Estimation of periodicities in hydrologic data

Periodicites in hydrologic data are frequently estimated and studied. In some cases the periodic components are subtracted from the data to obtain the stochastic components. In other cases the physical reasons for the occurrence of these periodicities are investigated. Apart from the annual cycle in the hydrologic data, periods corresponding to the 11 year sunspot cycle, the Hale cycle and others have been detected.The conclusions from most of these studies depend on the reliability and robustness of the methods used to detect these periodicities. Several spectral analysis methods have been proposed to investigate periodicities in time series data. Several of these have been compared to each other. The methods by Siddiqui and Wang and by Damsleth and Spjotvoll, which are stepwise procedures of spectrum estimation, have not been evaluated.     

The Medieval and Modern Maximum solar activity imprints in tree ring data from Chile and stable isotope records from Antarctica and Peru

This work presents a study of the relations between solar and climate variations during the last millennia by spectral and multi-resolution analysis for oxygen-18 and tree ring width time series. The spectral and wavelet analysis of tree ring data shows that main solar cycle periodicities are present in our time series at the 0.95 confidence level. This result suggests the possibility of a solar modulation of climate variations detected in accumulated ice oxygen-18. Results of spectral and wavelet analysis have shown that both solar and climate factors are also recorded in the oxygen-18 data.     

Discrete wavelet‐based trend identification in hydrologic time series

Trend identification is a substantial issue in hydrologic series analysis, but it is also a difficult task in practice due to the confusing concept of trend and disadvantages of methods. In this article, an improved definition of trend was given as follows: ‘a trend is the deterministic component in the analysed data and corresponds to the biggest temporal scale on the condition of giving the concerned temporal scale’. It emphasizes the intrinsic and deterministic properties of trend, can clearly distinguish trend from periodicities and points out the prerequisite of the concerned temporal scale only by giving which the trend has its specific meaning. Correspondingly, the discrete wavelet‐based method for trend identification was improved. Differing from those methods used presently, the improved method is to identify trend by comparing the energy difference between hydrologic data and noise, and it can simultaneously separate periodicities and noise. Furthermore, the improved method can quantitatively estimate the statistical significance of the identified trend by using proper confidence interval. Analyses of both synthetic and observed series indicated the identical power of the improved method as the Mann–Kendall test in assessing the statistical significance of the trend in hydrologic data, and by using the former, the identified trend can adaptively reflect the nonlinear and nonstationary variability of hydrologic data. Besides, the results also showed the influences of three key factors (wavelet choice, decomposition level choice and noise content) on discrete wavelet‐based trend identification; hence, they should be carefully considered in practice. Copyright © 2012 John Wiley & Sons, Ltd.     

Prediction of sunspot number amplitude and solar cycle length for cycles 24 and 25

The prediction of solar activity strength for solar cycles 24 and 25 is made on the basis of extrapolation of sunspot number spectral components. Monthly sunspot number data during the 1850–2007 interval (solar cycles 9–23) are decomposed into several levels and searched for periodicities by iterative regression in each level. For solar cycle 24, the peak is predicted in November 2013 with a sunspot number of 113.3. The cycle is expected to be weak, with a length of 133 mo (months) or 11.1 yr. The sunspot number maximum in cycle 25 is predicted to occur in April 2023 with a sunspot number 132.1 and a solar cycle length of 118 mo or 9.8 yr. Thus, solar cycle 24 is predicted to have an intensity 23% lower than cycle 23, and cycle 25 will be 5% lower than cycle 23.     

AR and ARMA spectral estimation

Autoregressive (AR) and Autoregressive-moving average (ARMA) methods of spectral analysis have been developed and are being increasingly used as alternatives to traditional methods of spectral analysis. Two of these methods developed by Marple and Friedlander are tested in this study by using generated data from models with known spectra. The Blackman-Tukey spectral estimates are also compared to the Marple and Friedlander estimates. The variability of the Marple and Friedlander estimates with sample sizes is investigated. Although both Marple's and Friedlander's methods are satisfactory, Friedlander's method is preferred because of its ability to handle a wider class of models.     

Non-stationary response of structures excited by random seismic processes with time variable frequency content

Seismic random processes are characterized by high non-stationarity and, in most cases, by a marked variability of frequency content. The hypothesis modeling seismic signal as a simple product of a stationary signal and a deterministic modulation function, consequently, is hardly ever applicable. Several mathematical models aimed at expressing the recorded process by means of a system of stationary random processes and deterministic amplitude and frequency modulations are proposed. Models oriented into the frequency domain with subsequent response analysis based on integral spectral resolution and models oriented into the time domain based on the multicomponent resolution are investigated. The resolution into individual components (non-stationary signals) is carried out by three methods. The resolution into intrinsic mode functions seems to possess the best characteristics and yields results almost not differing from the results obtained by stochastic simulation. An example of the seismic response of an existing bridge obtained by two older models and three variants of multicomponent resolution is given.     

