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Technical Report No. 11

INDICES FOR DIFFERENT TYPES OF DROUGHTS AND FLOODS AT DIFFERENT SCALES

Henny A.J. van Lanen, Zbigniew W. Kundzewicz, Lena M. Tallaksen, Hege Hisdal, Miriam Fendeková & Christel Prudhomme

First version: 24 December 2008

Technical Report No. 11 ii

WATCH is an Integrated Project Funded by the European Commission under the Sixth Framework Programme, Global Change and Ecosystems Thematic Priority Area (contract number: 036946). The WACH project started 01/02/2007 and will continue for 4 years.

Title: Indices for different types of droughts and floods at different scales Authors: Henny A.J. van Lanen, Zbigniew W. Kundzewicz, Lena M. Tallaksen,

Hege Hisdal, Miriam Fendeková & Christel Prudhomme

Organisations: - Wageningen University - Hydrology and Quantitative Water Management Group (WUR) - Research Centre for Agricultural and Forest Environment, Polish Academy of Sciences, Poznan (PAS) - University of Oslo – Department of Geosciences (UiO) - Norwegian Water Resources and Energy Directorate, Oslo (NVE) - Comenius University, Bratislava (UC) - Centre for Ecology and Hydrology (CEH Wallingford)

Submission date: December 2008

Function: This report is an output from Work Block 4; Task 4.2.1 Drought and flood indices at different scales. It is an open report (Version 1) implying that the report has a preliminary nature and that it will be further completed and revised until 1 November 2010.

Deliverable WATCH deliverable D 4.2.1 and contributes to M4.2-5.

Photos cover: flooding River Meuse (1995) dry river bed in the Upper-Guadiana Basin (2008)

Technical Report No. 11 iii

Table of Contents Page 1. Introduction 1 2. Drought indices 3 2.1. At site indices 3 2.1.1. Streamflow indices 3 2.1.2. Groundwater drought indices 5 2.2. Areal drought indices 8 3. Flood indices 11 3.1. At-site indices 11 3.1.1. Annual maxima and QMED 11 3.2.1. Peak-Over-Threshold 12 3.2. Areal flood indices 12 4. Concluding remarks 14 References 15

Technical Report No. 11 1

1. Introduction One of the most important steps in the analysis of hydrological extremes is to decide on the hydrological characteristics to be studied (e.g. Hisdal et al, 2004). Drought and floods affect many sectors in society and therefore there is a need for different ways of defining or characterizing these extreme events. Data availability and climatic and regional characteristics will influence the choice. Therefore no single drought or flood characteristic is suitable to assess and describe hydrological extremes for any type of analyses in any region. However, it is important to be aware of how various ways of characterizing a drought or flood might lead to different conclusions regarding the hydrological extreme phenomenon. When calculating drought or flood characteristics it is important to be aware of the processes underlying the generation of the hydrological extreme. For example, floods can be generated through intense, and long-lasting rainfall, snowmelt or flow obstruction (e.g. ice jam, landslide). Droughts can be caused either by low precipitation often combined with high evaporation losses, or result from precipitation being stored as snow (e.g. van Lanen et al., 2004). This task will be building on experiences from the EC–supported project ASTHyDA (Hisdal et al., 2004) and others for the floods, identify and define physical indices (simple and composite) for droughts and floods. In the WATCH project the floods are restricted to large-scale floods. For the droughts different types will be distinguished (soil moisture, groundwater, streamflow). These indices will contribute to the analyses undertaken in WP4.1 “Detection and attribution of extremes in the 20th century”, WP4.3 “Likely frequency, severity and scale of future extremes” and will be used in WB6 “Assessing the vulnerability of global water resources” to develop indicators of water resources stress. The task will focus especially on the development of indices for gridded output from large-scale models (e.g. GHMs and LSHMs) at the regional and global scale and will represent the associated spatial aspects of the hydrological extremes (most indices presently apply at the river basin scale). The indices will be tested for different hydro-climatological regions around the world. The research undertaken in Task 4.2.1 Drought and flood indices at different scales, will be carried out in two phases. Phase 1 is an inventory of existing indices, which are readily available to the authors. The outcome is included in this Technical Report (Version 1). Clearly, the list with indices is not complete in this phase. For instance, overviews by Wilhite & Glanz (1985), Smakhtin & Toulouse (1998), Heim (2002), Smakhtin & Huges (2004) and Kallis (2008) or the EU project CECELIA1 are not included yet. The technical document is an open report implying that the it has a preliminary nature and that it will be finalized during the second part of the WATCH project (phase 2). This preliminary report does not include yet: - low streamflow indices, but only streamflow drought indices (for the difference between low

