Martinez-Villalobos C, Newman M, Vimont DJ, Penland C, Neelin JD. Observed El Niño–La Niña Asymmetry in a Linear Model. Geophysical Research Letters [Internet]. 2019;46 (16) :9909-9919. Publisher's VersionAbstract
Previous studies indicate an asymmetry in the amplitude and persistence of El Niño (EN) and La Niña (LN) events. We show that the observed EN–LN asymmetry can be captured with a linear model driven by “correlated additive and multiplicative (CAM) noise”, without resorting to a deterministic nonlinear model. The model is derived from 1-month lag statistics taken from monthly sea surface temperature (SST) datasets spanning the 20th century, in an extension of an empirical-dynamical technique called Linear Inverse Modeling. Our results suggest that noise amplitudes tend to be stronger for EN compared to LN events, which is sufficient to generate asymmetry in amplitude and also produces more persistent LN events on average. These results establish a null hypothesis for EN–LN asymmetry and suggest that strong EN events may not be more predictable that what can be accounted for by a multivariate linear system driven by CAM noise.
Martinez-Villalobos C, Neelin JD. Why Do Precipitation Intensities Tend to Follow Gamma Distributions?. Journal of the Atmospheric Sciences [Internet]. 2019;76 :3611-3631. Publisher's VersionAbstract
The probability distribution of daily precipitation intensities, especially the probability of extremes, impacts a wide range of applications. In most regions this distribution decays slowly with size at first, approximately as a power law with exponent between 0 and −1, and then more sharply, for values larger than a characteristic cutoff scale. This cutoff is important because it limits the probability of extreme daily precipitation occurrences in current climate. There is a long history of representing daily precipitation using a Gamma distribution—here we present theory for how daily precipitation distributions get their shape. Processes shaping daily precipitation distributions can be separated into non-precipitating and precipitating regime effects, the former partially controlling how many times in a day it rains, and the latter set by single-storm accumulations. Using previously developed theory for precipitation accumulation distributions—which follow a sharper power law range (exponent < −1) with a physically derived cutoff for large sizes—analytical expressions for daily precipitation distribution power law exponent and cutoff are calculated as a function of key physical parameters. Precipitating and non-precipitating regime processes both contribute to reducing the power-law range exponent for the daily precipitation distribution relative to the fundamental exponent set by accumulations. The daily precipitation distribution cutoff is set by the precipitating regime and scales with moisture availability, with important consequences for future distribution shifts under global warming. Similar results extend to different averaging periods, providing insight into how the precipitation intensity distribution evolves as a function of both underlying physical climate conditions and averaging time.
Martinez-Villalobos C, Neelin JD. Shifts in Precipitation Accumulation Extremes during the Warm Season over the United States. Geophysical Research Letters [Internet]. 2018;45 :8586–8595. Publisher's VersionAbstract
Precipitation accumulations, integrated over precipitation events in hourly data, are examined from 1979 to 2013 over the contiguous United States during the warm season (May–October). As expected from theory, accumulation distributions have a characteristic shape, with an approximate power law decrease with event size followed by an exponential drop at a characteristic cutoff scale sL for each location. This cutoff is a predictor of the highest accumulation percentiles and of a similarly defined daily precipitation cutoff PL. Comparing 1997–2013 and 1979–1995 periods, there are significant regional increases in sL in several regions. This yields distribution changes that are weighted disproportionately toward extreme accumulations. In the Northeast, for example, risk ratio (conditioned on occurrence) for accumulations larger than 109 mm increases by a factor of 2–4 (5th–95th). These changes in risk ratio as a function of size, and connection to underlying theory, have counterparts in the observed daily precipitation trends.
Thomas EE, Vimont DJ, Newman M, Penland C, Martinez-Villalobos C. The Role of Stochastic Forcing in Generating ENSO Diversity. Journal of Climate [Internet]. 2018;31 :9125-9150. Publisher's VersionAbstract