Stochastic models in hydrology

A stochastic approach to the analysis of hydrologic processes is defined along with a discussion of causes of tendency, periodicity and stochasticity in hydrologic series. Sources of temporal non-stationarity are described along with objectives and methods of analysis of processes and, in general, of information extraction from data. Transferred information as measured by correlation coefficients is compared with the transferable information as measured by entropy coefficients. Various multivariate approaches to hydrologic stochastic modeling are classified in light of complexities of spatial/temporal hydrologic processes. Alternatives of time series structural decomposition and modeling are compared. A special approach to modeling of space properties further contributes to approximate simulations of spatial/temporal processes over large areas. Several aspects of stochastic models in hydrology are concisely reviewed.     

The North-South Asymmetry in the Green Corona

The north-south asymmetry of the Fe XIV 530.3 nm coronal emission line (the green corona) over cycle 22 was investigated. The green corona line brightness was dominant in the southern hemisphere during cycle 22 (A = –0.07), except for short periods of the ascending phase of the activity cycle. The asymmetry of the semi-annual mean over the period 1940 – 1996 was also studied. The asymmetry, during these years, reached its maximum in 1962 – 1966, and then decreased. Important periodicities of the asymmetry in cycle 22, e.g., 158 and 350 days, 2.39 years were found. Similar periodicities were also detected in the years 1940 – 1996. An FFT analysis was used to detect these periodicities.     

Exploratory spectral analysis of hydrological times series

Current methods of estimation of the univariate spectral density are reviewed and some improvements are made. It is suggested that spectral analysis may perhaps be best thought of as another exploratory data analysis (EDA) tool which complements, rather than competes with, the popular ARMA model building approach. A new diagnostic check for ARMA model adequacy based on the nonparametric spectral density is introduced. Additionally, two new algorithms for fast computation of the autoregressive spectral density function are presented. For improving interpretation of results, a new style of plotting the spectral density function is suggested. Exploratory spectral analyses of a number of hydrological time series are performed and some interesting periodicities are suggested for further investigation. The application of spectral analysis to determine the possible existence of long memory in natural time series is discussed with respect to long riverflow, treering and mud varve series. Moreover, a comparison of the estimated spectral densities suggests the ARMA models fitted previously to these datasets adequately describe the low frequency component. Finally, the software and data used in this paper are available by anonymous ftp from fisher.stats.uwo.ca.     

The 11-year solar cycle,the sun’s rotation,and the middle stratosphere in winter: Part I: Response of zonal means

The effect of the 11-year solar cycle on the response of the stratospheric geopotential height and temperature fields at 10 and 30 hPa in winter to solar activity oscillations with periods related to the period of the Sun’s rotation (27.2 days) is discussed, applying methods of statistical spectral analysis to daily data for the period from 1965 to 1996. Atmospheric responses for three periodicities — 27.2 days (period of the Sun’s rotation), 25.3 days (periodicity caused by the modulation of the 27.2 days oscillation by annual atmospheric variation), and 54.4 days (doubled period of the solar rotation) — are studied. A significant effect of the 11-year solar cycle on the atmospheric response to the 27.2 days solar periodicity has not been found. We explain it by a frequency shift of the response from the 27.2 days to the 25.3 days periodicity via amplitude modulation. For the 25.3 days oscillation, prominent differences between the maximum and minimum of the 11-year solar cycle have been found in the coherence between the 10.7 cm solar radio flux and the height/temperature fields: the relationships are stronger at solar maximum than at the minimum of the 11-year cycle. The same differences, but to a greater extent, are revealed for the oscillation with a period of 54.4 days. Coherence and amplitude estimates for this doubled solar rotation periodicity exhibit strong differences between extrema of the 11-year solar cycle. Phase estimates also demonstrate a clear difference between high and low solar activity: on the average, the delay of the atmospheric response after the solar signal is smaller at solar maximum than at solar minimum. Thus, we conclude that the mechanism of the influence of the 11-year solar cycle on the winter middle stratosphere can include both a direct effect of the frequency corresponding to the doubled solar rotation periodicity and an indirect effect of modulation of the intensity of the interaction between the solar 27.2 days oscillation and seasonal atmospheric variations.     