streamflow and streamflow drought indices, readers are referred to Hisdal et al. (2004); - meteorological (e.g. precipitation, temperature) or soil moisture indices, but only groundwater and

streamflow drought indices. For example the widely used Standardized Precipitation Index (SPI) is not described yet. The SPI an index based on the probability of precipitation for any time scale (McKee et al., 1993);

- complex indices, such as the Palmer Drought Severity Index (PDSI) and the Surface Water Supply Index (SWSI). The PDSI is a meteorological drought indicator that also addresses soil moisture (Palmer, 1965). The SWSI is The SWSI is designed to complement the PDSI and also includes snowpack, streamflow, and reservoir storage (Shafer & Dezman, 1982);

- indices suitable for the analysis of gridded output from large-scale models. 1 CECELIA: Central and Eastern Europe Climate Change Impact and Vulnerability Assessment, http://www.cecilia-eu.org/


Chapter 2 provides indices for drought. A difference has been made between indices that are used for at-site analyses and areal analyses. For the at-site analysis, streamflow and groundwater have been separated. Chapter 3 proceeds with indices for large-scale floods. Like for droughts, it also includes indices for at-site analysis and areal analyses. The report concludes with some remarks.


2. Drought indices Firstly drought indices are described that are derived from a gauging station (streamflow indices) or from a groundwater observation well (groundwater indices). Next indices that reflect areal drought characteristics are explained. 2.1. At site indices In a drought situation flows are low or even zero and groundwater levels are low. A drought index is a single number that characterizes the drought behaviour of streamflow or groundwater. As opposed to low flow indices such as percentiles from the flow duration curve, the mean annual minimum flow or the Base Flow Index, drought indices are based on defining a threshold below which the flow or groundwater is regarded as being in a drought situation. It is then possible to define the start, the end, the total duration and the deficit volume of drought events, and various drought indices or statistics can be derived. 2.1.1. Streamflow indices Streamflow deficits are periods when the river is below a defined threshold which defines a drought or critical deficit (Hisdal et al., 2004). There are two main methods to select and characterize deficits, the threshold level method and the sequent peak algorithm initially used for reservoir storage-yield analysis. The threshold level method is used for providing estimates of the frequency of low flow periods and for designing and operating regulating reservoirs where reservoir releases are made to support downstream abstractions. Examples of water use include hydropower, public water supply and irrigation. Figure 2.1 shows the definition of the timing, durations and volumes of deficits below a threshold discharge in a river. Streamflow deficits can also be characterized by intensity and spatial extent. The threshold level method was initially named the “method of crossing theory” and is also referred to as “run sum analysis” because it generally studies runs below or above a given threshold. A detailed discussion of the method applied to a global data set is given in Fleig et al. (2006).

Time (days)

Flow

(m3 s

-1)

d 1 d 2 d 3 d 4v 2

Q min

v 3 v 4v 1Q 0

Figure 2.1 Definition of deficit characteristics (modified from Hisdal et al., 2004; reproduced by permission of Elsevier) The threshold level Q0, is also referred to as the truncation level and is used to define whether the flow in a river is in a deficit (Figure 2.1). The deficit starts when the flow goes below the threshold and ends


as soon as the flow returns above the threshold. In this way the beginning and the end of a deficit period can be defined. In addition the following deficit characteristics can be defined: • the duration - the period of time where the flow is below the threshold level, also referred to as

drought duration, low flow spell or run-length (di, Figure 2.1); • the volume or severity, also referred to as drought volume or run-sum (vi, Figure 2.1); • the intensity also referred to as deficit or drought magnitude, mi, the ratio between deficit volume

and deficit duration; • the minimum flow of each deficit event (Qmin, Figure 2.1); • the time of occurrence, for example the starting date, the mean of the onset and termination, or

the date of the minimum flow. Based on the time series of the deficit characteristics it is possible to derive indices, such as the average deficit duration or average deficit volume. Details about the method, including the choice of threshold level can be found in Hisdal et al. (2004) A procedure for preliminary design of reservoirs based on annual average streamflow data is the mass curve or its equivalent, the Sequent Peak Algorithm (SPA) (e.g. Vogel & Stedinger, 1987). SPA can also be used for daily data to derive drought events. Let Qt denote the daily inflow to a reservoir and Q0 the desired yield or any other predefined flow, then the storage St required at the beginning of the period t reads (Tallaksen et al., 1997):

