Stochastic modeling of daily temperature fluctuations

Persistent urban heat

Urban surface and near-surface air temperatures are known to be often higher than their rural counterparts, a phenomenon now labeled as the urban heat island effect. However, whether the elevated urban temperatures are more persistent than rural temperatures at timescales commensurate to heat waves has not been addressed despite its importance for human health. Combining numerical simulations by a global climate model with a surface energy balance theory, it is demonstrated here that urban surface and near-surface air temperatures are significantly more persistent than their rural counterparts in cities dominated by impervious materials with large thermal inertia. Further use of these materials will result in even stronger urban temperature persistence, especially for tropical cities. The present findings help pinpoint mitigation strategies that can simultaneously ameliorate the larger magnitude and stronger persistence of urban temperatures.

Global-Scale Synchronization in the Meteorological Data: A Vectorial Analysis That Includes Higher-Order Differences

To examine the evidence of global warming, in recent years, there has been a growing interest in the statistical analysis of time-dependent meteorological data. In this paper, for 116 observational stations in the world, sequential variations of the monthly distributions of meteorological data are analyzed vectorially. For specific monthly data, temperatures and precipitations are chosen, both of which are averaged over three decades. Climate change can be revealed through the intersecting angle between two 33-dimensional vectors being composed with monthly mean values. Subsequently, the angle data for the entire stations are analyzed statistically and compared between the former (1931–1980) and the latter (1951–2010) periods. Irrespective of the period and the hemisphere, the variation of the angles is found to show the exponential growth as a function of their latitudes. Furthermore, consistent with other studies, this trend is shown to become stronger in the latter period, indicating that the so-called snow/ice-albedo feedback occurs. In contrast to the temperatures, for the precipitations, no significant correlation is found between the angle and the latitude. To examine the albedo effect in more detail, a regional analysis for 75 stations in Japan is carried out as well. Numerical results show that the effect is significant even for the relatively narrow latitudinal range (19%) of the hemisphere. Finally, a synchronization of the monthly patterns of temperatures is given between the northern district of Japan and both North America and Eastern Europe.

Simulation models of dengue transmission in Funchal, Madeira Island: Influence of seasonality

The recent emergence and established presence of Aedes aegypti in the Autonomous Region of Madeira, Portugal, was responsible for the first autochthonous outbreak of dengue in Europe. The island has not reported any dengue cases since the outbreak in 2012. However, there is a high risk that an introduction of the virus would result in another autochthonous outbreak given the presence of the vector and permissive environmental conditions. Understanding the dynamics of a potential epidemic is critical for targeted local control strategies. Here, we adopt a deterministic model for the transmission of dengue in Aedes aegypti mosquitoes. The model integrates empirical and mechanistic parameters for virus transmission, under seasonally varying temperatures for Funchal, Madeira Island. We examine the epidemic dynamics as triggered by the arrival date of an infectious individual; the influence of seasonal temperature mean and variation on the epidemic dynamics; and performed a sensitivity analysis on the following quantities of interest: the epidemic peak size, time to peak, and the final epidemic size. Our results demonstrate the potential for summer and autumn season transmission of dengue, with the arrival date significantly affecting the distribution of the timing and peak size of the epidemic. Late-summer arrivals were more likely to produce large epidemics within a short peak time. Epidemics within this favorable period had an average of 11% of the susceptible population infected at the peak, at an average peak time of 95 days. We also demonstrated that seasonal temperature variation dramatically affects the epidemic dynamics, with warmer starting temperatures producing large epidemics with a short peak time and vice versa. Overall, our quantities of interest were most sensitive to variance in the date of arrival, seasonal temperature, transmission rates, mortality rate, and the mosquito population; the magnitude of sensitivity differs across quantities. Our model could serve as a useful guide in the development of effective local control and mitigation strategies for dengue fever in Madeira Island.