Numerous oceanic and atmospheric phenomena influence El Niño–Southern Oscillation (ENSO) variability, complicating both prediction and analysis of the mechanisms responsible for generating ENSO diversity. Predictability of ENSO events depends on the characteristics of both the forecast initial conditions and the stochastic forcing that occurs subsequent to forecast initialization. Within a linear inverse model framework, stochastic forcing reduces ENSO predictability when it excites unpredictable growth or interference after the forecast is initialized, but also enhances ENSO predictability when it excites optimal initial conditions that maximize deterministic ENSO growth. Linear inverse modeling (LIM) allows for straightforward separation between predictable signal and unpredictable noise and so can diagnose its own skill. While previous LIM studies of ENSO focused on deterministic dynamics, here we explore how noise forcing influences ENSO diversity and predictability. This study identifies stochastic forcing details potentially contributing to the development of central Pacific (CP) or eastern Pacific (EP) ENSO characteristics. The technique is then used to diagnose the relative roles of initial conditions and noise forcing throughout the evolution of several ENSO events. LIM results show varying roles of noise forcing for any given event, highlighting its utility in separating deterministic from noise-forced contributions to the evolution of individual ENSO events. For example, the strong 1982 event was considerably more influenced by noise forcing late in its evolution than the strong 1997 event, which was more predictable with long lead times due to its deterministic growth. Furthermore, the 2014 deterministic trajectory suggests that a strong event in 2014 was unlikely.

Martinez-Villalobos C, Vimont DJ, Penland C, Newman M, Neelin JD. Calculating State Dependent Noise in a Linear Inverse Model Framework. Journal of the Atmospheric Sciences [Internet]. 2018;75 (2) :479-496. Publisher's VersionAbstract

The most commonly used version of a linear inverse model (LIM) is forced by state-independent noise. Although having several desirable qualities, this formulation can only generate long-term Gaussian statistics. LIM-like systems forced by correlated additive–multiplicative (CAM) noise have been shown to generate deviations from Gaussianity, but parameter estimation methods are only known in the univariate case, limiting their use for the study of coupled variability. This paper presents a methodology to calculate the parameters of the simplest multivariate LIM extension that can generate long-term deviations from Gaussianity. This model (CAM-LIM) consists of a linear deterministic part forced by a diagonal CAM noise formulation, plus an independent additive noise term. This allows for the possibility of representing asymmetric distributions with heavier- or lighter-than-Gaussian tails. The usefulness of this methodology is illustrated in a locally coupled two-variable ocean–atmosphere model of midlatitude variability. Here, a CAM-LIM is calculated from ocean weather station data. Although the time-resolved dynamics is very close to linear at a time scale of a couple of days, significant deviations from Gaussianity are found. In particular, individual probability density functions are skewed with both heavy and light tails. It is shown that these deviations from Gaussianity are well accounted for by the CAM-LIM formulation, without invoking nonlinearity in the time-resolved operator. Estimation methods using knowledge of the CAM-LIM statistical constraints provide robust estimation of the parameters with data lengths typical of geophysical time series, for example, 31 winters for the ocean weather station here.

Martinez-Villalobos C, Vimont DJ. An analytical framework for understanding tropical Meridional Modes. Journal of Climate [Internet]. 2017;30 (9) :3303-3323. Publisher's VersionAbstract

