Conventional Frequency Analysis Research Articles

Bivariate Frequency Analysis of Annual Maximum Rainfall Event Series in Seoul, Korea

AbstractThe return period of a rainfall event is estimated by the frequency analysis for a given rainfall duration. Thus, it is possible to derive different return periods with different rainfall durations for a given rainfall event. The longest derived return period is generally cited to represent the rainfall event. However, it is not clear if the longest derived return period is a representative measure of the given rainfall event. In this study, as a solution for this problem, a bivariate frequency analysis was introduced. As a first step, annual maximum rainfall events were selected by applying a bivariate exponential distribution. As an application, a total of 1,534 rainfall events observed in Seoul, Korea, over the last 46 years were analyzed. The annual maximum rainfall event series were then analyzed by applying a bivariate logistic model. The results were also compared with those from a conventional univariate frequency analysis. The findings of this study are summarized as follows: (1) the biva...

A copula-based multivariate analysis of Canadian RCM projected changes to flood characteristics for northeastern Canada

In the present work, climate change impacts on three spring (March–June) flood characteristics, i.e. peak, volume and duration, for 21 northeast Canadian basins are evaluated, based on Canadian regional climate model (CRCM) simulations. Conventional univariate frequency analysis for each flood characteristic and copula based bivariate frequency analysis for mutually correlated pairs of flood characteristics (i.e. peak–volume, peak–duration and volume–duration) are carried out. While univariate analysis is focused on return levels of selected return periods (5-, 20- and 50-year), the bivariate analysis is focused on the joint occurrence probabilities P1 and P2 of the three pairs of flood characteristics, where P1 is the probability of any one characteristic in a pair exceeding its threshold and P2 is the probability of both characteristics in a pair exceeding their respective thresholds at the same time. The performance of CRCM is assessed by comparing ERA40 (the European Centre for Medium-Range Weather Forecasts 40-year reanalysis) driven CRCM simulated flood statistics and univariate and bivariate frequency analysis results for the current 1970–1999 period with those observed at selected 16 gauging stations for the same time period. The Generalized Extreme Value distribution is selected as the marginal distribution for flood characteristics and the Clayton copula for developing bivariate distribution functions. The CRCM performs well in simulating mean, standard deviation, and 5-, 20- and 50-year return levels of flood characteristics. The joint occurrence probabilities are also simulated well by the CRCM. A five-member ensemble of the CRCM simulated streamflow for the current (1970–1999) and future (2041–2070) periods, driven by five different members of a Canadian Global Climate Model ensemble, are used in the assessment of projected changes, where future simulations correspond to A2 scenario. The results of projected changes, in general, indicate increases in the marginal values, i.e. return levels of flood characteristics, and the joint occurrence probabilities P1 and P2. It is found that the future marginal values of flood characteristics and P1 and P2 values corresponding to longer return periods will be affected more by anthropogenic climate change than those corresponding to shorter return periods but the former ones are subjected to higher uncertainties.

Uncertainty analysis on extreme value analysis of significant wave height at eastern coast of Korea

In this study, we considered the problem of estimating long-term predictions of design wave height based on the observation data collected over 10–15 years along the eastern-coast of the Korean peninsula. We adopted a method that combines Bayesian method and extreme value theory. The conventional frequency analysis methods must be reconsidered in two ways. First, the conventional probability distributions used in the frequency analysis should be evaluated to determine whether they can accurately model the variation in extreme values. Second, the uncertainty in the frequency analysis should also be quantified. Therefore, we performed a comparative study of the Gumbel distribution and GEV distribution to show the higher efficiency of the latter. Further, we compared the Bayesian MCMC (Markov Chain Monte Carlo) scheme and the MLE (Maximum Likelihood Estimation) with asymptotic normal approximation for parameter estimation to confirm the advantage of the Bayesian MCMC with respect to uncertainty analysis.