−+

= −

otherwise, 0positiveif,01 tt

t

QQSS

An uninterrupted sequence of positive St, {St, t=τ0,…,τe}, defines a period with storage depletion and a subsequent filling up (Figure 2.2). The required storage in that period, max{S}, defines the drought deficit volume (vi) and the time interval, di, from the beginning of the depletion period, τ0, to the time of the maximum depletion, τmax, defines the drought duration (τmax-τ0+1= di).

Time (e.g days)

Flow

bel

ow th

resh

old

Req

uire

d st

orag

e

v i

d i

Figure 2.2 Definition of drought events using the sequent peak algorithm (SPA) method (modified from Tallaksen et al., 1997. Reproduced by permission of IAHS press.) This technique differs from the threshold level method in, that those periods when the flow exceeds the yield do not necessarily negate the storage requirement, and that several deficit periods may pass before sufficient inflow has occurred to refill the reservoir. Hence, based on this method two droughts are pooled if the reservoir has not totally recovered from the first drought when the second drought begins (St>0).


Many low flow indices exist and as illustrated, there are many indices to characterise droughts. The choice of index, or indices, for a specific study depends primarily on the purpose of the study but also on available data and the hydrological regime under study. However, even after the purpose has been well defined, there often are several indices that could be used. By studying the interrelationship between indices their similarity can be described and it will be easier to see how many indices that are needed to describe the most important aspects of the drought. A study of the interrelationship between low flow indices is described in Hisdal et al. (2004). Regarding drought indices, close relationships between indices have been found, for example, between drought duration and volumes (Zelenhasic & Salvai, 1987; Clausen & Pearson, 1995) and between drought deficit duration and volume and BFI (Clausen & Pearson, 1995). However, weak relationships were found between drought duration and percentiles from the FDC (Smakhtin & Toulouse, 1998). 2.1.2. Groundwater drought indices Groundwater is seldom incorporated in drought analyses. In an extensive overview of drought definitions by Wilhite & Glanz (1985) groundwater is mentioned only once as one of the variables that should be monitored. In the past many authors considered groundwater drought to result from over-exploitation of groundwater resources, rather than resulting from the natural variability of the climate (Day & Rodda, 1978). Thus there is only limited experience using groundwater drought characteristics that can be derived from variables such as groundwater recharge, levels, discharge and spring discharge. In recent years the number of groundwater drought studies has increased, e.g. to study the regional character of groundwater drought (Chang & Teoh, 1995). A recent study by Peters et al. (2003; 2006) is the first that investigates groundwater drought in a systematic way. Some examples of groundwater droughts with different characteristics are presented below. The threshold method (Section 2.1.1) is also used to define groundwater drought. However, the approach cannot straightforwardly be used to calculate the total deficit in groundwater head as the head is a state variable and not a flux. Rather than summing up the deficit in each time step as done for the flux, the average deficit is calculated. The deficit volume in head for a drought event is thus defined as the sum of deviations from the threshold over an uninterrupted number of timesteps with a head below the threshold divided by the number time steps in a drought (Fig. 2.3).

Figure 2.3 Groundwater drought characteristics derived from the groundwater hydrograph using the threshold approach.


In addition to the deficit volume, other drought characteristics can be derived, such as the onset, the duration, the maximum deviation and the deficit volume over maximum deviation. The sequent peak algorithm (Section 2.2.1) is inappropriate to characterize groundwater drought because groundwater is a state variable. Baseflow Drought Index The index describing the baseflow drought, which is developed by the Comenius University, also uses the threshold level method. The following procedure was applied to derive the baseflow drought index: a. daily streamflow for the period of at least 30 years were used for derivation of the baseflow for each

day (except of number of days in the beginning and end of the calculation period depending on the selected procedure);

0

0,5

1

1,5

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0 10 20 30 40 50 60 70 80 90 100

Percentiles

Base

flow

[m3 /s

]

