KR101856042B1 - Bias correction method of extreme precipitation data in global climate model using mixture distributions - Google Patents

Abstract

The present invention relates to a method of correcting errors in extreme precipitation data of a global climate model using a mixed distribution type.
The error correction method of the extreme precipitation data of the global climate model using the mixed distribution type according to the present invention comprises the steps of: setting a climate scenario of the global climate model (GCM) or regional climate model (RCM) (QM) to adjust the probability distribution of the variables of the regional climate model (RCM) to the probability distribution of the observed data, to correct deviations of the global climate model (GCM) or regional climate model (RCM) ; Testing models of multiple mixed distribution functions for evaluation of climate change impacts based on a probability distribution of variables of the adjusted regional climate model (RCM); Estimating parameters of the mixed distribution function models using a meta-heuristic maximum likelihood (MHML) technique; Among the plurality of mixed distribution function models tested, the result data obtained by a model of the best mixed distribution function having the best ability to produce a distribution pattern closest to the distribution pattern of the observation data without producing an ideal value and the estimated parameters Performing shift correction based on the correction; And correcting the error of the extreme precipitation data of the climate model by reflecting the result of the correction to the extreme precipitation data of the climate model.

Description

[0001] The present invention relates to a method for correcting errors of extreme precipitation data of a global climate model using a mixed distribution type,

The present invention relates to a method of correcting errors in extreme precipitation data produced by a global climate model using a mixed distribution type, more particularly, by mixing a general characteristic probability distribution type of climatic data with a characteristic probability distribution type of extreme values, This paper deals with the correction method of the error of the extreme precipitation data of the global climate model using the mixed distribution type which can overcome the disadvantage that the extreme value is generated at the extreme of the extreme value and can produce reliable data for all the quartiles.

Climate change mainly affects the frequency and magnitude of extreme precipitation (rainfall), which is a major cause of flooding. Global climate models (GCMs), which simulate future climates and simulate observed climate change as a result of anthropogenic greenhouse gas emissions, are the best resources to obtain climate change scenarios for current extreme precipitation (rainfall) source. The regional climate model (RCM), an epidemiological detail of the global climate model output, provides increased resolution, enabling analysis of climate change impacts on the lower lattice scale. However, there are still systematic deviations from factors (eg, precipitation and temperature) generated by local climate models, making direct use difficult for hydrological applications. This improvement in the results of the local climate model, which still has no error correction, can be improved by applying the deviation correction method.

Many deviation correction methods such as delta method, polynomial regression, analog method, local intensity scaling, quantile mapping (QM) method, etc. have been proposed to eliminate the error of data generated in global or regional climate models come. Most deviation correction methods mainly focus on the mean value, and there are obvious differences in other statistical properties such as standard deviation or percentile. Regional climate models were used to compare variance correction methods for daily precipitation and it was concluded that the declination method had the best performance, especially for extreme precipitation (rainfall) events. While using the nonparametric method empirical distribution can successfully correct the current climate, it is not suitable for application to future climate data beyond the range of observed values. For this reason, parameter approaches have been used to correct future climate scenarios and distribution types such as exponential, gamma and weibull have been applied. However, since distributions such as exponential and gamma are light-tailed distributions, they are still unstable to future extreme values. These general distributions have some limitations in expressing climate change in daily precipitation (rainfall).

On the other hand, Japanese Patent Laid-Open Publication No. 10-2014-0111822 (Patent Document 1) discloses a method of correcting an error of a global climate model applying an abnormal seismic pattern. In this method, Obtaining a simulation result by applying a decimal mapping to the value; Obtaining long-term time series data of a future period; Obtaining a linear regression equation for the simulation result and the long-term time series data; Obtaining a bias at a point where each of the linear regression equations meets; Calculating a new linear regression equation (y = ax + b ') by correcting the y-axis intercept (b) of the linear regression equation (y = ax + b) for the long term time series data of the future period; And mapping the statistical distribution parameters using the parameters of the linear regression equation before and after the correction.

Since the error correction method of Patent Document 1 adopts the abnormal seismic mapping method, it is possible to prevent the long-term time series data from underestimating even if applied to long-term time series data having abnormality, If there is an effect, it is possible to prevent the occurrence of nonconformity between the past period and the simulation period. However, this also depends on the statistical distribution, and it is difficult to overcome the disadvantage that the abnormal value is generated in the existing extreme. .

Japanese Patent Application Laid-Open No. 10-2014-0111822 (Feb.