Rainfall frequency analysis using a mixed GEV distribution: a case study for annual maximum rainfalls in South Korea

Extreme rainfalls in South Korea result mainly from convective storms and typhoon storms during the summer. A proper way for dealing with the extreme rainfalls in hydrologic design is to consider the statistical characteristics of the annual maximum rainfall from two different storms when determining design rainfalls. Therefore, this study introduced a mixed generalized extreme value (GEV) distribution to estimate the rainfall quantile for 57 gauge stations across South Korea and compared the rainfall quantiles with those from conventional rainfall frequency analysis using a single GEV distribution. Overall, these results show that the mixed GEV distribution allows probability behavior to be taken into account during rainfall frequency analysis through the process of parameter estimation. The resulting rainfall quantile estimates were found to be significantly smaller than those determined using a single GEV distribution. The difference of rainfall quantiles was found to be closely correlated with the occurrence probability of typhoon and the distribution parameters.

독립 호우사상에 대한 이변량 강우빈도해석 및 강우-유출해석

본 연구에서는 독립 호우사상을 이용하여 이변량 빈도해석 및 유출해석을 수행하고, 이를 기존 단변량 빈도해석 결과와 비교 평가하였다. 본 연구는 규모가 다른 중랑천, 청계천, 우이천유역 등 세 유역에 대해 수행되었다. 유출모형으로 Clark 모형을 이용하였고, 유효우량은 SCS 방법을 적용하여 계산하였다. 강우의 시간분포 모형으로 교호블록 방법 및 Huff 방법을 적용하여 그 결과가 비교될 수 있도록 하였다. 그 결과를 정리하면 다음과 같다. (1) 연최대치 독립 호우사상계열의 이변량 빈도해석 결과, 지속기간이 짧은 경우에는 단변량 빈도해석 결과와의 차이가 매우 크나 지속기간이 길어짊에 따라서 그 차이가 현저히 줄어드는 것으로 나타났다. 아울러 지속기간이 짧은 경우, 단변량 빈도해석 결과가 이변량 빈도해석 결과보다 더욱 크게 나타났으나 특정 지속기간 이상부터 그 결과가 역전되는 것으로 나타났다. (2) 교호블록 시간분포 방법을 적용하는 경우가 Huff 방법을 적용한 경우보다 더욱 큰 첨두유출량을 발생시키는 것으로 나타났다. 아울러 교호블록 방법을 적용하는 경우에는 강우 지속기간의 증가에 따라서 첨두유출량이 점차 증가하는 것으로 나타났으나, 강우 지속기간이 대략 24시간 정도 되었을 때 그 값이 거의 수렴하는 것으로 나타났다. (3) 중랑천 유역에 대해 Huff 방법을 적용하여 유출해석을 수행한 결과에서는 이변량 설계강우를 적용한 경우가 단변량 설계강우를 적용한 경우보다 더욱 큰 홍수량을 발생시키는 것으로 나타났다. 반면에 청계천 및 우이천 유역의 경우에는 이변량 설계강우를 적용한 경우보다 단변량 설계강우를 적용한 경우의 홍수량이 다소 큰 것으로 나타났다. 그러나 교호블록 방법을 적용한 경우에서는 모든 유역에 대해 이변량 설계강우를 적용한 경우가 단변량 설계강우를 적용한 경우보다 큰 홍수량을 발생시키는 것으로 나타났다. In this study, the bivariate frequency analysis of the independent annual rainfall event series was done to be used for the runoff analysis, whose results were also compared with those from the conventional univariate frequency analysis. This study was applied to three differently-sized basins such as the Joongryang Stream, Chunggye Stream, and Ooyi Stream. The Clark model was used as the runoff model, and the SCS method was applied for the calculation of the effective rainfall. The alternating block method and the Huff method were considered to be compared for the temporal distribution of rainfall event. Summarizing the results are as follows. (1) The difference between the univariate and bivariate frequency analysis results were large when the rainfall duration was short, but significantly decreased as the rainfall duration increased. The univariate frequency analysis results were bigger when the rainfall duration was short, but smaller in opposite case. (2) The peak flow derived by applying the alternating block method was bigger than that by the Huff method. Also, the peak flow when applying the alternating block method increased as the rainfall duration increased, but converged smoothly around the rainfall duration of 24 hours. (3) For the Joongryang Stream, when applying the Huff method, the peak flow derived for the bivariate frequency analysis was bigger than that for the univariate case, but for the other two basins, the results were opposite. When applying the alternating block method, the results were consistent for all three basins that the peak flow derived by applying the bivariate frequency analysis was bigger than those by the univariate frequency analysis.

