NP Campfires: Mathematics of Planet Earth (NP1) and Scales, Scaling, and Nonlinear Variability (NP3)

Get ready for the last NP Campfires event! We explore two topics: Mathematics of Planet Earth (NP1) led by Dr. Tommaso Alberti, and Scales, Scaling, and Nonlinear Variability (NP3) led by Prof. Ioulia Tchiguirinskaia. Join us on 23rd of November at 2 pm CET (NP1) and at 3 pm CET (NP3) through Zoom.

MATHEMATICS OF PLANET EARTH

- Prof. Valerio Lucarini – University of Reading

Persistent Extreme Events – A Large Deviation Theory-based approach

- Dr. Meriem Krouma – Laboratoire des Sciences du Climat et de l’Environnement, France

Improving subseasonal forecast of precipitation in Europe by combining a stochastic weather generator with dynamical models

We propose a forecasting tool for precipitation based on analogs of circulation defined from 5-day hindcasts and a stochastic weather generator that we call “HC-SWG”. In this study, we aim to improve the forecast of European precipitation for subseasonal lead times (from 2 to 4 weeks) using the HC-SWG. We designed the HC-SWG to generate an ensemble precipitation forecast from the ECMWF and CNRM S2S ensemble reforecasts. We define analogs from 5-day ensemble reforecast of Z500 from the ECMWF (11 members) and CNRM (10 members) models. Then, we generate a 100-member ensemble for precipitation over Europe. We evaluate the skill of the ensemble forecast using probabilistic skill scores such as the continuous probabilistic skill score (CRPSS) and ROC curve.

We obtain reasonable forecast skill scores within 35 days for different locations in Europe. The CRPSS shows positive improvement with respect to climatology and persistence at the station level. The HC-SWG shows a capacity to distinguish between events and non-events of precipitation within 15 days at the different stations. We compare the HC-SWG forecast with other precipitation forecasts to further confirm the benefits of our method. We found that the HC-SWG shows improvement against the ECMWF precipitation forecast until 25 days.

SCALES, SCALING, AND NONLINEAR VARIABILITY

– Prof. Daniel schertzer

Variability across geophysical scales: cascades, multiplicative chaos and multifractals

- Prof. Shaun Lovejoy

Scaling, dynamical regimes and stratification: How long does weather last? How big is a cloud?

Abstract. Until the 1980’s, scaling notions were restricted to self-similar homogeneous special cases. I review developments over the last decades, especially in multifractals and Generalized Scale Invariance (GSI). The former is necessary for characterizing and modelling strongly intermittent scaling processes while the GSI formalism extends scaling to strongly anisotropic (especially stratified) systems. Both of these generalizations are necessary for atmospheric applications. The theory and (some) of the now burgeoning empirical evidence in its favour is reviewed.

Scaling can now be understood as a very general symmetry principle. It is needed to clarify and quantify the notion of dynamical regimes. In addition to the weather and climate, there is an intermediate “macroweather regime” and at time scales beyond the climate regime, (up to Milankovitch scales) there is a macroclimate and megaclimate regime. By objectively distinguishing weather from macroweather it answers the question “how long does weather last?”. Dealing with anisotropic scaling systems – notably atmospheric stratification – requires new (non-Euclidean) definitions of the notion of scale itself. These are needed to answer the question “how big is a cloud?”. In anisotropic scaling systems morphologies of structures change systematically with scale even though there is no characteristic size. GSI shows that it is unwarranted to infer dynamical processes or mechanisms from morphology.

Two “sticking points” preventing the more widespread acceptance of the scaling paradigm are also discussed. The first is an often implicit phenomenological “scalebounded” thinking that postulates a priori the existence of new mechanisms, processes every factor of two or so in scale. The second obstacle is the reluctance to abandon isotropic theories of turbulence and accept that the atmosphere’s scaling is anisotropic. Indeed there is currently appears to be no empirical evidence that the turbulence in any atmospheric field is isotropic.

Most atmospheric scientists rely on General Circulation Models, and these are scaling – they inherited the symmetry from the (scaling) primitive equations upon which they are built. Therefore, the real consequence of ignoring wide range scaling is that it blinds us to alternative scaling approaches to macroweather and climate – especially to new models for long range forecasts and to new scaling approaches to climate projections. Such stochastic alternatives are increasingly needed notably to reduce uncertainties in climate projections to the year 2100.

- Dr. Auguste Gires – Hydrologie Météorologie et Complexité (HM&Co), Ecole des Ponts ParisTech, Champs-sur-Marne, France

Downscaling and reconstructing the missing half of geophysical fields with blunt extension of discrete Universal Multifractal cascades

Scale issues are ubiquitous in geosciences and particularly in atmospheric sciences, notably for rainfall. This has been often illustrated with the help of discrete multiplicative cascades, whose tree structure is rather intuitive and pedagogic, but has problematic consequences in particular with respect to translation invariance. In spite of these drastic limitations, discrete cascades have also been used for engineering applications. Fortunately, continuous in scale cascades had enabled to straightforwardly overcome these difficulties and link them to pushback transforms of fields and pull forward transforms of measures, i.e. their transforms under change of space-time scale that could be not only continuous, but also infinitesimal. This is essential for generating fractional differential equations.

In this talk, we discuss a recently introduced approach that is based on the parsimonious framework of Universal Multifractals (UM) and enables to tackle the scale invariance issue while preserving the simple structure of discrete cascades. It basically consists in smoothing at each cascade step the random multiplicative increments with the help of a geometric interpolation over a moving window whose size is tailored to the resolution to preserve scale invariance. Theoretically expected multifractal behaviour is theoretically derived and numerically confirmed in 1D, 2D and 2D + time.

Finally, straightforward applications of this framework to two very common issues in geosciences are discussed through illustrations with rainfall fields. The first one is downscaling to generate ensemble of realistic realizations of rainfall fields at resolutions higher than observed or simulated. The second one is to reconstruct the missing half of a field. Considering applications in 2D+time, it is a needed step towards nowcasting of rainfall fields.

If you have any questions about ‘NP Campfires: Mathematics of Planet Earth (NP1) and Scales, Scaling, and Nonlinear Variability (NP3)’, please contact us via webinars@egu.eu.