SUMMARY OF THE INVENTION The present invention has been made in order to overcome the problems of the prior art as described above, and it is an object of the present invention to overcome the disadvantage that a general characteristic probability distribution type of climatic data and a characteristic probability distribution type of extreme values are mixed, The purpose of this study is to provide a method for correcting errors in extreme precipitation data of a global climate model using a mixed distribution type that can produce reliable data for all quartiles.

In order to achieve the above object, there is provided a method for correcting errors in extreme precipitation data of a global climate model using a mixed distribution type,

A method for correcting an error of extreme precipitation data of a climate model by executing an algorithm (software program) for correcting an error of precipitation data of a predetermined climate model mounted on a computer,

a) establishing a climate scenario of global climate model (GCM) or regional climate model (RCM) outputs by execution of the algorithm;

(b) using the quantile mapping (QM) to calibrate the deviation of the global climate model (GCM) or regional climate model (RCM) Adjusting a probability distribution of the variable;

c) testing models of a plurality of mixture distribution functions for evaluation of climate change impacts based on a probability distribution of the parameters of the adjusted regional climate model (RCM);

d) estimating parameters of the mixed distribution function models using a meta-heuristic maximum likelihood (MHML) technique;

e) comparing the result data obtained by the model of the mixed distribution function showing the graph characteristic closest to the Observation Data (Obs.) graph characteristic with respect to the extreme precipitation among the plurality of mixed distribution function models tested, Performing shift correction based on the estimated parameters; And

and f) correcting the error of the extreme precipitation data of the climate model by reflecting the result of the deviation correction on the extreme precipitation data of the climate model.

Here, the climate scenario of the global climate model (GCM) or local climate model (RCM) products in step a) may consist of a basic (historical) period and a future period.

In the step b), the probability distribution (y) of the observed data may be defined by the following equation.

Also, in the step c), the mixed distribution function may be defined by the following equation.

Further, in the step d), the estimator of the parameter may be determined through maximization of the likelihood function.

Also, a G-U (Gamma-Gumbel) mixture distribution may be used to perform the deviation correction in step e).

According to the present invention, by applying the general characteristic probability distribution type of climatic data and the characteristic probability distribution type of extreme values to each other, it is possible to overcome the disadvantage that abnormal values are generated in extreme values in the conventional technology, There is an advantage in producing data.

FIG. 1 is a flowchart illustrating a method of correcting an error of extreme precipitation data of a global climate model using a mixed distribution type according to an embodiment of the present invention.
Figure 2 is a plot showing QQ (quantile-quantile) plots between observed values and RCM output (blue diamonds) as well as corrected RCM (BCRCM) outputs (red squares) for daily precipitation for station 119 (source).
Figure 3 is a plot showing the same plot as Figure 2 for station 189 (Seogwipo).
4 is a view showing a reproduction period corresponding to an observed value (cross display) and an RCM output (blue diamond) as well as a BCRCM (red square) in which the deviation is corrected with respect to an extreme precipitation amount of 100 mm or more with respect to the observation station 119 .
Figure 5 is a plot showing the same plot as in Figure 4 for station 189 (Seogwipo).
Figure 6 shows the mean absolute error between the observed values and the RCM output (raw) as well as the BCRCM with the four non-mixed and mixed different distribution types for daily precipitation and extreme precipitation of 60 observatories in South Korea over the period 1979-2005 (MAE). ≪ / RTI >
Figure 7 shows the mean square root error (RMSE) between observed values and RCM output (raw) as well as BCRCMs with different distribution types of four non-mixing and mixing for daily precipitation and extreme precipitation of 60 observatories in South Korea to be.
Figure 8 shows a box plot of the average of more than 99 percent extreme values for BCRCM of 1979-2005 and BCRCM of 2006-2055 with RCR 4.5 and RCP 8.5, with observed values and distribution types selected for 60 observatories in South Korea Fig.
Figure 9 is a plot of the spatial distribution of mean extreme precipitation (greater than 99 percent) observed over the period 1979-2005 in South Korea.
10 is a graph showing the difference between the mean of extreme values (over 99%) observed using specific mixed distribution types over the 1979-2005 observation period and the extreme values of the BCRCM product.
Figure 11 is a plot of the difference between the mean of extreme values (over 99 percent) observed over the period 1979-2005 and the extreme values of the RCP 4.5 BCRCM over the duration of the future scenario of 2006-2055.
Figure 12 is a plot of the difference between the mean of extreme values (over 99 percent) observed over the period 1979-2005 and the extreme values of the RCP 8.5 BCRCM over the duration of the future scenario of 2006-2055.