혼합 검벨분포모형을 이용한 확률강우량의 산정

최근 다양한 기후변동성으로 인해 전 세계적으로 극한호우사상이 동시다발적으로 일어나고 있다. 우리나라의 극한호우사상은 주로 여름철 태풍으로 인한 호우와 국지성 집중호우에 의해서 발생한다. 극한호우사상에 대한 적절한 확률강우량을 추정하기 위해서, 본 연구에서는 연최대치일강우를 태풍으로 인한 강우와 집중호우로 인한 강우로 구분하여 확률적 거동을 고려하였다. 일반적인 강우빈도해석법은 연최대치강우가 단일 모집단을 이룬다고 가정하여 단일 분포함수를 적용하여 확률강우량을 추정하는 반면, 본 연구에서는 연최대치강우를 구성하는 두 가지 호우의 통계적 특성을 수문빈도해석에서 고려하기 위해, 혼합 분포함수를 적용하였다. 비교적 긴 관측강우자료를 보유한 15개 지점을 선정하여, 일강우량에 대한 확률강우량을 산정하고 비교분석을 실시하였다. 혼합 검벨분포모형에 의한 확률강우량은 단일 검벨분포함수를 적용한 확률강우량과 비교하여 지역에 따라 증감이 나타났으며, 이러한 결과는 홍수방어시스템의 계획 및 설계에서 유용한 정보를 제공할 것이다. Recently, due to various climate variabilities, extreme rainfall events have been occurring all over the world. Extreme rainfall events in Korea mainly result from the summer typhoon storms and the localized convective storms. In order to estimate appropriate quantiles for extreme rainfall, this study considered the probability behavior of daily rainfall from the typhoons and the convective storms which compose the annual maximum rainfalls (AMRs). The conventional rainfall frequency analysis estimates rainfall quantiles based on the assumption that the AMRs are extracted from an identified single population, whereas this study employed a mixed distribution function to incorporate the different statistical characteristics of two types of rainfalls into the hydrologic frequency analysis. Selecting 15 rainfall gauge stations where contain comparatively large number of measurements of daily rainfall, for various return periods, quantiles of daily rainfalls were estimated and analyzed in this study. The results indicate that the mixed Gumbel distribution locally results in significant gains and losses in quantiles. This would provide useful information in designing flood protection systems.

W-O-115 DEVELOPMENT OF A PATIENT TRACKING AND REPORTING SYSTEM

Introduction and Objectives: Imaging motor, sensorial, emotional and cognitive activities in humans is a longstanding and unfinished quest (Maquet 2000; Schwartz, Maquet 2002). In dreams analyses several EEG correlations were found: a reduced coupling between frontal and perception regions (Corsi-Cabrera et al., 2003); visual activities and alpha attenuation (Bertolo et al., 2003), reduced delta activity and dream length (Palagini et al., 2004); reduced alpha power and mentation recall (Esposito et al., 2004); emotions and alpha asymmetry (Daoust et al., 2008); sharing properties of dreams and lucid dreaming in the low frequency bands (Voss et al., 2009); frontal alpha asymmetries recognized as a measure of physical and emotional distress during sleep (Flo et al., 2011). Objectives The objectives were 1) Dreams EEG mapping according to content; 2) EEG asymmetries in frequency bands and dream contents correlations; 3) Classification by cluster analysis the EEG asymmetries and the dream contents. Materials and Methods: Eight adult normal subjects (4 males) without medical or psychiatric disorders and medication were recorded for 2 consecutive nights; PSG included 21 EEG channels. REM awakenings dreams were collected. Dream contents were evaluated by the Hall van Castle method and the 5 minutes EEG prior to the awakening were selected and submitted to conventional frequency analysis. Asymmetries were evaluated in Fp2/Fp1, F4/F3, F8/F7, C4/C3, P4/P3, T4/T3, O2/O1. Analysis included: each subject, each dream and groups. Analysis of variance, correlation and cluster analysis were used. Results: Forty four dreams were evaluated (5.5 per subject, min 1; max 10). Asymmetries in frequency bands varied among subjects and with dream contents: characters, emotions, success, visual, rationalfast and low bands; activities, verbal, objects fast bands; failure – low bands. Cluster analysis of the EEG asymmetries provided 2 clusters, while cluster analysis of dream contents could only identify a single cluster. Conclusion: EEG frequency bands vary among subjects and according to dream contents; the effect is enhanced by the corresponding left/right asymmetries in the different electrode regions.

