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1.
BELLIE SIVAKUMAR 《水文科学杂志》2013,58(2):203-219
Abstract The problem of transformation of rainfall data from one scale to another has been gaining considerable importance in recent years. Though the application of the concept of fractal theory, in the studies conducted thus far, nearly unanimously points at the possibility of such a transformation, the suitability of the theory to the highly variable rainfall in time and space has very often been questioned. A preliminary attempt is made herein to address this issue by investigating the existence of temporal scaling behaviour in rainfall data observed in two different climatic regions: (a) a subtropical climatic region (Leaf River basin, Mississippi, USA) and (b) an equatorial climatic region (Singapore). Rainfall data of three different resolutions, six-hourly, daily, and weekly, observed over a period of 25 years, are investigated. A mono- or simple-scaling method (box dimension method) is employed. The results achieved for the different data sets clearly indicate the existence of temporal scaling in rainfall observed in the two regions, an encouraging news on the suitability of fractal theory in understanding and modelling the rainfall process. However, the insufficiency of a single dimension to characterize the rainfall behaviour is realized, as the dimension depends on the rainfall intensity level, which, in turn, may be related to the rainfall generating mechanisms. A comparison of the box-dimension results obtained for data of different resolutions, from each of the regions, seems to indicate a possible connection between them, a prospect of tremendous practical importance. Another interesting observation is the similarity between the box dimension results obtained for rainfall data from Leaf River basin and Singapore, but this is also clearly related to the intensity level. The dependence of the dimension on the intensity threshold suggests the use of a multi-dimensional fractal approach, where the process is characterized by more than one dimension (or a dimension function) instead of one single dimension. On the basis of the present results, some potential areas for further study are identified. 相似文献
2.
Bellie Sivakumar 《水文研究》2001,15(6):943-955
An Erratum has been published for this article in Hydrological Processes 15 (12) 2001, 2381–2382. Applications of the ideas gained from fractal theory to characterize rainfall have been one of the most exciting areas of research in recent times. The studies conducted thus far have nearly unanimously yielded positive evidence regarding the existence of fractal behaviour in rainfall. The studies also revealed the insufficiency of the mono‐fractal approaches to characterizing the rainfall process in time and space and, hence, the necessity for multi‐fractal approaches. The assumption behind multi‐fractal approaches for rainfall is that the variability of the rainfall process could be directly modelled as a stochastic (or random) turbulent cascade process, since such stochastic cascade processes were found to generically yield multi‐fractals. However, it has been observed recently that multi‐fractal approaches might provide positive evidence of a multi‐fractal nature not only in stochastic processes but also in, for example, chaotic processes. The purpose of the present study is to investigate the presence of both chaotic and fractal behaviours in the rainfall process to consider the possibility of using a chaotic multi‐fractal approach for rainfall characterization. For this purpose, daily rainfall data observed at the Leaf River basin in Mississippi are studied, and only temporal analysis is carried out. The autocorrelation function, the power spectrum, the empirical probability distribution function, and the statistical moment scaling function are used as indicators to investigate the presence of fractal, whereas the presence of chaos is investigated by employing the correlation dimension method. The results from the fractal identification methods indicate that the rainfall data exhibit multi‐fractal behaviour. The correlation dimension method yields a low dimension, suggesting the presence of chaotic behaviour. The existence of both multi‐fractal and chaotic behaviours in the rainfall data suggests the possibility of a chaotic multi‐fractal approach for rainfall characterization. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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Abstract The scale invariance of rainfall series in the Tunis area, Tunisia (semi-arid Mediterranean climate) is studied in a mono-fractal framework by applying the box counting method to four series of observations, each about 2.5 years in length, based on a time resolution of 5 min. In addition, a single series of daily rainfall records for the period 1873–2009 was analysed. Three self-similar structures were identified: micro-scale (5 min to 2 d) with fractal dimension 0.44, meso-scale (2 d to one week) and synoptic-scale (one week to eight months) with fractal dimension 0.9. Interpretation of these findings suggests that only the micro-scale and transition to saturation are consistent, while the high fractal dimension relating to the synoptic scale might be affected by the tendency to saturation. A sensitivity analysis of the estimated fractal dimension was performed using daily rainfall data by varying the series length, as well as the intensity threshold for the detection of rain. Editor Z.W. Kundzewicz; Associate editor S. Grimaldi Citation Ghanmi, H., Bargaoui, Z., and Mallet, C., 2013. Investigation of the fractal dimension of rainfall occurrence in a semi-arid Mediterranean climate. Hydrological Sciences Journal, 58 (3), 483–497. 相似文献
5.