The terms and words used in the present specification and claims should not be construed as limited to ordinary or dictionary terms and the inventor can properly define the concept of the term to describe its invention in the best way Should be construed in accordance with the principles and meanings and concepts consistent with the technical idea of the present invention.

Throughout the specification, when an element is referred to as "comprising ", it means that it can include other elements as well, without excluding other elements unless specifically stated otherwise. Also, the terms " part, "" module, "and" device " Lt; / RTI >

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

FIG. 1 is a flowchart illustrating a method of correcting an error of extreme precipitation data of a global climate model using a mixed distribution type according to an embodiment of the present invention.

Referring to FIG. 1, an error correction method for extreme precipitation data generated in a global climate model using a mixed distribution type according to the present invention includes an algorithm for correcting an error of precipitation data of a predetermined climate model installed in a computer (GCM) or local climate model (RCM) products by the execution of the algorithm, as set forth in step S101 ). Here, the climate scenario of the Global Climate Model (GCM) or Regional Climate Model (RCM) deliverables may consist of a base (historical) period and a future period.

(GCM) or regional climate model (RCM) deliverables upon completion of the establishment of the climate scenario of the global climate model (GCM) or regional climate model (RCM) the probability distribution of the variables of the regional climate model (RCM) is adjusted for the probability distribution of the observation data using quantile mapping (QM) (step S102). Here, the probability distribution (y) of the observed data can be defined by the following mathematical relation. This is explained again later.

Thus, when the adjustment of the probability distribution of the RCM variables is completed, a mixture distribution (RCM) is estimated for the assessment of the climate change impact based on the probability distribution of the adjusted RCM variables ) Function (step S103). Here, the mixed distribution function can be defined by the following equation. Likewise, this will be explained later.

Then, parameters of the mixed distribution function models are estimated using a meta-heuristic maximum likelihood (MHML) technique (step S104). Here, the estimator of the parameter may be determined by maximizing the likelihood function.

When the estimation of the parameters of the mixed distribution function models is completed, the graph of the observation data (Obs.) Graph nearest to the extreme precipitation (Extreme precip.) Among the plurality of mixed distribution function models tested in step S103 And performs deviation correction based on the resultant data obtained by the model of the mixed distribution function showing the characteristics and the estimated parameter (step S105). At this time, a G-U (Gamma-Gumbel) mixed distribution can be used to perform such deviation correction.

When the deviation correction is completed as described above, the correction result is reflected in the extreme precipitation data of the climate model, thereby completing the error correction of the extreme precipitation data of the climate model (step S106).

Hereinafter, the method of correcting the error of the extreme precipitation data of the global climate model using the mixed distribution type according to the present invention will be described in detail.

The present invention applies a mixed distribution type on the mantle to compensate for variations in local precipitation, particularly among local climate model calculations. Mixed distribution types have been widely used in the area of precipitation and flood frequency analysis. Furthermore, it is reported that heterogeneous mixed-distribution types can be a good alternative for the analysis of extreme precipitation frequency in South Korea, since various resources of extreme precipitation events affect these regions.

The inventors of the present invention have tested mixed distribution types to find the most suitable distribution type for compensating future precipitation variations of local climate model outputs, in particular, to preserve statistical properties of extreme events.

<Mathematical Explanation>

Climate scenarios of the Global Climate Model (GCM) or Regional Climate Model (RCM) deliverables consist of a basic (historical) period and a future period. The necessary parameters for the mantle mapping are estimated with data from the baseline period, and the estimated parameters are applied to the data for the future period to assess the impact of climate change as an extreme precipitation event.

Hereinafter, a deconvolution process for correcting deviations in simulated meteorological variables (i.e., local climate model outputs) as well as the probability distribution employed in the present invention is described.

<Quadratic mapping (QM) and employed probability distribution>

Quadratic mapping (QM) maps the probability distribution of regional climate model (RCM) variables (denoted by x) to the cumulative distribution function (CDF) of two distributions for the probability distribution of observed data It is possible to adjust through matching. Through the decadent mapping, the cumulative distribution function of the regional climate model (RCM) output data is shifted to one of the observed data. In simple terms, the idempotent can be expressed as

은 관측 데이터에 대한 누적 분포 함수의 역함수를 나타내고,

은 RCM 산출의 누적 분포 함수를 나타낸다.here,

Represents the inverse of the cumulative distribution function for the observed data,

Represents the cumulative distribution function of the RCM calculation.