北京台磁暴出现频次及△Z/△H的初步分析/

本文利用北京台1957-1978年共22年的磁暴资料,统计分析了磁暴出现频次及△Z/△H随世界时、季节和年份的变化,初步研究了它们的频谱和与太阳活动性的关系,获得了可供磁暴预报与地磁预报地震探索研究参考的若干有意义的结果。      

Power spectrum analysis of atmospheric ozone during the summer

Summary This paper describes a study of the fluctuations in total atmospheric ozone amount as measured with a Dobson Spectrophotometer during the summer season over three north Indian stations, using the technique of power spectrum analysis. In all 19 spectra have been constructed. The long term trend was removed by applying a high pass filter. The main conclusions are: (1) The nature of the spectrum at a station generally differs from year to year. (2) Spectra of different stations during the same year, are generally different. (3) From the significance study of the spectral peaks, most of the spectra revealed the presence of two types of periodicities. One of these is in the range of 10–17 days while the other is found to have a range of 4.5–8.3 days. (4) It has been suggested that the former periodicity may be closely linked to the index cycle, while the latter may be related to the long waves in the Westerlies.     

Studying the dynamics of the lunar daily geomagnetic variations

Results of studying the lunar daily geomagnetic variations in the spectral and time regions at the network of observatories are presented. The seasonal variations in the amplitudes of the fundamental harmonic constituents of three lunar variation components have been revealed. The seasonal time variations have been analyzed using the digital bandpass filtering and harmonic synthesis based on the data of the Kakioka and Memambetsu geomagnetic observatories. The 11-year solar cycle and annual and semiannual periods have been distinguished in the seasonal variation spectrum. Studying the spectral singularities of the lunar daily variation at these observatories and the sea level variations in daytime and nighttime hours has made it possible to identify the contribution of the oceanic dynamo to the lunar variation vertical component.     

Evapotranspiration modelling from climatic data using a neural computing technique

Evapotranspiration is one of the basic components of the hydrologic cycle and essential for estimating irrigation water requirements. This paper investigates the modelling of evapotranspiration using the feed‐forward artificial neural network (ANN) technique with the Levenberg–Marquardt (LM) training algorithm. The LM algorithm has never been used in evapotranspiration estimation before. The LM is used for the optimization of network weights, since this algorithm is more powerful and faster than the conventional gradient descent. Various combinations of daily climatic data, i.e. wind speed, air temperature, relative humidity and solar radiation, from three stations in Los Angeles, USA, are used as inputs to the ANN so as to evaluate the degree of effect of each of these variables on evapotranspiration. A comparison is made between the estimates provided by the ANN and those of the following empirical models: Penman, Hargreaves, Turc. Mean square error, mean absolute error and determination coefficient statistics are used as comparing criteria for the evaluation of the models' performances. Based on the comparisons, it was found that the neural computing technique could be employed successfully in modelling evapotranspiration process from the available climatic data. The results also indicate that the Hargreaves method provides better performance than the Penman and Turc methods in estimation of the evapotranspiration. The accuracy of the ANN technique in evapotranspiration estimation using nearby station data was also investigated. Copyright © 2007 John Wiley & Sons, Ltd.     

Peculiarities of geomagnetic variations in the central part of the Russian platform

The instrumental observations of geomagnetic variations in the middle latitudes are analyzed. The main periodicities are revealed in the background local variations of the magnetic field of the Earth. Besides the 27–29-day variations, which are associated with the rotation of the Sun around its axis, also the harmonic components with periods of ～1, 6–8, 13–14, 57–60 days, and about a year are identified. It is shown that the periodicities in the background variations are both regular and sporadic. The peculiarities in the time behavior of some spectral components of geomagnetic variations are established.     

Wavelet Characteristics of Hydrological and Dissolved Oxygen Time Series in a Lowland River

In this study, we investigated the temporal variability of dissolved oxygen and water temperature in conjunction with water level fluctuations and river discharge in the Narew lowland river reach. For this purpose, high resolution hydrologic and water quality time series have been used. Spectral analyses of time series using continuous wavelet transform scheme have been applied in order to identify characteristic scales, its duration, and localisation in time. The results of wavelet analysis have shown a great number of periodicities in time series at the inter-annual time scale when compared to the classical Fourier analysis. Additionally, wavelet coherence revealed the complex nature of the relationship between dissolved oxygen and hydrological variables dependent on the scale and localisation in time. Hence, the results presented in this paper may provide an alternative representation to a frequency analysis of time series.     