Bellie Sivakumar 《地球表面变化过程与地形》2006,31(4):414-427
Suspended sediment load estimation at high resolutions is an extremely difficult task, because: (1) it depends on the availability of high‐resolution water discharge and suspended sediment concentration measurements, which are often not available; (2) any errors in the measurements of these two components could significantly influence the accuracy of suspended sediment load estimation; and (3) direct measurements are very expensive. The purpose of this study is to approach this sampling problem from a new perspective of fractals (or scaling), which could provide important information on the transformation of suspended sediment load data from one scale to another. This is done by investigating the possible presence of fractal behaviour in the daily suspended sediment load data for the Mississippi River basin (at St. Louis, Missouri). The presence of fractal behaviour is investigated using five different methods, ranging from general to specific and from mono‐fractal to multi‐fractal: (1) autocorrelation function; (2) power spectrum; (3) probability distribution function; (4) box dimension; and (5) statistical moment scaling function. The results indicate the presence of multi‐fractal behaviour in the suspended sediment load data, suggesting the possibility of transformation of data from one scale to another using a multi‐dimensional model. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
6.
Abstract Modelling and prediction of hydrological processes (e.g. rainfall–runoff) can be influenced by discontinuities in observed data, and one particular case may arise when the time scale (i.e. resolution) is coarse (e.g. monthly). This study investigates the application of catastrophe theory to examine its suitability to identify possible discontinuities in the rainfall–runoff process. A stochastic cusp catastrophe model is used to study possible discontinuities in the monthly rainfall–runoff process at the Aji River basin in Azerbaijan, Iran. Monthly-averaged rainfall and flow data observed over a period of 20 years (1981–2000) are analysed using the Cuspfit program. In this model, rainfall serves as a control variable and runoff as a behavioural variable. The performance of this model is evaluated using four measures: correlation coefficient, log-likelihood, Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results indicate the presence of discontinuities in the rainfall–runoff process, with a significant sudden jump in flow (cusp signal) when rainfall reaches a threshold value. The performance of the model is also found to be better than that of linear and logistic models. The present results, though preliminary, are promising in the sense that catastrophe theory can play a possible role in the study of hydrological systems and processes, especially when the data are noisy. Citation Ghorbani, M. A., Khatibi, R., Sivakumar, B. & Cobb, L. (2010) Study of discontinuities in hydrological data using catastrophe theory. Hydrol. Sci. J. 55(7), 1137–1151. 相似文献
7.
Pore structure heterogeneity is a critical parameter controlling mechanical, electrical and flow transport behaviour of rock. Multi-fractal analysis method was used for a heterogeneity comparison of three-dimensional rock samples with different lithology. Six real digital samples, containing three sandstones and three carbonates, were used. Based on the mercury injection capillary pressure test on these samples, we found that the carbonate samples are more heterogeneous than sandstones, but primary results of multi-fractal behaviours for all samples were similar. We show that if multi-fractal is used to evaluate and compare heterogeneity of different samples, one needs to follow some considerations such as (1) all samples must have the same size in pixel, (2) samples volume must be bigger than representative volume element, (3) multi-fractal dimensions should be firstly normalized to a determined porosity value and (4) multi-fractal results should be interpreted based on resolution of the imaging tool (effects of fine scale sub-resolution pores are missed). Results revealed that using normalized fractal dimensions, the real samples were divided to less and high heterogeneous groups. Moreover, the study of scale effect also showed that porous structures of these samples are scale invariant in a wide range of scales (from one to eight times bigger). 相似文献
8.
Edson Paixao Heather Auld M. Monirul Qader Mirza Joan Klaassen Mark W. Shephard 《水文科学杂志》2013,58(7):1067-1089
Abstract Southern Ontario, Canada, has been impacted in recent years by many heavy rainfall and flooding events that have exceeded existing historical estimates of infrastructure design rainfall intensity–duration–frequency (IDF) values. These recent events and the limited number of short-duration recording raingauges have prompted the need to research the climatology of heavy rainfall events within the study area, review the existing design IDF methodologies, and evaluate alternative approaches to traditional point-based heavy rainfall IDF curves, such as regional IDF design values. The use of additional data and the regional frequency analysis methodology were explored for the study area, with the objective of validating identified clusters or homogeneous regions of extreme rainfall amounts through Ward's method. As the results illustrate, nine homogeneous regions were identified in Southern Ontario using the annual maximum series (AMS) for daily and 24-h rainfall data from climate and rate-of-rainfall or tipping bucket raingauge (TBRG) stations, respectively. In most cases, the generalized extreme value and logistic distributions were identified as the statistical distributions that provide the best fit for the 24-h and sub-daily rainfall data in the study area. A connection was observed between extreme rainfall variability, temporal scale of heavy rainfall events and location of each homogeneous region. Moreover, the analysis indicated that scaling factors cannot be used reliably to estimate sub-daily and sub-hourly values from 24- and 1-h data in Southern Ontario. Citation Paixao, E., Auld, H., Mirza, M.M.Q., Klaassen, J. & Shephard, M.W. (2011) Regionalization of heavy rainfall to improve climatic design values for infrastructure: case study in Southern Ontario, Canada. Hydrol. Sci. J. 56(7), 1067–1089. 相似文献
9.