Wavelet Decomposition for Power Balancing Analysis

Wavelets are a mathematical tool for analyzing time-varying signals. Unlike conventional frequency analysis methods, wavelets give information about the frequency components as a function of time. Wavelets are applied in situations where there are large discrepancies in the frequencies to be analyzed and when the signal to analyze cannot be assumed periodic. In power systems, wavelets are usually applied to determine power-quality issues. In this paper, however, applying wavelets to analyze fluctuations in load and generation profiles is proposed. As generation and load in any power system must always be balanced, wavelets can be applied to identify the required amount of balancing capacity from observing the time-varying nature of the dominant frequencies contained in the power signals.

독립호우사상의 확률론적 해석 : 2. 호우사상의 재현기간

본 연구에서는 이변량 극치분포를 이용하여 연최대치 호우사상을 평가하였다. 이를 위해 특정 재현기간을 가지는 호우사상의 강우량을 비동시결합 재현기간, 동시결합 재현기간 그리고 구간조건부 결합재현기간의 세 가지를 이용하여 산정하였다. 이때, 결합재현기간별 호우사상의 값의 크기가 서로 다르게 산정되는 이유를 이변량 분포의 확률특성을 보여주는 사분면을 이용하여 설명하였다. 호우지속기간 24시간인 경우에 동시결합재현기간을 이용하여 산정한 확률강우량은 전통적인 방법으로 얻어진 강우지속기간 24시간의 확률강우량과 유사하게 나타났다. 이러한 결과는 전통적인 강우빈도해석의 제약사항을 극복하는데 도움이 될 것으로 보여진다. 이변량 빈도해석으로 얻어진 확률호우사상은 저류시설물의 계획시 통계적으로 보다 유용하면서도 간단한 설계 호우사상을 제공할 수 있을 것으로 보여진다. In this study, annual maximum storm events are evaluated by applying the bivariate extremal distribution. Rainfall quantiles of probabilistic storm event are calculated using OR case joint return period, AND case joint return period and interval conditional joint return period. The difference between each of three joint return periods was explained by the quadrant which shows probability calculation concept in the bivariate frequency analysis. Rainfall quantiles under AND case joint return periods are similar to rainfall depths in the univariate frequency analysis. The probabilistic storm events overcome the primary limitation of conventional univariate frequency analysis. The application of these storm event analysis provides a simple, statistically efficient means of characterizing frequency of extreme storm event.

Characterisation of anomalies embedded in graphite fibre reinforced aluminium composite by chirplet parameters

To characterise anomalies embedded in graphite fibre reinforced aluminium matrix composite, chirplet parameters of ultrasonic signals were obtained by chirplet signal decomposition method. It was confirmed that the parameters of decomposed chirplets can represent the characteristic of ultrasonic signals in time and frequency domains compared with conventional time and frequency analysis method. Chirplet parameters were used to identify three types of anomalies embedded in graphite fibre reinforced aluminium matrix composite. The variations of centre frequency and phase of three anomalies were interpreted by frequency dependent attenuation coefficient of composite and frequency dependent reflection coefficient of thin anomalies embedded in composite.