Size effects on correlation measures

The detection and quantification of long-range correlations in time series is a fundamental tool to characterize the properties of different dynamical systems, and is applied in many different fields, including physics, biology or engineering. Due to the diversity of applications, many techniques for measuring correlations have been designed. Here, we study systematically the influence of the length of a time series on the results obtained from several techniques commonly used to detect and quantify long-range correlations: the autocorrelation analysis, Hurst's analysis, and detrended fluctuation analysis (DFA). Using the Fourier filtering method, we generate artificial time series with known and controlled long-range correlations and with a broad range of lengths, and apply on them the different correlation measures we have studied. Our results indicate that while the DFA method is practically unaffected by the length of the time series, and almost always provides accurate results, the results from Hurst's analysis and the autocorrelation analysis strongly depend on the length of the time series.

Time-asymmetric fluctuations in the atmosphere: daily mean temperatures and total-column ozone

Fluctuations breaking time-reversal symmetry are common attributes of dissipative systems operating far from equilibrium. Recent developments in non-equilibrium statistical physics represent a significant step towards an understanding of how time-reversible microscopic laws can yield to inherent irreversibility on meso- or macroscopic scales. Most of the theoretical conclusions consider quantities (e.g. entropy production) that are difficult to obtain with an appropriate accuracy in real systems. Probably less-complicated measures, such as the simple step-number ratio used in this work, can also help to characterize time-asymmetric fluctuations. In the first part, we give a short summary of recent results on asymmetric daily mean temperature changes. The second part discusses total-column ozone fluctuations, where statistically significant asymmetries are also detected. A detailed correlation analysis of ozone signals and high-altitude temperature records supports the strong coupling between tropospheric dynamics and stratospheric processes on synoptic time scales.

Amplitude-frequency fluctuations of the seasonal cycle, temperature anomalies, and long-range persistence of climate records

The presence of long-term persistence of climate records on scales from 2 to 15 yr has been reported in the literature, even if the universality of this result is controversial. In the present paper results from monthly temperature records measured for about 250 yr in Prague and Milan are reported. Because of the nonlinear and nonstationary character of temperature time series the seasonal contribution has been identified through the empirical mode decomposition. We find that the seasonal component of the climate records is characterized by some time scales showing both amplitude and phase fluctuations. By using a more suitable definition of temperature anomalies, and thus excluding persistence effects due to seasonal oscillations and trends, the occurrence of long-term persistence has been investigated through the detrended fluctuation analysis. Our results indicate persistence on scales from 3 to 10 yr with similar values for the detrended fluctuation analysis indices.

Stochastic eco-epidemiological model of dengue disease transmission by Aedes aegypti mosquito

We present a stochastic dynamical model for the transmission of dengue that takes into account seasonal and spatial dynamics of the vector Aedes aegypti. It describes disease dynamics triggered by the arrival of infected people in a city. We show that the probability of an epidemic outbreak depends on seasonal variation in temperature and on the availability of breeding sites. We also show that the arrival date of an infected human in a susceptible population dramatically affects the distribution of the final size of epidemics and that early outbreaks have a low probability. However, early outbreaks are likely to produce large epidemics because they have a longer time to evolve before the winter extinction of vectors. Our model could be used to estimate the risk and final size of epidemic outbreaks in regions with seasonal climatic variations.

A stochastic spatial dynamical model for Aedes aegypti

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.

A stochastic population dynamics model for Aedes aegypti: formulation and application to a city with temperate climate

Aedes aegypti is the main vector for dengue and urban yellow fever. It is extended around the world not only in the tropical regions but also beyond them, reaching temperate climates. Because of its importance as a vector of deadly diseases, the significance of its distribution in urban areas and the possibility of breeding in laboratory facilities, Aedes aegypti is one of the best-known mosquitoes. In this work the biology of Aedes aegypti is incorporated into the framework of a stochastic population dynamics model able to handle seasonal and total extinction as well as endemic situations. The model incorporates explicitly the dependence with temperature. The ecological parameters of the model are tuned to the present populations of Aedes aegypti in Buenos Aires city, which is at the border of the present day geographical distribution in South America. Temperature thresholds for the mosquito survival are computed as a function of average yearly temperature and seasonal variation as well as breeding site availability. The stochastic analysis suggests that the southern limit of Aedes aegypti distribution in South America is close to the 15 degrees C average yearly isotherm, which accounts for the historical and current distribution better than the traditional criterion of the winter (July) 10 degrees C isotherm.