The presence of scaling statistical properties in temporal rainfall has been well established in many empirical investigations during the latest decade. These properties have more and more come to be regarded as a fundamental feature of the rainfall process. How to best use the scaling properties for applied modelling remains to be assessed, however, particularly in the case of continuous rainfall time‐series. One therefore is forced to use conventional time‐series modelling, e.g. based on point process theory, which does not explicitly take scaling into account. In light of this, there is a need to investigate the degree to which point‐process models are able to ‘unintentionally’ reproduce the empirical scaling properties. In the present study, four 25‐year series of 20‐min rainfall intensities observed in Arno River basin, Italy, were investigated. A Neyman–Scott rectangular pulses (NSRP) model was fitted to these series, so enabling the generation of synthetic time‐series suitable for investigation. A multifractal scaling behaviour was found to characterize the raw data within a range of time‐scales between approximately 20 min and 1 week. The main features of this behaviour were surprisingly well reproduced in the simulated data, although some differences were observed, particularly at small scales below the typical duration of a rain cell. This suggests the possibility of a combined use of the NSRP model and a scaling approach, in order to extend the NSRP range of applicability for simulation purposes. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
10.
The spatial scaling effect of continuous canopy Leaves Area Index retrieved by remote sensing 总被引：1，自引：0，他引：1
Leave Area Index (LAI) is one of the most basic parameters to describe the geometric structure of plant canopies. It is also important input data
for climatic model and interaction model between Earth surface and atmosphere, and some other things. The spatial scaling
of retrieved LAI has been widely studied in recent years. Based on the new canopy reflectance model, the mechanism of the scaling effect of
continuous canopy Leaf Area Index is studied, and the scaling transform formula among different scales is found. Both the
numerical simulation and the field validation show that the scale transform formula is reliable.
Supported by National Basic Research Program of China (Grant No. 2007CB714402) and National Natural Science Foundation of
China (Grant Nos. 40401036, 40734025 and 40401036) 相似文献
11.
This study investigated the spatial scaling properties of Canadian flood flows, namely, annual maximum mean 1‐, 5‐ and 7‐day flows using both the product moments (PMs) and probability weighted moments (PWMs). Both approaches demonstrate that flood flows in climatic regions 1 (Pacific), 2 (South British Columbia mountains), 3 (Yukon and northern British Columbia), 6 (Northeastern forest), 7 (Great Lakes and St. Lawrence rivers), 8 (Atlantic), and 10 (Arctic tundra) exhibit simple scaling with scaling exponent θ/H close to 0·90, while flood flows in regions 4 (Prairie provinces), 5 (Northwestern forest), and 9 (Mackenzie) does not with scaling exponent θ/H close to 0·50. The plots of coefficient of variations of flood flows versus drainage area indicate that Cv remains almost constant in regions 1, 2, 3, 6, 7, 8, and 10, while it decreases as drainage area increases in regions 4, 5, and 9. These results demonstrate that the index flood method is applicable in climatic regions 1, 2, 3, 6, 7, 8, and 10, while it is not in climatic regions 4, 5, and 9. The physical backgroud of the simple scaling of flood flows in most Canadian climatic regions is that snowmelt or rain‐on‐snow runoff is a dominant flood‐generating mechanism across the country. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
12.
IntroductionEarthquake occurrence is resulted from the movement of the Earth's crust and the fr~re ofrock. It is a phenomenon of instability and self-organized criticality. It is possible that the phenomenon only occurs in non-linear syStem. As a pat of non-linear science, the fractal thatfounded by Mandelbrot in 1977 pioneered a new way tO solve inhomogeneous and complex phenomenon and offered a new tool. Some natural or social phenomena seem difficult to deal withbecause they are disordere… 相似文献
13.
