emission emerged from near the nose of the CME when $M_A$ was in the range 1.4-2.4 at a heliocentric distance of $\sim$1.6 $R_\odot$. The emission ceased when the CME nose reached $\sim$2.4 $R_\odot$, despite an increasing Alfvén Mach number (up to 4). We suggest the radio emission cessation is due to the lack of quasi-perpendicular geometry at this altitude, which inhibits efficient electron acceleration and subsequent radio emission.

astro-ph.SR↗

arXiv2019

Multiple Regions of Shock-accelerated Particles during a Solar Coronal Mass Ejection

The Sun is an active star that can launch large eruptions of magnetised plasma into the heliosphere, called coronal mass ejections (CMEs). These ejections can drive shocks that accelerate particles to high energies, often resulting in radio emission at low frequencies (<200 MHz). To date, the relationship between the expansion of CMEs, shocks and particle acceleration is not well understood, partly due to the lack of radio imaging at low frequencies during the onset of shock-producing CMEs. Here, we report multi-instrument radio, white-light and ultraviolet imaging of the second largest flare in Solar Cycle 24 (2008-present) and its associated fast CME (3038+/-288 km/s). We identify the location of a multitude of radio shock signatures, called herringbones, and find evidence for shock accelerated electron beams at multiple locations along the expanding CME. These observations support theories of non-uniform, rippled shock fronts driven by an expanding CME in the solar corona.

astro-ph.SR↗

arXiv2019

A Comparison of Flare Forecasting Methods. III. Systematic Behaviors of Operational Solar Flare Forecasting Systems

A workshop was recently held at Nagoya University (31 October - 02 November 2017), sponsored by the Center for International Collaborative Research, at the Institute for Space-Earth Environmental Research, Nagoya University, Japan, to quantitatively compare the performance of today's operational solar flare forecasting facilities. Building upon Paper I of this series (Barnes et al. 2016), in Paper II (Leka et al. 2019) we described the participating methods for this latest comparison effort, the evaluation methodology, and presented quantitative comparisons. In this paper we focus on the behavior and performance of the methods when evaluated in the context of broad implementation differences. Acknowledging the short testing interval available and the small number of methods available, we do find that forecast performance: 1) appears to improve by including persistence or prior flare activity, region evolution, and a human "forecaster in the loop"; 2) is hurt by restricting data to disk-center observations; 3) may benefit from long-term statistics, but mostly when then combined with modern data sources and statistical approaches. These trends are arguably weak and must be viewed with numerous caveats, as discussed both here and in Paper II. Following this present work, we present in Paper IV a novel analysis method to evaluate temporal patterns of forecasting errors of both types (i.e., misses and false alarms; Park et al. 2019). Hence, most importantly, with this series of papers we demonstrate the techniques for facilitating comparisons in the interest of establishing performance-positive methodologies.

astro-ph.SR↗

arXiv2019

A Comparison of Flare Forecasting Methods. II. Benchmarks, Metrics and Performance Results for Operational Solar Flare Forecasting Systems

Solar flares are extremely energetic phenomena in our Solar System. Their impulsive, often drastic radiative increases, in particular at short wavelengths, bring immediate impacts that motivate solar physics and space weather research to understand solar flares to the point of being able to forecast them. As data and algorithms improve dramatically, questions must be asked concerning how well the forecasting performs; crucially, we must ask how to rigorously measure performance in order to critically gauge any improvements. Building upon earlier-developed methodology (Barnes et al, 2016, Paper I), international representatives of regional warning centers and research facilities assembled in 2017 at the Institute for Space-Earth Environmental Research, Nagoya University, Japan to - for the first time - directly compare the performance of operational solar flare forecasting methods. Multiple quantitative evaluation metrics are employed, with focus and discussion on evaluation methodologies given the restrictions of operational forecasting. Numerous methods performed consistently above the "no skill" level, although which method scored top marks is decisively a function of flare event definition and the metric used; there was no single winner. Following in this paper series we ask why the performances differ by examining implementation details (Leka et al. 2019, Paper III), and then we present a novel analysis method to evaluate temporal patterns of forecasting errors in (Park et al. 2019, Paper IV). With these works, this team presents a well-defined and robust methodology for evaluating solar flare forecasting methods in both research and operational frameworks, and today's performance benchmarks against which improvements and new methods may be compared.