Empirical mode decomposition and correlation properties of long daily ozone records

Correlations for daily data of total ozone column are investigated by detrended fluctuation analysis (DFA). The removal of annual periodicity does not result in a background-free signal for the tropical station Mauna Loa. In order to identify the remaining quasiperiodic constituent, the relatively new method of empirical mode decomposition (EMD) is tested. We found that the so-called intrinsic mode functions do not represent real signal components of the ozone time series, their amplitude modulation is very sensitive to local changes such as random data removal or smoothing. Tests on synthetic data further corroborate the limitations of decomposing quasiperiodic signals from noise with EMD. Nevertheless the EMD algorithm helps to identify dominating frequencies in the time series, which allows to separate fluctuations from the remaining background. We demonstrate that DFA analysis for the cleaned Mauna Loa record yields scaling comparable to a mid-latitude station.

Effect of nonlinear filters on detrended fluctuation analysis

When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal, using the detrended fluctuation analysis (DFA) which has been shown to accurately quantify power-law correlations in nonstationary signals. Specifically, we study the effect of three types of transforms: (i) linear ( y(i) =a x(i) +b) , (ii) nonlinear polynomial ( y(i) =a x(k)(i) ) , and (iii) nonlinear logarithmic [ y(i) =log ( x(i) +Delta) ] filters. We compare the correlation and scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power k of the polynomial filter, and (c) the offset Delta in the logarithmic filter. We further apply the DFA method to investigate the "apparent" scaling of three analytic functions: (i) exponential [exp (+/-x+a) ] , (ii) logarithmic [log (x+a) ] , and (iii) power law [ (x+a)(lambda) ] , which are often encountered as trends in physical and biological processes. While these three functions have different characteristics, we find that there is a broad range of values for parameter a common for all three functions, where the slope of the DFA curves is identical. We further note that the DFA results obtained for a class of other analytic functions can be reduced to these three typical cases. We systematically test the performance of the DFA method when estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider.

Superroughening by linear growth equations with spatiotemporally correlated noise

We give an extensive study on a class of interfacial superroughening processes with finite lateral system size in 1+1 dimensions described by linear growth equations with spatiotemporally power-law decaying correlated noise. Since some of these processes have an extremely long relaxation time, we first develop a very efficient method capable of simulating the interface morphology of these growth processes even in very late time. We numerically observe that this class of superrough growth processes indeed gradually develops macroscopic structures with the lateral size comparable to the lateral system size. Through the rigorous analytical study of the equal-time height difference correlation function, the different-time height difference correlation function, and the local width, we explicitly evaluate not only the leading anomalous dynamic scaling term but also all the subleading anomalous dynamic scaling terms which dominate over the ordinary dynamic scaling term. Moreover, the relation between the macroscopic structure formation and anomalous interfacial roughening of the superrough growth processes is analytically investigated in detail.

Nonuniversal atmospheric persistence: different scaling of daily minimum and maximum temperatures

An extensive investigation of 61 daily temperature records by means of detrended fluctuation analysis has revealed that the value of correlation exponent is not universal, contrary to earlier claims. Furthermore, statistically significant differences are found for daily minimum and maximum temperatures measured at the same station, suggesting different degrees of long-range correlations for the two extremes. Numerical tests on synthetic time series demonstrate that a correlated signal interrupted by uncorrelated segments exhibits an apparently lower exponent value over the usual time window of empirical data analysis. In order to find statistical differences between the two daily extreme temperatures, high frequency (10 min) records were evaluated for two distant locations. The results show that daily maxima characterize better the dynamic equilibrium state of the atmosphere than daily minima, for both stations. This provides a conceptual explanation why scaling analysis can yield different exponent values for minima and maxima.