Regional analysis of the annual maximum daily rainfall in the province of Malaga (southern Spain) using the principal component analysis

AbstractThe flood and drought cycles suffered of old by the province of Malaga, the variability in the distribution of rainfall throughout the province and the reduced length of the data series make it of interest to carry out a regional analysis (RA) of the yearly maximum daily precipitation data to obtain appropriate rainfall quantiles. By taking these maximum precipitations values from 72 weather stations, and their physiographic parameters latitude and altitude, four regions with similar rainfall patterns have been determined by the principal component analysis statistical technique. Then, carrying out an RA of the yearly maximum daily precipitations for each of the regions discriminated, it was observed that three of them were homogeneous for the parameter being studied. In those homogeneous regions that grouped data of different stations but close rainfall pattern, frequency curves could be calculated for several return periods by means of the functions that best fit the data of each region. With these regional curves, it has been possible to obtain more accurate values of the maximum daily quantiles for each of the stations analysed than through the conventional local frequency analysis.

Reducing uncertainty in estimates of frequency distribution parameters using composite likelihood approach and copula‐based bivariate distributions

Conventional multivariate hydrological frequency analysis utilizes only the concurrent parts of data sets, leaving a lot of nonconcurrent data unutilized. Simultaneous inclusion of such nonconcurrent data can significantly reduce uncertainty in hydrologic design estimates. The methodology proposed in this paper allows varied length multivariate data to be combined and analyzed in an integrated framework through a “Composite Likelihood Approach.” The method employs copula‐based multivariate distributions in order to provide necessary flexibility of admitting arbitrary marginals. The paper presents the theoretical basis of the approach and highlights its advantages through two applications. A significant reduction in uncertainty in design flood quantiles of a relatively shorter flood series is achieved by utilizing an associated downstream flood data. The advantage of the methodology is further demonstrated by establishing significant information gain for six different combinations of Gaussian and non‐Gaussian marginals. The proposed approach marks a paradigm shift in hydrologic design procedures, particularly for partially gauged basins, wherein a higher precision in hydrologic designs is achieved by leveraging associated information that has hitherto remained unutilized. It is opined that the approach will enable offsetting the impact of dwindling hydrological observation networks around the world by enhancing information that is derivable from existing networks.

Probabilistic Forecast and Uncertainty Assessment of Hydrologic Design Values Using Bayesian Theories

ABSTRACT Researches on hydrologic extreme events have great significance in reducing and avoiding the severe losses and impacts caused by natural disasters. When forecasting hydrologic design values of the hydrologic extreme events of interest by the conventional hydrologic frequency analysis (HFA) model, the results cannot take uncertainties and risks into account. In this article, in order to overcome conventional HFA model's disadvantages and to improve hydrologic design values’ forecast results, an improved HFA model named AM-MCMC-HFA is proposed by employing the AM-MCMC algorithm (adaptive Metropolis-Markov chain Monte Carlo) to HFA process. Differing with conventional HFA model, which is seeking single optimal forecast result, the AM-MCMC-HFA model can not only get the optimal but also the probabilistic forecast results of hydrologic design values. By applying to two obviously different hydrologic series, the performances of the model proposed have been verified. Analysis results show that four factors have great influence on hydrologic design values’ reliability, and also indicate that AM-MCMC-HFA has the ability of assessing the uncertainties of parameters and hydrologic design values. Therefore, by using the AM-MCMC-HFA model, hydrologic designs tasks can be operated more reasonably, and more rational decisions can be made by governmental decision-makers and public in practice.

Design Flood Hydrograph Based on Multicharacteristic Synthesis Index Method

Flood events consist of flood peaks and flood volumes for various durations that are mutually correlated and need to be described by multiple variables. Conventional flood frequency analysis methods are generally based on the univariate distributions of either flood peaks or flood volumes, and hence only provide a limited assessment of flood events. In this paper, a multicharacteristic synthesis index (MSI) method is developed to describe flood hydrographs in an integrated way by considering the multiple characteristics synthetically, such as flood peak, 1-day maximum flood volume, 3-day maximum flood volume, 7-day maximum flood volume, etc. Annual maximum flood hydrograph series are sampled and then are transformed into corresponding MSI series by the MSI method. The quantile of the MSI series corresponding to a specified design return period is estimated by conventional flood frequency analysis method. A procedure for derivation of design flood hydrograph based on the MSI quantile is proposed. An applic...