1951 1952 1953 1954 19551956 1957 1958 1959 19601961 1962 1963 1964 19651966 1967 1968 1969 19701971 1972 1973 1974 19751976 1977 1979 1980 19811982 1983 1984 1985 19861987 1988 1989 1990 19911992 1993 1994 1995 19961997 1998 1999 2000 20012002 2003 2004 2005 Average_BF_30

Figure 2.4 Baseflow duration curves and the master curve (Average_BF_30) for the Nedozery gauging station (River Nitra pilot basin) b. the BF+2.0 programme (Gregor, 2008) was developed to calculate the baseflow. The programme is

based on the original procedure of the Institute of Hydrology (1980) implementing suggestions proposed by Tallaksen & van Lanen (2004). The program enables utilization of x-day non-overlapping consecutive periods for calculation of the minimum discharge values used for the identification of the baseflow hydrograph. X-day represents different length of the periods starting from 5 through 10, 15 and 20 up to 30 days. Introduction of different period’s length was conditioned by the fact that the 5-day period used in the original BFI method of the Institute of Hydrology (1980) overestimated the baseflow in comparison with other methods (procedure of Kille and others) widely used for the baseflow calculation for the complicated hydrogeological conditions of the Slovak Republic. The BF +2.0 programme comprises also some other methods used for baseflow estimation;

c. the daily baseflow was calculated for different x-day periods (5 to 30 days);


d. flow duration curves of baseflow values (baseflow duration curves) for each hydrological year (from November 1st to October 31st of the next year) were constructed for the period 1951 – 2005 (Fig. 2.4). The graph shows the baseflow duration curves based on the 30-day baseflow estimation procedure (QB30 values);

e. the master baseflow duration curve was calculated as the arithmetic mean values for percentiles of 0.1, 1, 5, 10, 20, 30, 50, 60, 70, 80, 90, 95, 99, 99.9;

f. the master baseflow duration curves were constructed; g. average baseflow estimated using 5-day and 30-day baseflow periods were compared with the

mean baseflow value estimated by method of Kille; h. baseflow derivation using a 30-day period is more representative, i.e. shows a smaller difference in

comparison with the long-term average baseflow calculated by the method of Kille; i. threshold levels of QB5_90 (90th percentile of baseflow using a 5-day averaging period) and

QB30_90 (90th percentile of baseflow using a 30-day averaging period) were tested as the groundwater drought descriptors indicating baseflow drought occurrence;

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Time [days]

Base

flow

[m3 /s

]

daily BF BF30_90 BF30_80 BF30_70

Figure 2.5 Daily baseflow and three groundwater drought thresholds for the Nedozery gauging station (River Nitra pilot basin). j. time series of daily baseflow were constructed with implementing of the QB30_90 QB30_80 and

QB30_70 values as different groundwater drought threshold levels characterizing the drought severity. An example of results is given in Fig. 2.5. The evaluated time period was extended up to 1941, the baseflow was cut on the value of 5.0 m3 s-1 (the highest baseflow reaches 62.8 m3 s-1. The cut of values on the y-axis was used for enabling visualisation of the low flow values;

k. the classification scheme of the groundwater drought occurrence could be as follows. It is proposed to classify the years according to the baseflow (QB) as years with extremely low baseflow (average yearly baseflow is less than 70% of its long-term average), very low baseflow (QB lies in the interval of 70 – 79%) and low baseflow (QB in the interval of 80 – 89%). Years with the QB within the interval of 90 –110 % of the long-term average baseflow are classified as normal years. Also severity could be classified using the same threshold levels: baseflow below the threshold value of 70% of QB long-term average characterizes extremely severe groundwater drought, baseflow ranging in the interval 70 – 79% characterizes very severe drought and baseflow within the interval


of 80 – 89% characterizes severe drought occurrence. QB above the threshold level of QB90 characterize no drought occurrence;

l. periods of baseflow drought were identified in the late 1940s, late 1980s to early 1990s of the last century and in the 2003-2005 period;

m. more frequent baseflow drought occurrence in the 21st century (Fig. 4.5); n. identification of x-day length suitable for baseflow estimation in various typical hydrogeological

