scholarly journals Stochastic Analysis of Hourly to Monthly Potential Evapotranspiration with a Focus on the Long-Range Dependence and Application with Reanalysis and Ground-Station Data

Hydrology ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 177
Author(s):  
Panayiotis Dimitriadis ◽  
Aristoteles Tegos ◽  
Demetris Koutsoyiannis
Keyword(s):  
Long Range ◽  
Hydrological Cycle ◽  
Potential Evapotranspiration ◽  
Global Scale ◽  
Reanalysis Data ◽  
Shortwave Radiation ◽  
Long Range Dependence ◽  
Dependence Structure ◽  
Ground Station ◽  
Cycle Path

The stochastic structures of potential evaporation and evapotranspiration (PEV and PET or ETo) are analyzed using the ERA5 hourly reanalysis data and the Penman–Monteith model applied to the well-known CIMIS network. The latter includes high-quality ground meteorological samples with long lengths and simultaneous measurements of monthly incoming shortwave radiation, temperature, relative humidity, and wind speed. It is found that both the PEV and PET processes exhibit a moderate long-range dependence structure with a Hurst parameter of 0.64 and 0.69, respectively. Additionally, it is noted that their marginal structures are found to be light-tailed when estimated through the Pareto–Burr–Feller distribution function. Both results are consistent with the global-scale hydrological-cycle path, determined by all the above variables and rainfall, in terms of the marginal and dependence structures. Finally, it is discussed how the existence of, even moderate, long-range dependence can increase the variability and uncertainty of both processes and, thus, limit their predictability.

scholarly journals Investigating Interannual Variability of Precipitation at the Global Scale: Is There a Connection with Seasonality?

2012 ◽  
Vol 25 (16) ◽  
pp. 5512-5523 ◽  
Author(s):  
S. Fatichi ◽  
V. Yu. Ivanov ◽  
E. Caporali
Keyword(s):  
Interannual Variability ◽  
Long Range ◽  
Coefficient Of Variation ◽  
Spatial Organization ◽  
Global Scale ◽  
Reanalysis Data ◽  
Annual Precipitation ◽  
Long Range Dependence ◽  
Robust Property ◽  
Precipitation Records

Abstract Interannual variability of precipitation can directly or indirectly affect many hydrological, ecological, and biogeochemical processes that, in turn, influence climate. Despite the significant importance of the phenomenon, few studies have attempted to elucidate spatial patterns of this variability at the global scale. This study uses land gauge precipitation records of the Global Historical Climatology Network, version 2, as well as reanalysis data to provide an assessment of the spatial organization of characteristics of precipitation interannual variability. The coefficient of variation, skewness, and short- and long-range dependence of the precipitation variability are analyzed. Among the major inferences is that the coefficient of variation of annual precipitation shows a significant correlation with intra-annual seasonality. Specifically, subyearly precipitation anomalies occurring in locations with pronounced seasonality affect the total yearly amount, imposing a higher variability in the annual precipitation fluctuations. Furthermore, the study illustrates that a positive skewness of the distribution of annual precipitation is a robust property worldwide and its magnitude is related to the coefficient of variation. Additionally, annual precipitation exhibits very weak small-lag autocorrelation. Conversely, the intensity of long-memory–long-range dependence is significantly larger than zero, hinting that organized long-term variations are an important feature of the interannual variability of precipitation.

Parametric modelling of turbulence

1990 ◽  
Vol 332 (1627) ◽  
pp. 439-455 ◽  
Keyword(s):  
Long Range ◽  
Three Dimensional ◽  
Large Data ◽  
Theoretical Work ◽  
Long Range Dependence ◽  
Dependence Structure ◽  
Data Sets ◽  
Parametric Modelling ◽  
First Order ◽  
Log Linear

Some steps are taken towards a parametric statistical model for the velocity and velocity derivative fields in stationary turbulence, building on the background of existing theoretical and empirical knowledge of such fields. While the ultimate goal is a model for the three-dimensional velocity components, and hence for the corresponding velocity derivatives, we concentrate here on the stream wise velocity component. Discrete and continuous time stochastic processes of the first-order autoregressive type and with one-dimensional marginals having log-linear tails are constructed and compared with two large data-sets. It turns out that a first-order autoregression that fits the local correlation structure well is not capable of describing the correlations over longer ranges. A good fit locally as well as at longer ranges is achieved by using a process that is the sum of two independent autoregressions. We study this type of model in some detail. We also consider a model derived from the above-mentioned autoregressions and with dependence structure on the borderline to long-range dependence. This model is obtained by means of a general method for construction of processes with long-range dependence. Some suggestions for future empirical and theoretical work are given.