Application of bivariate frequency analysis to the derivation of rainfall–frequency curves

Bivariate distributions have been recently employed in hydrologic frequency analysis to analyze the joint probabilistic characteristics of multivariate storm events. This study aims to derive practical solutions of application for the bivariate distribution to estimate design rainfalls corresponding to the desired return periods. Using the Gumbel mixed model, this study constructed rainfall–frequency curves at sample stations in Korea which provide joint relationships between amount, duration, and frequency of storm events. Based on comparisons and analyses of the rainfall–frequency curves derived from univariate and bivariate storm frequency analyses, this study found that conditional frequency analysis provides more appropriate estimates of design rainfalls as it more accurately represents the natural relationship between storm properties than the conventional univariate storm frequency analysis.

Analog preamplifier measurement for a microphone array

An analog preamplifier measurement system for a microphone array builds on conventional microphone arrays by providing an integral “self-calibration system.” This self-calibration system automatically injects an excitation pulse of a known magnitude and phase to all preamplifier inputs within the microphone array. The resulting analog waveform from each preamplifier output is then measured. A frequency analysis, such as, for example, a Fourier or Fast Fourier Transform (FFT), or other conventional frequency analysis, of each of the resulting waveforms is then performed. The results of this frequency analysis are then used to automatically compute frequency-domain compensation gains (e.g., magnitude and phase gains) for each preamplifier for matching or balancing the responses of all of the preamplifiers with each other.

An analysis of the spatial pattern of summer persistent moderate-to-heavy rainfall regime in Guizhou Province of Southwest China and the control factors

In this study, we investigated spatial and temporal variation patterns of persistent moderate-to-heavy rainfall events in Guizhou Province of southwest China during 1951–2004. We first performed conventional frequency analysis using the annual maximum daily series at 36 weather stations fit to log-normal distribution curves. Then, we examined the frequencies of moderate-to-heavy rainfall events (> = 20 mm/day) and persistent rainfall events (10–day running sum > = 100 mm) during the summer season (June through August). Using principal component analysis, we identified various spatial patterns of the rainfall regime and macroscale atmospheric conditions that influence these patterns. It was found that a minor mode of variation in the 500 hPa geopotential height anomaly field over East Asia (the third principal component) had a very good relationship to the dominant regional precipitation regime (Spearman’s correlation coefficient = –0.623). This mode of circulation represents the N–S variation of the upper-air pressure gradients over East Asia. During its positive phase, the pressure gradient south of 40°N is reduced and accompanied by a ridge over the East China coast, while the pressure gradient north of this latitude is enhanced. Correspondingly, the study region experiences fewer persistent moderate-to-heavy rainfall events. In its negative phase, the pattern in the 500 hPa geopotential height anomaly field is reversed and the study region experiences more persistent moderate-to-heavy rainfall events. This circulation mode is related to both East Asian and Indian summer monsoons. It is also associated with the northward intrusion of the West Pacific subtropical high, the size of the circumpolar vortex over the Pacific, and the impact of the Tibetan Plateau.

Region-of-influence approach to a frequency analysis of heavy precipitation in Slovakia

Abstract. The paper compares different approaches to regional frequency analysis with the main focus on the implementation of the region-of-influence (ROI) technique for the modelling of probabilities of heavy precipitation amounts in the area of the Western Carpathians. Unlike the conventional regional frequency analysis where the at-site design values are estimated within a fixed pooling group (region), the ROI approach as a specific alternative to focused pooling techniques makes use of flexible pooling groups, i.e. each target site has its own group of sufficiently similar sites. In this paper, various ROI pooling schemes are constructed as combinations of different alternatives of sites' similarity (pooling groups defined according to climatological characteristics and geographical proximity of sites, respectively) and pooled weighting factors. The performance of the ROI pooling schemes and statistical models of conventional (regional and at-site) frequency analysis is assessed by means of Monte Carlo simulation studies for precipitation annual maxima for the 1-day and 5-day durations in Slovakia. It is demonstrated that a) all the frequency models based on the ROI method yield estimates of growth curves that are superior to the standard regional and at-site estimates at most individual sites, and b) the selection of a suitable ROI pooling scheme should be adjusted to the dominant character of the formation of heavy precipitation.