conditions will be further studied. As shown above (Fig. 2.5), drought in groundwater discharge is not derived from the whole streamflow hydrograph, but a hydrograph separation technique is used. The separation techniques can use only streamflow, but also other hydrological variables, such as groundwater head (e.g. Peters & van Lanen, 2005). 2.2. Areal drought indices Drought affects all components of the water cycle as it develops from its origin as a meteorological drought through a deficit in soil moisture, reduced groundwater recharge and levels, and finally shows up as a low streamflow or dried-up river. Regional characteristics, such as the area covered by the drought and the total deficit over an area, are thus important measures of the severity of the event. The methods presented in this section can be applied to time series of hydrometeorological variables like precipitation, soil moisture, groundwater and streamflow (observed or simulated) as well as time series of derived drought indices. Apart from streamflow, which is by nature an areal value observed at-site, observations are point values that need to be aggregated in space. Areal values can be obtained by spatial interpolation and model simulations. Spatial variability in drought properties like the area affected, varies in time as the drought develops, sustains and finally resolves. The space-time characteristics of a drought can be analysed in several ways depending on the purpose of the study and data available. Here two main approaches are described:

I. Analysis of spatial patterns of at-site drought indices by displaying results on maps as point values, isolines or area units;

II. Derivation of regional or catchment scale drought characteristics where the area covered is incorporated in the characterisation of the event, e.g. the total deficit over the area.

In the first approach drought indices are derived separately for individual points or area units, whereas in the second approach values of individual area units are aggregated over the area or region of interest. Drought characteristics can be compiled for a given date (instantaneous), averaged over a given time period, or displayed as a development over time. Given that time series of sufficient length exist, the frequency and probability of occurrence of a given historical event can be derived. This includes analysis of regional drought characteristics as presented in Section 2.2.2. 2.2.1 Analysis of spatial patterns of at-site droughts At-site droughts can be characterized by several indices as described in Section 2.1. The indices are derived based on observations or model simulations and can represent both point values (e.g. observed precipitation and soil moisture), and areal values (e.g. observed streamflow or modeled soil moisture). In either case the spatial variability can be analysed by simply displaying the results on a map using a coding system like coloring, for instance Zaidman et al. (2001) for at-site streamflow indices in Europe and Sheffield & Wood (2007) for gridded drought indices at the global scale. Additionally, isolines have


been used to spatially map point values, e.g. the 1976 summer rainfall in England (Beran & Rodier, 1985) or areal values, e.g. gridded drought duration (1976) in recharge (Peters et al., 2006). Similar techniques can also be used to mapped the spatial pattern of composite or derived indices like the Palmer Drought Severity Index (PDSI), using either point values (e.g. Wheaton et al., 2005; Figure 2.6) or area averages (e.g. Soule, 1992).

Figure 2.6 Spatial comparison of major droughts of 2002, 2001, 1988, 1961, and 1931 using the summer (June, July, August) Palmer Drought Severity Index isoline of -2 (from Wheaton et al., 2005). 2.2.2 Regional drought characteristics The threshold level method, which defines drought as periods during which the variable is below a certain threshold level, has proved to be a flexible approach for characterizing various types of drought (Section 2.1), and is frequently used to define drought events also at the regional scale. Regional drought characteristics can be derived based on gridded time series of observed (e.g. rainfall) or simulated variables (e.g. groundwater recharge). In Figure 2.7 the average area covered by drought in recharge is displayed as a percentage of the total catchment area. Other spatial resolutions, like polygons are also applicable. Drought events are selected from the time series of the individual areal units and all events below the threshold are included. Commonly a percentile from the duration curve is used as a threshold and calculated separately for each area unit and variable to identify whether the unit is experiencing drought or not. As drought is viewed as an event covering a certain spatial scale, it has been suggested to impose a second threshold or minimum area in the definition of the drought event, i.e. a drought exists only if a certain percentage of the catchment area is experiencing a deficit in each time step (Santos, 1983). Regional or catchment scale drought characteristics are then derived for each variable and event, like:

i. the duration of the drought (number of consecutive months where a minimum area is experiencing drought in each time step);

ii. the area covered by the drought (summed up over all areal units); either at a given time step, or as an average or maximum area covered for each event;

iii. the deficit volume of the drought, e.g. the sum of the average deficit volume (averaged over all affected units) for each time step in a drought.


The approach applies to a wide range of spatial scales and variables. For instance at the catchment scale for studying the propagation of drought in different variables (Peters et al., 2006; Tallaksen et al., 2006), and at the regional scale covering the whole of Denmark (Hisdal & Tallaksen, 2003).