The use of the exponent K(q) function to delimit homogeneous regions in regional frequency analysis of extreme annual daily rainfall 
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下载免费PDF全文 A. P. García‐Marín J. Estévez C. Sangüesa‐Pool R. Pizarro‐Tapia J. L. Ayuso‐Muñoz F. J. Jimenez‐Hornero 《水文研究》2015,29(1):139-151
The regional frequency analysis of extreme annual rainfall data is a useful methodology in hydrology to obtain certain quantile values when no long data series are available. The most crucial step in the analysis is the grouping of sites into homogeneous regions. This work presents a new grouping criterion based on some multifractal properties of rainfall data. For this purpose, a regional frequency analysis of extreme annual rainfall data from the Maule Region (Chile) has been performed. Daily rainfall data series of 53 available stations have been studied, and their empirical moments scaling exponent functions K(q) have been obtained. Two characteristics parameters of the K(q) functions (γmax and K(0)) have been used to group the stations into three homogeneous regions. Only five sites have not been possible to include into any homogenous regions, being the local frequency analysis of extreme daily rainfall the most appropriate method to be used at these locations. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
14.
In this work, the multifractal properties of hourly rainfall data recorded at a location in Southern Spain have been related to the scale properties of the corresponding intensity–duration–frequency (IDF) curves. Four parametric models for the IDF curves have been fitted to the quantiles of rainfall obtained using the generalized Pareto frequency distribution function with the extreme data series obtained for the same place. The scaling of the rainfall intensity moments has been analysed, and the empirical moments scaling exponent function has been obtained. The corresponding values of q1 and γ1 have been empirical and theoretically calculated and compared with some characteristics of the different IDF models. Thus, the scaling behaviour of IDF curves has been analysed, and the best model has been selected. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
Comparing satellite derived precipitation datasets using the Hillslope River Routing (HRR) model in the Congo River Basin 总被引：1，自引：0，他引：1
R. E. Beighley R. L. Ray Y. He H. Lee L. Schaller K. M. Andreadis M. Durand D. E. Alsdorf C. K. Shum 《水文研究》2011,25(20):3216-3229
In this paper, three satellite derived precipitation datasets (TRMM, CMORPH, PERSIANN) are used to drive the Hillslope River Routing (HRR) model in the Congo Basin. The precipitation data are compared spatially and temporally in two forms: (1) precipitation magnitudes, and (2) resulting streamflow and water storages. Simulated streamflow is assessed using historical monthly discharge data from in situ stream gauges and recent stage data based on water surface elevations derived from ENVISAT radar altimetry data. Simulated total water storage is assessed using monthly storage change values derived from GRACE data. The results show that the three precipitation datasets vary significantly in terms of magnitudes but generally produce a reasonable hydrograph throughout much of the basin, with the exception of the equatorial regions of the watershed. The satellite datasets provide unreasonably high values for specific periods (e.g. all three in Oct–Nov; only CMORPH and PERSIANN in Mar–Apr) in the equatorial regions. Overall, TRMM (3B42) provides the best spatial and temporal distributions and magnitudes or rainfall based on the assessment measures used here. Both CMORPH and PERSIANN tend to overestimate magnitudes, especially in the equatorial regions of the Basin. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
16.
ENSO and the natural variability in the flow of tropical rivers 总被引：1，自引：0，他引：1
Kishan N. Amarasekera Robert F. Lee Earle R. Williams Elfatih A. B. Eltahir 《Journal of Hydrology》1997,200(1-4):24-39
This paper examines the relationship between the annual discharges of the Amazon, Congo, Paran á, and Nile rivers and the sea surface temperature (SST) anomalies of the eastern and central equatorial Pacific Ocean, an index of El Niño-Southern Oscillation (ENSO). Since river systems are comprehensive integrators of rainfall over large areas, accurate characterization of the flow regimes in major rivers will increase our understanding of large-scale global atmospheric dynamics. Results of this study reveal that the annual discharges of two large equatorial tropical rivers, the Amazon and the Congo, are weakly and negatively correlated with the equatorial Pacific SST anomalies with 10% of the variance in annual discharge explained by ENSO. Two smaller subtropical rivers, the Nile and the Paraná, show a correlation that is stronger by about a factor of 2. The Nile discharge is negatively correlated with the SST anomaly, whereas the Paraná river discharge shows a positive relation. The tendency for reduced rainfall/discharge over large tropical convection zones in the ENSO warm phase is attributed to global scale subsidence associated with major upwelling in the eastern Pacific Ocean. 相似文献
17.
Bellie Sivakumar Ashish Sharma 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(4):451-459
High-resolution temporal rainfall data sequences serve as inputs for a range of applications in planning, design and management
of small (especially urban) water resources systems, including continuous flow simulation and evaluation of alternate policies
for environmental impact assessment. However, such data are often not available, since their measurements are costly and time-consuming.