Biological heterogeneity and length-biased sampling in asymptomatic neurosurgical patients

Increased numbers of asymptomatic intracranial lesions are being identified because of recent advances in imaging technology. Understanding of the natural history of these diseases, together with length bias is highly important in refining treatment strategy. Two sample models of hypothetical healthy cohorts were constructed, in which diseases showed either dual-type or multiple-type heterogeneity. Relative preclinical interval (PCI) of asymptomatic lesions including length-biased sampling was calculated, confirming that relative PCI increased according to heterogeneity of the disease. Length-biased sampling in asymptomatic lesions results from biological heterogeneity of the disease. Because lesions of longer PCI always are over-represented in a healthy population, conventional frequency analysis will tend to over-estimate risks in these patients.

이차원 가뭄빈도해석을 통한 서울지역의 가뭄 평가

가뭄에 대한 대책을 수립하기 위해서는 가뭄의 심도 및 지속기간 등 가뭄특성을 산정하여 가뭄을 정량화하는 것이 필요하다. 본 연구에서는 표준강수지수(SPI)를 도입하여 가뭄특성을 정량적으로 산정하였다. 가뭄은 일정기간 지속되는 특성을 지니고 있기 때문에 일정 관측기간동안 제한된 가뭄사상을 가지게 된다. 본 연구에서는 조선시대에 기록된 측우기 자료(1770년 <TEX>${\sim}$</TEX> 1907년)를 이용하여 관측자료를 확장하였고, 이를 이용하여 보다 많은 가뭄특성자료를 획득하여 가뭄빈도해석을 실시하였다. 측우기 자료와 관측자료를 이용하여 산정된 SPI로부터 절단수준법 개념을 이용하여 SPI의 -1이하를 가뭄으로 정의하고, 가뭄 심도 및 가뭄 지속기간을 구하였다. 가뭄의 심도와 지속기간은 가뭄을 특성화하는데 있어서 중요한 인자로서 최근 이 두 특성을 함께 고려하는 빈도해석법들이 제안되고 있다. 기존의 단일변수 빈도해석을 가뭄에 적용하였을 경우, 가뭄의 심도와 지속기간을 이용하여 구한 각각의 재현특성이 상이하게 나타나는 경우가 있는데, 이는 하나의 가뭄사상의 재현특성을 표현하는데 적절하지가 않다. 본 연구에서는 이변수 감마분포를 이용하여 가뭄심도와 지속기간의 결합확률밀도함수를 추정하고, 이를 통하여 가뭄의 이변수 재현 기간을 산정하여 분석하였다. Drought characteristics need to be preceded before establishing a drought mitigation plan. In this study, using a Standardized Precipitation Index (SPI), a hydrologic drought was defined as an event during which the SPIs are continuously below a certain truncation level. Then, a methodology of drought frequency analysis was performed to quantitatively characterize droughts considering drought duration and severity simultaneously. The theory of runs was used to model drought recurrence and to determine drought properties like duration and severity. Short historical records usually do not allow reliable bivariate analyses. However, more than hundred years of precipitation data (1770 <TEX>${\sim}$</TEX> 1907) collected in Chosun Kingdom Age using an old Korean rain gage called Chukwooki can provide valuable information about past events. It is shown that a bivariate gamma distribution well represented the joint probabilistic properties of Korean drought duration and severity. The overall results of this study show that the proposed bivariate drought frequency analysis overcomes the drawbacks of the conventional univariate frequency analysis by providing a consistent representation of the drought recurrent property.