In general, gamma distributions have been widely used to fit local climate model data, as well as observational data, particularly for precipitation variables. The probability distribution function (PDF) and the cumulative distribution function (CDF) of the gamma distribution can be expressed as follows.

는 감마 함수이고,

와

는 각각 크기와 형태 매개변수이다.here,

Is a gamma function,

Wow

Are size and shape parameters, respectively.

In the present invention, the inventors have further tested possible distribution types commonly employed in hydrological applications such as "Exponential "," Gumbel ", and "GEV (Generalized Extreme Value) ". Their probability distribution functions and cumulative distribution functions are defined as follows. The probability distribution function and the cumulative distribution function of the GEV distribution can be expressed as follows.

는 위치 매개변수이고,

와

는 각각 크기와 형태 매개변수이다.here,

Is a positional parameter,

Wow

Are size and shape parameters, respectively.

In addition, the probability distribution function and the cumulative distribution function of the "Gumbel" distribution can be expressed as follows.

In addition, the probability distribution function and the cumulative distribution function of the "Exponential" distribution can be expressed as follows.

On the other hand, most of the daily precipitation records are zero values (referred to as dry days) called intermittent, but local climate model rainfall data do not adequately contain these intermittency. The intermittent part must be fitted in advance to the baseline (observation data) period and the limit value that gives the local climate model day zero value of precipitation data should be estimated as one parameter. The probability of zero values in the observed daily precipitation data can be expressed as:

는 기초 기간에 있어서의 연간 총일수이고,

는

중의 건조일수이다. 지역 기후 모델 산출에 있어서의 일일 강수량의 제로(zero) 부분은 일반적으로 관측 데이터의 부분보다 더 작다. 즉, 기초 기간에 대하여

의 관계를 갖는다. 그러므로, 지역 기후 모델 강수량 값들의 일부는 다음의 수식과 같이

가 되도록 제로(zero)로 할당되어야 한다.here,

Is the total number of days per year in the base period,

The

Lt; / RTI &gt; The zero portion of the daily precipitation in the local climate model output is generally smaller than the portion of the observed data. That is,

. Therefore, some of the local climate model precipitation values are given by

To be zero.

는 상기 수학식 3을 적용하여

가 되도록 하기 위한 한계값이다. 이러한 한계값

는 미래 지역 기후 모델 강수량에도 바로 적용되도록 한다.here,

Lt; RTI ID = 0.0 &gt; (3) &lt;

. &Lt; / RTI &gt; These limits

To be applied immediately to future climate model precipitation.

The present inventors have also considered several mixed distribution models since extreme precipitation events are derived from various climatic or meteorological sources such as tropical cyclones (so-called typhoons) and seasonal rainfall (rainy season).

<Mixed distribution>

The mixed distribution function f (x) can be expressed as a metered sum of element densities as follows.

는 j번째 밀도 요소들의 매개변수 세트이고,

는 j번째 혼합 부분 또는 가중치이다.

는 1보다 크지 않은 음수가 아닌 값이고, h는 적용된 혼합형들의 개수이다.here,

Is the parameter set of the jth density elements,

Is the jth mixing part or weight.

Is a nonnegative value that is not greater than 1, and h is the number of hybrid types applied.

Many combinations of mixed distribution types have been tested. Based on their performance such as Exponential-Exponential (EE), Exponential-Gamma (EG), Gamma-Gumbel (GU), and Gamma- . Their probability distribution functions can be expressed by the following equations 13-16.

The inventor also tested the GEV-GEV combination. This results in too many parameters without showing significant improvement. Mixed models with more than two elements have not been considered because of its complexity and stinginess.

<Meta-Heuristic Maximum Likelihood (MHML)>

이지만 알려지지 않은 매개변수

로부터 무작위 샘플들

을 가지고, 우도함수는 무작위 샘플의 결합 분포가 된다. 이것은 다음과 같이 나타낼 수 있다.Several methods have been developed to estimate the parameters of distribution models, such as Method of Moment, Maximum Likelihood, and Probability Weighted Moment. The maximum likelihood (ML) is one of the most common alternatives for estimating the parameters of the general distribution models. The parameter estimator is determined by maximizing the likelihood function. Known (or assumed) density function

But unknown parameters

From random samples

And the likelihood function is the joint distribution of the random samples. This can be expressed as:

Where n is the number of data points. The logarithm was taken for the likelihood function for easy calculation as shown in Equation 18 below.