One alternative to obtain high-resolution data is to try to derive them from available low-resolution information through
a disaggregation procedure. This study evaluates a random cascade approach for generation of high-resolution rainfall data
at a point location. The approach is based on the concept of scaling in rainfall, or, relating the properties associated with
the rainfall process at one temporal scale to a finer-resolution scale. The procedure involves two steps: (1) identification
of the presence of scaling behavior in the rainfall process; and (2) generation of synthetic data possessing same/similar
scaling properties of the observed rainfall data. The scaling identification is made using a statistical moment scaling function,
and the log–Poisson distribution is assumed to generate the synthetic rainfall data. The effectiveness of the approach is
tested on the rainfall data observed at the Sydney Observatory Hill, Sydney, Australia. Rainfall data corresponding to four
different successively doubled resolutions (daily, 12, 6, and 3 h) are studied, and disaggregation of data is attempted only
between these successively doubled resolutions. The results indicate the presence of multi-scaling behavior in the rainfall
data. The synthetic data generated using the log–Poisson distribution are found to exhibit scaling behaviors that match very
well with that for the observed data. However, the results also indicate that fitting the scaling function alone does not
necessarily mean reproducing the broader attributes that characterize the data. This observation clearly points out the extreme
caution needed in the application of the existing methods for identification of scaling in rainfall, especially since such
methods are also prevalent in studies of the emerging satellite observations and thus in the broader spectrum of hydrologic
modeling. 相似文献
18.
《Journal of Atmospheric and Solar》2007,69(15):1825-1832
Multi-fractal analysis under the self-organized criticality (SOC) hypothesis is performed for the VHF electromagnetic noises observed before an earthquake. A rather strong (M=7.2) earthquake took place in the off-sea of Sendai, and we have utilized the corresponding VHF noise (at 49.5 MHz) data at several stations in the Tohoku area. Among the three observing stations used for analysis, the VHF data only at one station (Kunimi) have exhibited significant precursors; that is, a significant increase in multi-fractal complexity at the last stage of the rupture. The use of fractal analysis enables to sort out the lithospheric effect following the SOC, among the few possible noise sources at VHF. The change observed only at this station might be related with the geological structure around this station because there are fault regions around the station. 相似文献
19.
We investigate the time dynamics of monthly rainfall series intermittently recorded on seven climatic stations in northern Lebanon from 1939 to 2010 using the detrending fluctuation analysis (DFA) and the Fisher-Shannon (FS) method. The DFA is employed to study the scaling properties of the series, while the FS method to analyze their order/organization structure. The obtained results indicate that most all the stations show a significant persistent behavior, suggesting that the dynamics of the rainfall series is governed by positive feedback mechanisms. Furthermore, we found that the Fisher Information Measure (the Shannon entropy power) seems to decrease (increase) with the height of the rain gauge; this indicates that the rainfall series appear less organized and less regular for higher-located stations. Such findings could be useful for a better comprehension of the climatic regimes governing northern Lebanon. 相似文献
20.
Vegetation indices derived from remote sensing data still remain to be used for analysing the relationship between climatic factors and vegetation seasonal phenology in middle latitudes with subtropical conditions forests such as the Canarian laurel forest. The Garajonay National Park, located in the La Gomera Island, protects one of the best preserved examples of the Macaronesian laurel forest, due to the cloud banks produced by trade winds, with rainfall and temperature field data showing a clear Mediterranean climatic pattern. We have analysed seasonal vegetation indices trend for different types of forest inside the Garajonay National Park using normalized difference vegetation index (NDVI) and enhanced vegetation index (EVI) products derived from moderate resolution imaging spectrometer (MODIS) Aqua data for two hydrological years (October 2003 to September 2005) in relationship with the existing field climatic data: rainfall, net fog water and temperature. Maximum annual EVI maps show the highest vegetation indices in the laurel forest of La Gomera that occur during the dry season, mainly in late spring to early summer, with EVI temporal profiles showing that valley‐bottom laurel forest areas have the most clear seasonal trend. Difference maps of EVI values between months with the lowest and highest rainfall of each hydrological year clearly confirm the highest photosynthetic activity in the laurel forest during the dry season. In addition, these forests show a significative temporal correlation between EVI values and the temperature in the forest (p < 0·001). Our results prove the absence of summer drought stress in the laurel forest implying that the fog drip income is high enough to maintain enough soil moisture to allow the forest fully transpire when temperatures are higher. As the laurel forest of La Gomera occurs in the main recharge area of the island's aquifer system, our analysis of EVI data suggests that fog drip constitutes a key hydrological factor. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献