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This chapter discusses aspects of the statistical analysis of trends in extremes of precipitation (typically maximum intensities, of different durations) and streamflow (typically annual maximum instantaneous discharges; annual maximum mean daily discharges). An important feature of such data is that they are unlikely to follow a Gaussian distribution, so that analyzing for trend using theory based on the Normal distribution (e.g., regression analysis) is no longer appropriate. Although non-parametric methods can be used to test for trend, they do not provide a means for estimating the probability of occurrence of extremes in future periods. The parametric methods described in this chapter deal with analyses of trend in annual maxima (e.g., annual maximum one-day rainfall), and in “peaks over a threshold” (POT) approach, in which a threshold event is selected, and all events larger than this threshold are included for analysis. Analytical techniques are illustrated with examples from the La Plata basin; adaptations are presented for cases where records are only partially complete, and the concept of return period in the presence of non-stationarity is discussed. 199 CHAPTER STATISTICAL ANALYSIS OF EXTREME EVENTS IN A NON-STATIONARY CONTEXT ABSTRACT Robin Clarke 1 1 Instituto de Pesquisas Hidráulicas, UFRGS, in Porto Alegre, RS Brazil. XV
15.1. Introduction Statistical analysis of extreme events in a non-stationary context At a time when the possibility of climate change might be bringing about extreme events of increasing severity, good analytical procedures are required to detect the existence of trends in extreme values of hydrological variables, such as rainfall intensity and peak discharges; of meteorological variables such as extreme wind speeds, the frequency of hurricane occurrence, and the frequency and intensity of hail storms; and of oceanographic variables such as the magnitude and frequency of occurrence of large waves. This section is concerned with some aspects in the statistical analysis of trends in extremes of precipitation (typically maximum intensities, of different durations) and streamflow (typically annual maximum instantaneous discharges; annual maximum mean daily discharges). Irrespective of the existence of trend, two approaches to the analysis of extremes are possible: (a) the “Block” method, in which a period is selected, commonly of one year's duration, and the maximum of a variable of interest (for example discharge) is selected from each block, thus giving rise to a series of annual events that are used to draw inferences about the distribution of extreme events, the presence or absence of trend, and - where no trend exists - on the return period of events of interest. (b) the “peaks over a threshold” (POT) approach, in which a threshold event is selected. In the case of flood discharges and rainfall intensities, all events (“peaks”) exceeding the threshold are used for analysis; the threshold event is taken as one which commonly gives about three or four peaks over the threshold, on average, in any year. This approach has the advantage that more data are included for analysis than in the “Block” method, a point of particular importance when records are of limited length (in the Block method, only one observation is used per year). This section discusses aspects of both the Block and POT methods. Both approaches are very fully described in the book by Coles (2001). In the above paragraph, the account given of the POT method referred to peaks over a threshold because one of the principal applications has been in the analysis of flood frequencies. However in principle there is no theoretical reason why the selected events should not lie below the threshold, as when drought periods are of interest. Where used in flood frequency analysis, a possible limitation of the POT method in the particular context of large drainage basins of South America is that the annual hydrograph (that is, the plot of discharge against time) is smooth, typically showing just one well-defined maximum and one well-defined minimum. For basins of this kind, the peaks of the POT method are identical with the annual maxima of the Block approach, and the two methods are indistinguishable. However, the POT approach will still be useful for frequency analysis of runoff records from small basins which respond rapidly to rainfall, and where runoff records are short. An important requirement for the POT approach is that the “peaks” be independent of each other. This will not be the case where, for example, the peaks occur in “clusters”; if, for example, a threshold of 40mm were selected when analyzing a series of daily rainfall, one storm might perhaps give rise to two 200
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CLIMATE CHANGE IN THE LA PLATA BASI
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INDEX FOREWORD . . . . . . . . . .
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7.3. Methodology . . . . . . . . .
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13.3. Regional validation of GCM fo
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1.1. Dropping the hypothesis of sta
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Introduction as they pour water ove
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A better understanding of the obser
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References Introduction Barros, V.
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ABSTRACT The hydrologic cycle of th
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La Plata basin climatology Within t
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in this last description, although
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warm season (October-April), in the
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La Plata basin climatology b. Upper
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La Plata basin climatology 2.3.3. R
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La Plata basin climatology Fig. 2.8
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2.3.7. West and South borders La Pl
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References La Plata basin climatolo
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La Plata basin climatology Robertso
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3.1. Introduction Interannual low f
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Interannual low frequency variabili
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1989). This signal varies along eac
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Interannual low frequency variabili
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The main physiographic and hydrolog
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SUB-BASIN COUNTRY Argentina Bolivia
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the most important stretches of the
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Physiography and Hydrology The Para
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Physiography and Hydrology The Pant
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Physiography and Hydrology forcings
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Physiography and Hydrology It is no
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Physiography and Hydrology tion of
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Physiography and Hydrology INTERNAV
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5.1. Introduction Precipitation and
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From 1956 to 1991, in most of the A
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-15 -20 -25 -30 -35 -40 -15 -20 -25
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Regional precipitation trends 5.3.2
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Regional precipitation trends and L
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trast, other regions suffer floodin
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ABSTRACT The main hydrological tren
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Following are the observed changes:
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In the case of the Paraná River th
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Hydrological trends In order to com
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Hydrological trends In table 6.1 it
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Hydrological trends On the other ha
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the central area of the high basin
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7.1. Introduction Several authors,
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Real evaporation trends a) PET > Pi
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a) b) c) Mean Temperature Real evap
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The positive trends of the mean tem
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d) e) f) Mean Temperature Real evap
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7.5. Discussion and final comments
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ABSTRACT The water, as resource, is
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puts in risk large number of person
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The main services and problems of w
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There are similar problems in diffe
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8.3.3. Energy a. Hydroelectric depe
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(chapters 12 and 13), because of th
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The main services and problems of w
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9.1. Introduction The emissions of
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9.4. Greenhouse effect The atmosphe
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Temperature anomalies (°C) 0.8 0.6
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Global climatic change at a global
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In view of the unavoidability of th
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Background on other regional aspect
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Considering the non-linear interact
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SST anomalies also have influence o
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ABSTRACT The purpose of this chapte
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Global climate models Mid-1970’s
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Global climate models Table 11.1. B
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Global climate models Table 11.2. M
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Page 155 and 156: of the global climate system to the
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Page 161 and 162: Climate scenarios From Table 12.2 i
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Page 175 and 176: Regional climatic scenarios Fig. 13
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Page 185 and 186: Low-frequency variability 14.1. Bac
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Page 191 and 192: 14.4. SST composites Low-frequency
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Page 199: Low-frequency variability Mantua, N
Page 203 and 204: Statistical analysis of extreme eve
Page 217 and 218: CURRÍCULA OF THE AUTHORS Vicente B
Page 219 and 220: Curricula of the autors Rubén Mari
Page 221: Proyect: SGP II 057: “Trends in t
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