A theoretical framework is developed for understanding the transient growth and propagation characteristics of thermodynamically coupled, meridional mode–like structures in the tropics. The model consists of a Gill–Matsuno-type steady atmosphere under the long-wave approximation coupled via a wind–evaporation–sea surface temperature (WES) feedback to a “slab” ocean model. When projected onto meridional basis functions for the atmosphere the system simplifies to a nonnormal set of equations that describes the evolution of individual sea surface temperature (SST) modes, with clean separation between equatorially symmetric and antisymmetric modes. The following major findings result from analysis of the system: 1) a transient growth process exists whereby specific SST modes propagate toward lower-order modes at the expense of the higher-order modes; 2) the same dynamical mechanisms govern the evolution of symmetric and antisymmetric SST modes except for the lowest-order wavenumber, where for symmetric structures the atmospheric Kelvin wave plays a critically different role in enhancing decay; and 3) the WES feedback is positive for all modes (with a maximum for the most equatorially confined antisymmetric structure) except for the most equatorially confined symmetric mode where the Kelvin wave generates a negative WES feedback. Taken together, these findings explain why equatorially antisymmetric “dipole”-like structures may dominate thermodynamically coupled ocean–atmosphere variability in the tropics. The role of nonnormality and the role of realistic mean states in meridional mode variability are discussed.

Martinez-Villalobos C. Deterministic and stochastic models of tropical climate variability. University of Wisconsin - Madison [Internet]. 2016. Publisher's VersionAbstract

The first part of this thesis studies the low-frequency ocean-atmosphere coupling relevant to describe tropical meridional modes using an analytical framework and simple sensitivity experiments. We consider a simple Gill-Matsuno atmospheric model coupled to a thermo- dynamic slab ocean model to describe the wind-evaporation-sea surface temperature (WES) feedback. We develop an analytical understanding of the coupled processes responsible for the growth and propagation of meridional mode-like structures by projecting the ocean and steady-state atmosphere equations onto parabolic cylinder functions. By doing this the cou- pling simplifies to the non-normal interaction of dierent sea surface temperature (SST) modes mediated by atmospheric Kelvin and Rossby waves. Under a homogeneous coupling the system simplifies to independent, coupled equatorially symmetric and antisymmetric (meridional mode-like) modes, with the following major findings: the non-normal interaction is responsible for a propagation from high latitudes to low latitudes, and this process works similarly for equatorially symmetric and antisymmetric coupled structures. That similarity breaks near the equator where the antisymmetric structure grows through a positive feedback mediated by the first antisymmetric Rossby wave, while the symmetric structure is subjected to a negative WES feedback arising from the atmospheric Kelvin wave interaction. Taken all together this explains why the WES feedback preferentially sustains meridional mode-like structures.

The second part of this thesis deals with the stochastic parameterization of tropical climate variability. Although usually seen as arising from slow non-linear interactions, devi- ations from Gaussianity in the Tropical Pacific may originate through fast variability that may be parameterized as multiplicative noise. We develop and apply a stochastic parameter- ization that accounts for the Tropical Pacific SSTs deviations from Gaussianity. This model, termed CAM-LIM retains the successful elements of the regular Linear Inverse Model (LIM) but it improves in the representation of the higher order statistical moments. The CAM-LIM is used to correctly model the marginal and conditional probability density functions of the different SST principal components. It is found that the model is successful at describing the observed deviations from Gaussianity such as: it rightfully describes the ratio between positive and negative Niño events, and the frequency of extreme Niño events as well. 

Martinez-Villalobos C, Vimont DJ. The Role of the Mean State in Meridional Mode Structure and Growth. Journal of Climate [Internet]. 2016;29 (10) :3907-3921. Publisher's VersionAbstract

This study uses a simple linear coupled model to investigate the role of the WES feedback and ITCZ mean states in meridional mode variability. Optimal structures that maximize transient growth are calculated for mean states characteristic of boreal spring and boreal fall in the tropical Atlantic. During boreal spring the leading optimal structure is a zonal mode that propagates westward and does not resemble the observed meridional mode. In contrast, the leading optimal structure during fall is a sea surface temperature (SST) monopole over the Northern Hemisphere (NH) that propagates equatorward and westward and that closely matches meridional mode variability during this season. It is found that the boreal fall optimal growth greatly exceeds growth of the corresponding optimal during boreal spring, despite the observed boreal spring peak in Atlantic meridional mode variance.