APPLYING BUCKET RANDOM PERMUTATIONS TO STATIONARY SEQUENCES WITH LONG-RANGE DEPENDENCE

Fractals ◽  
2007 ◽  
Vol 15 (02) ◽  
pp. 105-126 ◽  
Author(s):  
YINGCHUN ZHOU ◽  
MURAD S. TAQQU
Keyword(s):  
Long Range ◽  
Short Range ◽  
Random Permutation ◽  
Stationary Sequence ◽  
Long Range Dependence ◽  
Finite Variance ◽  
Dependence Structure ◽  
Random Permutations ◽  
Medium Range ◽  
The Time Domain

Bucket random permutations (shuffling) are used to modify the dependence structure of a time series, and this may destroy long-range dependence, when it is present. Three types of bucket permutations are considered here: external, internal and two-level permutations. It is commonly believed that (1) an external random permutation destroys the long-range dependence and keeps the short-range dependence, (2) an internal permutation destroys the short-range dependence and keeps the long-range dependence, and (3) a two-level permutation distorts the medium-range dependence while keeping both the long-range and short-range dependence. This paper provides a theoretical basis for investigating these claims. It extends the study started in Ref. 1 and analyze the effects that these random permutations have on a long-range dependent finite variance stationary sequence both in the time domain and in the frequency domain.

scholarly journals Student processes

2005 ◽  
Vol 37 (02) ◽  
pp. 342-365 ◽  
Author(s):  
C. C. Heyde ◽  
N. N. Leonenko
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Long Range ◽  
Risky Asset ◽  
Long Range Dependence ◽  
Dependence Structure

Stochastic processes with Student marginals and various types of dependence structure, allowing for both short- and long-range dependence, are discussed in this paper. A particular motivation is the modelling of risky asset time series.

scholarly journals Evaluation of the hydrological cycle of MATCH driven by NCEP reanalysis data: comparison with GOME water vapor measurements

2005 ◽  
Vol 5 (4) ◽  
pp. 887-908 ◽  
Author(s):  
R. Lang ◽  
M. G. Lawrence
Keyword(s):  
Water Vapor ◽  
Regional Differences ◽  
Hydrological Cycle ◽  
Transport Model ◽  
Global Precipitation Climatology Project ◽  
Global Scale ◽  
Reanalysis Data ◽  
Model Parameters ◽  
Ncep Reanalysis ◽  
Inter Tropical Convergence Zone

Abstract. This study examines two key parameters of the hydrological cycle, water vapor (WV) and precipitation rates (PR), as modelled by the chemistry transport model MATCH (Model of Atmospheric Transport and Chemistry) driven by National Centers for Environmental Prediction (NCEP) reanalysis data (NRA). For model output evaluation we primarily employ WV total column data from the Global Ozone Monitoring Experiment (GOME) on ERS-2, which is the only instrument capable measuring WV on a global scale and over all surface types with a substantial data record from 1995 to the present. We find that MATCH and NRA WV and PR distributions are closely related, but that significant regional differences in both parameters exist in magnitude and distribution patterns when compared to the observations. We also find that WV residual patterns between model and observations show remarkable similarities to residuals observed in the PR when comparing MATCH and NRA output to observations comprised by the Global Precipitation Climatology Project (GPCP). We conclude that deficiencies in model parameters shared by MATCH and NRA, like in the surface evaporation rates and regional transport patterns, are likely to lead to the observed differences. Monthly average regional differences between MATCH modelled WV columns and the observations can be as large as 2 cm, based on the analysis of three years. Differences in the global mean WV values are, however, below 0.1 cm. Regional differences in the PR between MATCH and GPCP can be above 0.5 cm per day and MATCH computes on average a higher PR than what has been observed. The lower water vapor content of MATCH is related to shorter model WV residence times by up to 1 day as compared to the observations. We find that MATCH has problems in modelling the WV content in regions of strong upward convection like, for example, along the Inter Tropical Convergence Zone, where it appears to be generally too dry as compared to the observations. We discuss possible causes for this bias and demonstrate the value of the GOME WV record for model evaluation.