astro-ph.SR↗

arXiv2019

Properties and magnetic origins of solar S-bursts

Context. Solar activity is often accompanied by solar radio emission, consisting of numerous types of solar radio bursts. At low frequencies (<100 MHz) radio bursts with short durations of milliseconds, such as solar S-bursts, have been identified. To date, their origin and many of their characteristics remain unclear. Aims. We report observations from the Ukrainian T-shaped Radio telescope, (UTR-2), and the LOw Frequency ARray (LOFAR) which give us new insight into their nature. Methods. Over 3000 S-bursts were observed on 9 July 2013 at frequencies of 17.4-83.1 MHz during a period of low solar activity. Leading models of S-burst generation were tested by analysing the spectral properties of S-bursts and estimating coronal magnetic field strengths. Results. S-bursts were found to have short durations of 0.5-0.9 s. Multiple instruments were used to measure the dependence of drift rate on frequency which is represented by a power law with an index of 1.57. For the first time, we show a linear relation between instantaneous bandwidth and frequency over a wide frequency band. The flux calibration and high sensitivity of UTR-2 enabled measurements of their fluxes, which yielded 11+3 SFU. The source particle velocities of S-bursts were found to be ~0.07 c. S-burst source heights were found to range from 1.3 R_Sun to 2 R_Sun. Furthermore, a contemporary theoretical model of S-burst generation was used to conduct remote sensing of the coronal magnetic field at these heights which yielded values of 0.9-5.8 G. Within error, these values are comparable to those predicted by various relations between magnetic field strength and height in the corona.

astro-ph.SR↗

arXiv2019

Persistent Quasi-Periodic Pulsations During a Large X-Class Solar Flare

Solar flares often display pulsating and oscillatory signatures in the emission, known as quasi-periodic pulsations (QPP). QPP are typically identified during the impulsive phase of flares, yet in some cases, their presence is detected late into the decay phase. Here, we report extensive fine structure QPP that are detected throughout the large X8.2 flare from 2017 September 10. Following the analysis of the thermal pulsations observed in the GOES/XRS and the 131 A channel of SDO/AIA, we find a pulsation period of ~65 s during the impulsive phase followed by lower amplitude QPP with a period of ~150 s in the decay phase, up to three hours after the peak of the flare. We find that during the time of the impulsive QPP, the soft X-ray source observed with RHESSI rapidly rises at a velocity of approximately 17 km/s following the plasmoid/coronal mass ejection (CME) eruption. We interpret these QPP in terms of a manifestation of the reconnection dynamics in the eruptive event. During the long-duration decay phase lasting several hours, extended downward contractions of collapsing loops/plasmoids that reach the top of the flare arcade are observed in EUV. We note that the existence of persistent QPP into the decay phase of this flare are most likely related to these features. The QPP during this phase are discussed in terms of MHD wave modes triggered in the post-flaring loops.

astro-ph.SR↗

arXiv2018

Expansion of High Speed Solar Wind Streams from Coronal Holes through the Inner Heliosphere

Coronal holes (CHs) are regions of open magnetic flux which are the source of high speed solar wind (HSSW) streams. To date, it is not clear which aspects of CHs are of most influence on the properties of the solar wind as it expands through the Heliosphere. Here, we study the relationship between CH properties extracted from AIA (Atmospheric Imaging Assembly) images using CHIMERA (Coronal Hole Identification via Multi-thermal Emission Recognition Algorithm) and HSSW measurements from ACE (Advanced Composition Explorer) at L1. For CH longitudinal widths $Δθ_{CH}<$67$^{\circ}$, the peak SW velocity ($v_{max}$) is found to scale as $v_{max}~\approx~330.8~+~5.7~Δθ_{CH}$~km~s$^{-1}$. For larger longitudinal widths ($Δθ_{CH}>$67$^{\circ}$), $v_{max}$ is found to tend to a constant value ($\sim$710~km~s$^{-1}$). Furthermore, we find that the duration of HSSW streams ($Δt$) are directly related to the longitudinal width of CHs ($Δt_{SW}$~$\approx$~0.09$Δθ_{CH}$) and that their longitudinal expansion factor is $f_{SW}~\approx 1.2~\pm 0.1$. We also derive an expression for the coronal hole flux-tube expansion factor, $f_{FT}$, which varies as $f_{SW} \gtrsim f_{FT} \gtrsim 0.8$. These results enable us to estimate the peak speeds and durations of HSSW streams at L1 using the properties of CHs identified in the solar corona.

astro-ph.SR↗

arXiv2018

A Detailed Model of the Irish High Voltage Power Network for Simulating GICs

Constructing a power network model for geomagnetically induced current (GIC) calculations requires information on the DC resistances of elements within a network. This information is often not known, and power network models are simplified as a result, with assumptions used for network element resistances. Ireland's relatively small, isolated network presents an opportunity to model a complete power network in detail, using as much real-world information as possible. A complete model of the Irish 400, 275, 220 and 110 kV network was made for GIC calculations, with detailed information on the number, type and DC resistances of transformers. The measured grounding resistances at a number of substations were also included in the model, which represents a considerable improvement on previous models of the Irish power network for GIC calculations. Sensitivity tests were performed to show how calculated GIC amplitudes are affected by different aspects of the model. These tests investigated: (1) How the orientation of a uniform electric field affects GICs. (2) The effect of including/omitting lower-voltage elements of the power network. (3) How the substation grounding resistances assumptions affected GIC values. It was found that changing the grounding resistance value had a considerable effect on calculated GICs at some substations, and no discernible effect at others. Finally, five recent geomagnetic storm events were simulated in the network. It was found that heavy rainfall prior to the 26-28 August 2015 geomagnetic storm event may have had a measurable impact on measured GIC amplitudes at a 400/220 kV transformer ground.

