Observed El Niño-La Niña Asymmetry in a Linear Model (published August 2019)

Previous studies indicate an asymmetry in the amplitude and persistence of El Niño (EN) and La Niña (LN) events. We show that this 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) data sets spanning the twentieth 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.

C., Martinez‐Villalobos, Newman, M., Vimont, D. J., Penland, C., & Neelin, J. D. ( 2019). Observed El Niño‐La Niña asymmetry in a linear model. Geophysical Research Letters, 46, 9909-9919. https://doi.org/10.1029/2019GL082922



The Role of Stochastic Forcing in Generating ENSO Diversity (published November 2018)

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.

Thomas, E.E., D.J. Vimont, M. Newman, C. Penland, and C. Martínez-Villalobos, 2018: The Role of Stochastic Forcing in Generating ENSO Diversity. J. Climate, 31, 9125–9150, https://doi.org/10.1175/JCLI-D-17-0582.1



Shifts in Precipitation Accumulation Extremes During the Warm Season Over the United States (published August 2018)

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.

Martinez‐Villalobos, C., & Neelin, J. D. (2018). Shifts in precipitation accumulation extremes during the warm season over the United States. Geophysical Research Letters, 45, 8586–8595. https://doi.org/10.1029/2018GL078465



Calculating State-Dependent Noise in a Linear Inverse Model Framework (published February 2018)

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., D.J. Vimont, C. Penland, M. Newman, and J.D. Neelin, 2018: Calculating State-Dependent Noise in a Linear Inverse Model Framework. J. Atmos. Sci., 75, 479–496, https://doi.org/10.1175/JAS-D-17-0235.1



An Analytical Framework for Understanding Tropical Meridional Modes (published May 2017)

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. and D.J. Vimont, 2017: An Analytical Framework for Understanding Tropical Meridional Modes. J. Climate, 30, 3303–3323,https://doi.org/10.1175/JCLI-D-16-0450.1



The Role of the Mean State in Meridional Mode Structure and Growth (published May 2016)

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.

Martinez-Villalobos, C. and D.J. Vimont, 2016: The Role of the Mean State in Meridional Mode Structure and Growth. J. Climate, 29, 3907–3921,https://doi.org/10.1175/JCLI-D-15-0542.1



Modified contour-improved perturbation theory (published November 2010)

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 α_{s}(M_{Z}^{2})=0.1211±0.0010.

G. Cvetič, M. Loewe, C. Martinez and C. Valenzuela, Phys. Rev. D 82, 093007. DOI: https://doi.org/10.1103/PhysRevD.82.093007



Thermal Corrections to pi-pi scattering lengths in the linear sigma model (published May 2008)

In this article we address the problem of getting the temperature dependence of the pi-pi 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 a_{0}^{0} and a_{2}^{0} associated to isospin I=0 and I=2, respectively. If we normalize with the zero temperature value it turns out that a_{0}^{0}(T)/a_{0}^{0} grows with temperature, whereas the opposite occurs with a_{0}^{2}(T)/a_{0}^{2} . Finally we compare our results with other determinations of the scattering lengths based on the Nambu-Jona-Lasinio model and chiral perturbation theory.

M. Loewe and C. Martinez-Villalobos, Phys. Rev. D 77, 106006. DOI: 10.1103/PhysRevD.77.105006