)함으로써 추정된다. 본 발명에서 최우도(ML) 기법이 "exponential", "Gamma", "Gumbel" 및 "GEV"와 같은 일반 분포형들의 매개변수를 추정하기 위해 채용되었다. 함수들의 도함수(미분계수)를 취함으로써 로그 우도함수들을 최대화하기 위한 분석적 해 및 수치적 해는 도함수의 값을 영(zero)으로 놓고 풀게 된다.The maximum likelihood (ML) method for the parameters θ (ie, θ ₁ , ..., θ _k ) is maximized across parameters

). In the present invention, a maximum likelihood (ML) technique has been employed to estimate parameters of common distribution types such as "exponential", "Gamma", "Gumbel", and "GEV". The analytic solution and the numerical solution for maximizing the log-likelihood functions by taking derivatives of the functions (differential coefficients) are solved by setting the value of the derivative to zero.

Furthermore, the log-likelihood function of the mixed distribution can be expressed as:

의 미분계수가 혼합 요소들의 역이 되기 때문에 혼합 분포형들의 우도함수의 최대화를 해결하기 위한 간단한 분석적 및 수치적 해는 존재하지 않는다. 하나의 가능한 접근법은 예상 최대화(Expectation Maximization;EM) 알고리즘이다. 하지만, 이것은 관측치들의 수가 불충분할 때 해를 추정하는 과정에서 수렴되지 않고 발산하게 된다.Where n is the number of data points.

There is no simple analytical and numerical solution to solve the maximization of the likelihood function of the mixed distribution types. One possible approach is the Expectation Maximization (EM) algorithm. However, this is not converged in the course of estimating the solution when the number of observations is insufficient.

Instead, meta-heuristic algorithms such as optimization algorithms are employed in the present invention to find a set of parameters that maximize the log likelihood function in Equation 19 above. Shin et al. (2014) employed a meta-heuristic maximum likelihood (MHML) method to fit the mixed distribution model. The results showed that the MHML method is superior to the conventional EM algorithm.

The meta-heuristic algorithm repeatedly tries to improve the given initial solution. Many meta-heuristic programs have been proposed, such as genetic algorithm (GA), particle swarm optimization, and harmony search (HS).

The present inventor has tested genetic algorithms and harmonic searches, and found that the harmonic searches show little computational time for the genetic algorithms without any difference in performance. Therefore, harmonic search is used in the present invention as a representative of meta-heuristic algorithms.

In order to solve the optimization problem, the procedure of the harmonic search method is as follows.

(1) A harmony memory (HM) is randomly simulated from a uniform distribution to a harmonic memory size (HMS, N _HM ) as shown in the following Equation (20).

Here, i = 1, ..., k , j = 1, ..., a N _HM, U _[i Low, Up _i] is the upper boundary from "Low _i" of the lower boundary i with respect to the second parameter, Up _i . The generated HM can be expressed as the following equation.

)를 다음의 수학식 22로 처리함.(2) a new set

) Is processed by the following equation (22).

에 대한 조화 메모리 고려율(harmony memory considering rate)이다. 이러한 절차는 HMCR의 확률에 대해서는 수학식 22에서 HM의 동일한 변수로부터 새로운 조화 세트의 각 결정 변수를 샘플링한다. 그 외에는 수학식 20에서와 같은 균일 분포로부터 조화 세트를 생성한다.In this case,

Is the harmony memory considering rate for the memory. This procedure samples each decision variable of the new harmonization set from the same variable of HM in equation (22) for the probability of HMCR. Otherwise, a harmonization set is generated from the uniform distribution as in Equation (20).

)의 각 변수를 조정함.(3) The probability of a pitch adjustment rate (PAR) as shown in equation (23)

) Are adjusted.

의 가변성도 또한 크고, 그 반대도 마찬가지이다.Here, ε is a uniform random variable as U [-h, h], and h is an arbitrary distance bandwidth. Here, when h is large,

Is also large, and vice versa.

(4) update HM (harmony memory) by replacing the worst harmonics corresponding to the worst objective function with a new set that is processed and adjusted.

(5) Repeat steps (2) to (4) until the termination criterion is satisfied.

Following an empirically based harmonic search parameter range is a sufficient solution of 10-50 for HMS (0.7-0.95 for HMCR, 0.2-0.5 for PAR, and HEM (Geem et al., 2001) It is recommended to calculate. In the present invention, the inventors have tested different values for ranges and ratios, found that the median values are fairly appropriate and there is no significant difference in performance. The results shown in the present invention were obtained with a median of ratios and numbers (i.e., HMCR = 0.8, PAR = 0.4, HMS = 20).