Sensitivity studies are used to explore the role of Northern or Southern Hemisphere initial conditions, ITCZ width, and ITCZ location in meridional mode growth and structure. It is found that growth is favored (i) for optimal structures that originate in the Northern Hemisphere, especially for boreal fall mean states; (ii) for symmetric mean states, equatorially symmetric structures maximize growth under narrow ITCZ configurations, and antisymmetric structures maximize growth under wider ITCZ configurations; and (iii) for antisymmetric mean states (and realistic ITCZ width), growth is maximized when the ITCZ is located off of the equator. The implications of these findings are discussed.

Martínez C. Uncertainties in the calculation of the tau lepton semi-hadronic decay, and a new perturbative expansion. (Spanish). Department of Physics. Universidad Catolica de Chile. [Internet]. 2010. Publisher's Version Thesis
Cvetič G, Loewe M, Martínez CV, Valenzuela C. A Modification of Contour-Improved Perturbation Theory. Nuclear Physics B - Proceedings Supplements [Internet]. 2010;207-208 :152-155. Publisher's VersionAbstract

We present a modification of the standard method of evaluating the semihadronic tau decay width. The method is based on a derivative expansion for the Adler function rather than the standard series in powers of the strong coupling. The extracted QCD coupling at the tau mass scale is by 2% lower than the “contour improved” value. We find &#x3B1;s(MZ2)=0.1211&#xB1;0.0010">.

Cvetic G, Loewe M, Martinez C, Valenzuela C. Modified contour-improved perturbation theory. Physical Review D [Internet]. 2010;82 (9) :093007. Publisher's VersionAbstract

The semihadronic tau decay width allows a clean extraction of the strong coupling constant at low energies. We present a modification of the standard “contour-improved” method based on a derivative expansion of the Adler function. The new approach has some advantages compared to contour-improved perturbation theory. The renormalization scale dependence is weaker by more than a factor of 2 and the last term of the expansion is reduced by about 10%, while the renormalization scheme dependence remains approximately equal. The extracted QCD coupling at the tau mass scale is by 2% lower than the contour-improved value. We find αs(M2Z)=0.1211±0.0010.

Loewe M, Martinez-Villalobos C. Thermal corrections to pi-pi scattering lengths in the linear sigma model. Physical Review D [Internet]. 2008;77 (10) :105006. Publisher's VersionAbstract

In this article we address the problem of getting the temperature dependence of the ππ scattering lengths in the frame of the linear sigma model. Using the real time formalism, we calculate all the relevant one loop diagrams. The temperature corrections are only considered in the pion sector, due to the Boltzmann suppression for heavier fields like the sigma meson. From this analysis we obtain the thermal behavior of the s waves scattering lengths a00 and a20 associated to isospin I=0 and I=2, respectively. If we normalize with the zero temperature value it turns out that a00(T)a00 grows with temperature, whereas the opposite occurs with a20(T)a20. Finally we compare our results with other determinations of the scattering lengths based on the Nambu-Jona-Lasinio model and chiral perturbation theory.

Martínez C. Thermal Corrections to Pion-Pion Scattering Lengths in the Linear Sigma Model (Spanish). Department of Physics. Universidad Catolica de Chile. [Internet]. 2007. Publisher's VersionAbstract

El proposito de este trabajo es calcular correcciones termicas a las longitudes de scattering pion-pion en el marco del modelo sigma lineal. Para eso se estudiaron los propagadores termicos en los formalismos de tiempo imaginario y real de teoria cuantica de campos a temperatura finita. Se estudio el formalismo para construir amplitudes de scattering con isospin definido. Inicialmente calculamos las longitudes de scattering y pendientes en el marco de este modelo a nivel arbol. Posteriormente se calcularon las correcciones termicas a las longitudes de scattering de momento angular ℓ = 0, al nivel de un loop y se comparo con otros resultados obtenidos en el marco de teoria quiral de perturbaciones y el modelo de Nambu-Jona-Lasinio, para las longitudes de scattering en los canales de isospın I = 0, 2. i