Figure 2.7 Simulated recharge in the Pang catchment (left; from Peters et al., 2006) and average area covered (in %) for single drought event using a minimum area threshold of 20% (right; number of events on the y-axis). A general approach for estimating regional drought characteristics is through stochastic modelling of monthly precipitation as reviewed by Rossi et al. (1992). In Hisdal & Tallaksen (2003), regional drought characteristics were calculated based on the threshold level method and time series of gridded monthly data (precipitation and streamflow). Gridded data were obtained from interpolated and simulated long time series derived using a combination of Empirical Orthogonal Functions, kriging and Monte Carlo simulations. This allowed not only the fraction of the area affected to be assigned an observed frequency, but also the probability of an area fraction to be affected by a drought of a given severity to be estimated by the derivation of severity-area-frequency (SAF) curves.

Recharge (20% area) - Ave. Area

05

101520

10 20 30 40 50 60 70 80 90 100


3. Flood indices Firstly flood indices are described that are derived from a gauging station (streamflow indices). Next indices that reflect areal drought characteristics are explained. 3.1. At-site indices At-site flood characteristics refer to one observation point (e.g. a particular river gauge). At this point, river water level (stage) is being observed/recorded, based on which river discharge can be calculated, using a rating curve, i.e. stage-discharge relationship. At-site flood indices are generally derived from discharge time series. In order to place a recently recorded at-site value into a proper context, it is necessary to analyze a long time series of records available for the site. According to the Flood Estimation Handbook (Robson & Reed, 1999), an index flood represents the typical magnitude of flood expected at a given site, measured in m3 s-1. Two common flood indices considered can be developed from high river flow data. The consequence of the tautology: extreme (rare) events are rare, is that even in a very long series of flood-related records there may only be a few really extreme values leading to catastrophic damages. Because extremes are rare, it is necessary to construct a data series that emphasizes extremes. In the case of floods, one option is to use an annual maxima series (AMS) of at-site river discharge, obtained by taking the largest value in each year of interest, a peak-over-threshold (POT) series (also called a partial duration series, PDS) can be used, consisting of independent data that exceed a certain threshold (this threshold is assumed to be the same throughout the time series). Important at-site indices refer to flood frequency statistics and are related to exceedence interval / return period, e.g. 100-year flood. These indices are essential for probabilistic design. Flood protection systems are typically designed to withstand a flood (so called design flood) of a particular exceedence interval (return period). This approach requires assumption of a distribution (such as the Gumbel, log-normal, or Generalized Extreme Value distribution) e.g. for AMS. Once distribution parameters are determined, one can calculate N-year floods. One has to note, though, that the differences between various distributions can be high in the “tails” region, of most interest for design. Computation of annual indices of extremes from daily data can include the total number of days above a given threshold (defined in absolute terms or via percentiles), the length of the longest time period above a given threshold, or more sophisticated indices. Analysis can be restricted to a specific season, or to a specific flood generation mechanism (rain, snowmelt, ice-jam). Different flood-related indices might be of interest, such as the frequency and severity of floods, number of incidences of independent flood events or the cumulative departure (excursion) above a prescribed threshold within a time interval, spring flood volume and the duration in days of the spring flood event. Timing of seasonal events is an important index of change. Such aspects may include: timing of annual maximum flow, or snowmelt flood-peak time. 3.1.1. Annual maxima and QMED The annual maximum is the largest river discharge in a given year of record. When possible, annual maxima should be abstracted and analysed from water-years rather than calendar years. In the UK and in Poland, for example, the standard water years starts on 1 October and 1 November, respectively. The Annual Maximum Series (AMS) are simply defined in selecting, for each water-year of the total period of