Land cover effects on runoff patterns in eastern Piedmont (USA) watersheds

Physiography and land cover determine the hydrologic response of watersheds to climatic events. However, vast differences in climate regimes and variation of landscape attributes among watersheds (including size) have prevented the establishment of general relationships between land cover and runoff patterns across broad scales. This paper addresses these difficulties by using power spectral analysis to characterize area‐normalized runoff patterns and then compare these patterns with landscape features among watersheds within the same physiographic region. We assembled long‐term precipitation and runoff data for 87 watersheds (first to seventh order) within the eastern Piedmont (USA) that contained a wide variety of land cover types, collected environmental data for each watershed, and compared the datasets using a variety of statistical measures. The effect of land cover on runoff patterns was confirmed. Urban‐dominated watersheds were flashier and had less hydrologic memory compared with forest‐dominated watersheds, whereas watersheds with high wetland coverage had greater hydrologic memory. We also detected a 10–15% urban threshold above which urban coverage became the dominant control on runoff patterns. When spectral properties of runoff were compared across stream orders, a threshold after the third order was detected at which watershed processes became dominant over precipitation regime in determining runoff patterns. Finally, we present a matrix that characterizes the hydrologic signatures of rivers based on precipitation versus landscape effects and low‐frequency versus high‐frequency events. The concepts and methods presented can be generally applied to all river systems to characterize multiscale patterns of watershed runoff. Copyright © 2013 John Wiley & Sons, Ltd.     

A framework for quantifying the impacts of climate change and human activities on hydrological drought in a semiarid basin of Northern China

Climate change and human activities are two major driving forces affecting the hydrologic cycle, which further influence the stationarity of the hydrologic regime. Hydrological drought is a substantial negative deviation from the normal hydrologic conditions affected by these two phenomena. In this study, we propose a framework for quantifying the effects of climate change and human activities on hydrological drought. First, trend analysis and change‐point test are performed to determine variations of hydrological variables. After that, the fixed runoff threshold level method (TLM) and the standardized runoff index (SRI) are used to verify whether the traditional assessment methods for hydrological drought are applicable in a changing environment. Finally, two improved drought assessment methods, the variable TLM and the SRI based on parameter transplantation are employed to quantify the impacts of climate change and human activities on hydrological drought based on the reconstructed natural runoff series obtained using the variable infiltration capacity hydrologic model. The results of a case study on the typical semiarid Laohahe basin in North China show that the stationarity of the hydrological processes in the basin is destroyed by human activities (an obvious change‐point for runoff series is identified in 1979). The traditional hydrological drought assessment methods can no longer be applied to the period of 1980–2015. In contrast, the proposed separation framework is able to quantify the contributions of climate change and human activities to hydrological drought during the above period. Their ranges of contributions to hydrological drought calculated by the variable TLM method are 20.6–41.2% and 58.8–79.4%, and the results determined by the SRI based on parameter transplantation method are 15.3–45.3% and 54.7–84.7%, respectively. It is concluded that human activities have a dominant effect on hydrological drought in the study region. The novelty of the study is twofold. First, the proposed method is demonstrated to be efficient in quantifying the effects of climate change and human activities on hydrological drought. Second, the findings of this study can be used for hydrological drought assessment and water resource management in water‐stressed regions under nonstationary conditions.     

A 22 yr hurricane cycle and its relation with geomagnetic activity

Applying spectral analysis to the Atlantic and Pacific hurricane time series, we found periodicities that coincide with the main sunspot and magnetic solar cycles. To assess the possibility that these periodicities could be associated with solar activity, we obtain correlations between hurricane occurrence and several solar activity-related phenomena, such as the total solar irradiance, the cosmic ray flux and the Dst index of geomagnetic activity. Our results indicate that the highest significant correlations are found between the Atlantic and Pacific hurricanes and the Dst index. Most importantly, both oceans present the highest hurricane–Dst correlations during the ascending part of odd solar cycles and the descending phase of even solar cycles. This shows not only the existence of a 22 yr cycle but also the nature of such periodicity. Furthermore, we found that the Atlantic hurricanes behave differently from the Pacific hurricanes in relation to the solar activity-related disturbances considered.     

Temperature variability in central Mexico and its possible association to solar activity

Minimum extreme temperature variability from five meteorological stations in the central part of Mexico covering a period from 1920 to 1990 is examined. We found a correlation coefficient (r=0.65) between these temperature records and geomagnetic activity. Furthermore, by performing spectral analysis peaks were obtained with similar periodicities to those found in the sunspot number, the magnetic solar cycle, cosmic ray fluxes and geomagnetic activity; all of these phenomena are modulated by solar activity. Signals with periodicities comparable to those observed in El Niño and the Quasi-Biennial Oscillation were also identified. We conclude that the solar signal is probably present in the minimum extreme temperature record of the central part of Mexico.