physics.space-ph↗

arXiv2018

Photospheric Shear Flows in Solar Active Regions and Their Relation to Flare Occurrence

Solar active regions (ARs) that produce major flares typically exhibit strong plasma shear flows around photospheric magnetic polarity inversion lines (MPILs). It is therefore important to quantitatively measure such photospheric shear flows in ARs for a better understanding of their relation to flare occurrence. Photospheric flow fields were determined by applying the Differential Affine Velocity Estimator for Vector Magnetograms (DAVE4VM) method to a large data set of 2,548 co-aligned pairs of AR vector magnetograms with 12-min separation over the period 2012-2016. From each AR flow-field map, three shear-flow parameters were derived corresponding to the mean ( ), maximum (S_max) and integral (S_sum) shear-flow speeds along strong-gradient, strong-field MPIL segments. We calculated flaring rates within 24 hr as a function of each shear-flow parameter, and also investigated the relation between the parameters and the waiting time (τ) until the next major flare (class M1.0 or above) after the parameter observation. In general, it is found that the larger S_sum an AR has, the more likely it is for the AR to produce flares within 24 hr. It is also found that among ARs which produce major flares, if one has a larger value of S_sum then τ generally gets shorter. These results suggest that large ARs with widespread and/or strong shear flows along MPILs tend to not only be more flare productive, but also produce major flares within 24 hr or less.

astro-ph.SR↗

arXiv2018

Three-dimensional magnetic reconnection in a collapsing coronal loop system

Magnetic reconnection is believed to be the primary mechanism by which non-potential energy stored in coronal magnetic fields is rapidly released during solar eruptive events. Unfortunately, owing to the small spatial scales on which reconnection is thought to occur, it is not directly observable in the solar corona. However, larger scale processes, such as associated inflow and outflow, and signatures of accelerated particles have been put forward as evidence of reconnection. We explore the origin of a persistent Type I radio source that accompanies a coronal X--shaped structure during its passage across the disk. Of particular interest is the time range around a partial collapse of the structure that is associated with inflow, outflow, and signatures of particle acceleration. Imaging radio observations from the NRH were used to localise the radio source. SDO AIA EUV observations from the same time period were analysed, looking for evidence of inflows and outflows. Further \texttt{mpole} magnetic reconstructions using SDO HMI observations allowed the magnetic connectivity associated with the radio source to be determined. The Type I radio source was well aligned with a magnetic separator identified in the extrapolations. During the partial collapse, gradual (1 km/s) and fast (5 km/s) inflow phases and fast (30 km/s) and rapid (80-100 km/s) outflow phases were observed, resulting in an estimated reconnection rate of ~ 0.06. The radio source brightening and dimming was found to be co-temporal with increased soft x-ray emission in both RHESSI and GOES. We interpret the brightening and dimming of the radio emission as evidence for accelerated electrons in the reconnection region responding to a gradual fall and rapid rise in electric drift velocity, in response to the inflowing and outflowing field lines. These results present a comprehensive example of 3D null-point reconnection.

astro-ph.SR↗

arXiv2018

Flare Forecasting Using the Evolution of McIntosh Sunspot Classifications

Most solar flares originate in sunspot groups, where magnetic field changes lead to energy build-up and release. However, few flare-forecasting methods use information of sunspot-group evolution, instead focusing on static point-in-time observations. Here, a new forecast method is presented based upon the 24-hr evolution in McIntosh classification of sunspot groups. Evolution-dependent $\geqslant$C1.0 and $\geqslant$M1.0 flaring rates are found from NOAA-numbered sunspot groups over December 1988 to June 1996 (Solar Cycle 22; SC22) before converting to probabilities assuming Poisson statistics. These flaring probabilities are used to generate operational forecasts for sunspot groups over July 1996 to December 2008 (SC23), with performance studied by verification metrics. Major findings are: i) considering Brier skill score (BSS) for $\geqslant$C1.0 flares, the evolution-dependent McIntosh-Poisson method ($\text{BSS}_{\text{evolution}}=0.09$) performs better than the static McIntosh-Poisson method ($\text{BSS}_{\text{static}} = -0.09$); ii) low BSS values arise partly from both methods over-forecasting SC23 flares from the SC22 rates, symptomatic of $\geqslant$C1.0 rates in SC23 being on average $\approx$80% of those in SC22 (with $\geqslant$M1.0 being $\approx$50%); iii) applying a bias-correction factor to reduce the SC22 rates used in forecasting SC23 flares yields modest improvement in skill relative to climatology for both methods ($\mathrm{BSS}^{\mathrm{corr}}_{\mathrm{static}} = 0.09$ and $\mathrm{BSS}^{\mathrm{corr}}_{\mathrm{evolution}} = 0.20$) and improved forecast reliability diagrams.

astro-ph.SR↗