scholarly journals Extremal clustering in non-stationary random sequences

Extremes ◽  
2021 ◽  
Author(s):  
Graeme Auld ◽  
Ioannis Papastathopoulos
Keyword(s):  
Asymptotic Distribution ◽  
Long Range ◽  
Extreme Values ◽  
Random Variables ◽  
Limiting Distribution ◽  
Long Range Dependence ◽  
Dependence Structure ◽  
Stationary Sequences ◽  
Random Sequences ◽  
Extremal Clustering

AbstractIt is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but identically distributed sequences of random variables subject to suitable long range dependence restrictions. We find that the limiting distribution of appropriately normalized sample maxima depends on a parameter that measures the average extremal clustering of the sequence. Based on this new representation we derive the asymptotic distribution for the time between consecutive extreme observations and construct moment and likelihood based estimators for measures of extremal clustering. We specialize our results to random sequences with periodic dependence structure.

DEPENDENCE STRUCTURE OF A RENEWAL-REWARD PROCESS WITH INFINITE VARIANCE

Fractals ◽  
2001 ◽  
Vol 09 (02) ◽  
pp. 185-192 ◽  
Author(s):  
JOSHUA B. LEVY ◽  
MURAD S. TAQQU
Keyword(s):  
Long Range ◽  
Power Function ◽  
Long Range Dependence ◽  
Infinite Variance ◽  
Dependence Structure ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Stable Noise

The on-off renewal-reward process used to explain long-range dependence in Ethernet traffic can be extended to the case where, not only the inter-renewal times but also the rewards have infinite variance. The covariation and the codifference, which generalize the covariance to the infinite variance case, are computed for the limiting process. It is shown that they decay like a power function. The exponent of that power is the same as for fractional stable noise, even though the increments of the limiting process are different from fractional stable noise.

scholarly journals Student processes

2005 ◽  
Vol 37 (2) ◽  
pp. 342-365 ◽  
Author(s):  
C. C. Heyde ◽  
N. N. Leonenko
Keyword(s):  
Time Series ◽  
Stochastic Processes ◽  
Long Range ◽  
Risky Asset ◽  
Long Range Dependence ◽  
Dependence Structure

Stochastic processes with Student marginals and various types of dependence structure, allowing for both short- and long-range dependence, are discussed in this paper. A particular motivation is the modelling of risky asset time series.

scholarly journals Measuring compound flood potential from river discharge and storm surge extremes at the global scale

2020 ◽  
Vol 20 (2) ◽  
pp. 489-504 ◽  
Author(s):  
Anaïs Couasnon ◽  
Dirk Eilander ◽  
Sanne Muis ◽  
Ted I. E. Veldkamp ◽  
Ivan D. Haigh ◽  
...  
Keyword(s):  
Storm Surge ◽  
River Discharge ◽  
Flood Hazard ◽  
Joint Probability ◽  
Global Scale ◽  
Statistical Dependence ◽  
Dependence Structure ◽  
Meteorological Forcing ◽  
Continental Scale ◽  
Bivariate Dependence

Abstract. The interaction between physical drivers from oceanographic, hydrological, and meteorological processes in coastal areas can result in compound flooding. Compound flood events, like Cyclone Idai and Hurricane Harvey, have revealed the devastating consequences of the co-occurrence of coastal and river floods. A number of studies have recently investigated the likelihood of compound flooding at the continental scale based on simulated variables of flood drivers, such as storm surge, precipitation, and river discharges. At the global scale, this has only been performed based on observations, thereby excluding a large extent of the global coastline. The purpose of this study is to fill this gap and identify regions with a high compound flooding potential from river discharge and storm surge extremes in river mouths globally. To do so, we use daily time series of river discharge and storm surge from state-of-the-art global models driven with consistent meteorological forcing from reanalysis datasets. We measure the compound flood potential by analysing both variables with respect to their timing, joint statistical dependence, and joint return period. Our analysis indicates many regions that deviate from statistical independence and could not be identified in previous global studies based on observations alone, such as Madagascar, northern Morocco, Vietnam, and Taiwan. We report possible causal mechanisms for the observed spatial patterns based on existing literature. Finally, we provide preliminary insights on the implications of the bivariate dependence behaviour on the flood hazard characterisation using Madagascar as a case study. Our global and local analyses show that the dependence structure between flood drivers can be complex and can significantly impact the joint probability of discharge and storm surge extremes. These emphasise the need to refine global flood risk assessments and emergency planning to account for these potential interactions.

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