measurements, the highest river discharge. The series has exactly the same number of values as the number of years. However, the information on some extremes may be insufficiently reflected in such a series. If during one water year two (or more) independent, high flow episodes occur, only one (highest) maximum discharge is taken and the other(s) is (are) ignored. Since the AMS contains one value for every year, it means that for some (e.g. dry) years when no flood occurs, the largest river discharge (included in the AMS series) can be considerably lower than the bankfull discharge. The QMED is the median annual maximum flood, and is the flood that is exceeded on average “every other year”. It is derived from the flood maximum series by ordering the annual maxima and taking the middle ranking value or the arithmetic mean of the two central values, in case of odd or even number of annual maxima, respectively. The QMED is the index recommended by the Flood Estimation Handbook. 3.1.2. Peak-Over-Threshold The main drawback of the annual maxima series is that, by construction, events are selected for every single year of measurement, i.e. in a dry year, the maximum flood observed can be relatively small; while in a wet year, several large floods could have occurred, but only the single largest one would be selected. The Peak-Over-Threshold (POT) method selects all flood peaks which exceed a selected threshold, and the derived series provide a more complete description of a flood behaviour than annual maximum data. For some years, POT series may contain none entries while for other years it may contain multiple entries from one year. Selection of POT series must insure that the selected flood peaks are all independent, i.e. the sampling does not select two “nearby” peaks which relate to the same larger flood mechanism. This approach has advantages over annual maxima series in that all major events are included (not just one largest in a year) and all data points in the POT series are indeed extreme events. Depending on the value of the threshold, the number of POT values may differ from the number of years. It is possible to choose a threshold so that exactly N peaks are selected for N years of record: this is the Annual Exceedance Series, a special case of the POT series (Shaw, 1983). 3.2. Areal flood indices The category of areal flood indices embraces generalization of all the at-site values, for a multi-site region where a number of point data series are available. A straightforward areal flood index refers to the inundated area (maximum inundated area or with consideration of the duration of inundation). For example, during the extensive 1998 flood nearly 70% of the area of Bangladesh was inundated. A category of areal flood indices embraces also impacts-related measures, related for example to flood damage (e.g. total material damage, insured material damage, number of fatalities, injured, evacuated, affected). The spatial occurrence of extremes can be studies using several different techniques:

• Principal Components Analysis (Empirical Orthogonal Function analysis) to extract the major modes of variation in the occurrence of extremes. The eigenvectors of the significant principal components can be plotted to explore spatial variations. The scores, or amplitudes, of these significant components can be plotted to understand variation in time.


• The relationship between the retained principal components and indices of the large-scale behaviour of the atmospheric circulation (e.g. the North Atlantic Oscillation and the Arctic Oscillation) can be explored using regression analysis.

• Canonical correlation analysis can be used to understand the relationship between the spatial pattern of extremes occurrence and the fields of potential explanatory variables.

The flood-related indices can be determined each grid cell. It is always advisable to present the spatial results on a map for exploratory analysis/expert assessment.


4. Concluding remarks - no single drought or flood characteristic is suitable to assess and describe hydrological extremes

for any type of analyses in any region. Hence, it is important to be aware of how various ways of characterizing a drought or flood might lead to different conclusions regarding the hydrological extreme phenomenon;

- indices include both at site characterization (e.g. streamflow gauging station, groundwater well) and areal characterization;

- in defining indices for drought and floods it is important to make a distinction between fluxes (e.g. streamflow, spring discharge) and state variables (e.g. groundwater head, stage);

- the threshold method is widely used for drought analysis providing at site drought characteristics, such as onset, duration, deficit volume;

- the Sequent Peak Algorithm (SPA) is also used for identifying drought in streamflow. This technique may lead to more pooled droughts because the flow in the inter-event period may be insufficient to cover storage requirements;

- SPA should not be used to identify drought in state variables; - drought in groundwater discharge is usually not derived from the whole streamflow hydrograph, but

a hydrograph separation technique is used implying that the indices are affected by the separation approaches;

- the threshold level method is also frequently used to define drought events at the regional scale. Spatial characteristics are introduced, e.g. area covered by a drought, average deficit for the drought area, average duration of the drought for the drought area;

- the annual maximum largest river flow in a given year of record (annual maxima series) is often used in flood hydrology implying that in each year a flood/peak flow occurs. The information on the extreme floods may be insufficiently reflected in such a series;

- the Peak-Over-Threshold (POT) method that selects all flood peaks which exceed a selected threshold, is a better measure. The derived series provide a more complete description of a flood behaviour than annual maximum data. For some years, POT series may contain no events while for other years it may contain multiple events;

- areal flood indices embrace generalization of all the at-site values, for a multi-site region (e.g. flood plain) where a number of point data series are available. Often digital terrain models are linked to this information.

- the current document is an open document that will be completed over the lifetime of the WATCH project, including all recent experiences.


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