<Study area and data explanation>

In this study, 60 meteorological stations were selected throughout South Korea for observational data to clarify the performance of the mixed distribution types employed in the deviation correction and to reflect them in extreme weather systems. Data were obtained from the Korea Meteorological Administration (KMA). For the consistency of the data applied across selected stations, the used recording period of the adopted Remote Control Processing Module (RCM) data is 1979-2005.

To assess future climate patterns of extreme precipitation, future RCM scenarios (RCP 4.5 and 8.5) were selected from meteorological stations (KMA). The selected scenarios are based on the regional climate model HadGEM3-RA based on the global atmospheric HadGEM2-AO at the Met Office Hadley Center (MOHC) and the National Weather Research Institute (CORDEX) through the Coordinated Regional Climate Downscaling Experiment NIMR) from the National Institute of Meteorological Research (NIMR). A detailed description of the mechanical core and physical packages can be found in "Davies et al. (2005)" and "Martin et al. (2006)". For high resolution experiments on the Korean Peninsula, the number of grid points is 184 (East - West) × 164 (South - North) and the horizontal resolution is about 12.5 km. The time scale applied is 1979-2005 for management practices and 2006-2100 for future scenarios.

<Application Methodology and Results>

1) Application Methodology

For the 60 meteorological stations across South Korea, the RCM daily rainfall data for the observation period are shown as Exponential (E), Gamma (G), Gumbel (U), GEV Gamma-Gumbel (GU) "and" Gamma-GEV (GV) "distribution types. The "Exponential (E)" and "Gamma (G)" distribution types were chosen because they have been commonly employed for daily precipitation data in literature. Two extreme value distributions (U & V) have been chosen because they have been extensively used in the extreme analysis of precipitation data.

Parameters of probability distributions were estimated from the data of the baseline period of the observed data and RCM data. The deviation-corrected RCM (BCRCM) precipitation data for the baseline period was obtained by the estimated parameters and RCM outputs on equation (1) and observations. The results of the BCRCM outputs were compared with the RCM outputs to determine how angular distribution was appropriate, while preserving the observations and, in particular, the statistical properties of observed extreme events. In addition, future RCP scenarios (RCP 4.5 and RCP 8.5) of the BCRCM data have been obtained and the results will show how future extreme values will change for future climate scenarios.

The overall results for 60 observatories in South Korea are given as box plots. The boxes represent the interquartile range (IQR) and whiskers extending to 1.5 × IQR. The horizontal lines inside the box represent the median of the data. Data outside the whiskers (1.5 × IQR) is indicated by the plus indicator (+).

Among the results of the 60 stations, two observatories with high latitude and low latitude geographical positions such as Observatory 119 (Suwon) and Observation 189 (Seogwipo) are selected and provided whenever all information can not be given due to limited space .

2) Results

To show the performance of the non-mixed and mixed distribution types, the pre-calibration RCM outputs of all 60 stations were calibrated to the selected distribution types for the observation period of 1979-2005. In FIGS. 2 and 3, the RCM (BCRCM) artifacts that have been corrected for the binomial are plotted as the RCM product (black cross) for pre-calibration of daily precipitation for two selected stations such as 119 (Suwon) and 189 (Seogwipo) (Quartile) (QQ) between the observed values for the axis and the BCRCM output (in the form of a red square) for the y-axis. Markers closer to the 45 degree line imply better coordination of the observed data and vice versa.

In Fig. 2, the BCRCM output from the GV distribution shows an outlier (defined here above 1000 mm), whereas only the BCRCM output with GU and GV mixed distribution types (see (f) and (h) Respectively. In FIG. 3, for Seogwipo, V, G-U, and G-V show good agreement with the observed data, while U, V, and G-V show anomalies.

These two figures (Figs. 2 and 3) clearly show that the G-U mixed distribution can be an excellent alternative for the shift correction of RCM data to preserve probabilistic distribution types.

More than 99 percent of extreme precipitation of RCM and BCRCM as well as observations were given to Suwon and Seogwipo according to corresponding reproduction periods in Figs. 4 and 5. Extreme precipitation observations fit the BCRCM with a G-U distribution without any anomalies, while the remaining distributions, except for the V and G-V distributions, estimate too little extreme precipitation observed over the entire replenishment period. These distributions indicate that estimated future estimates lead to lower trends than actual expectations. Such an underestimation would considerably less design rainfall considering these future climate scenarios for hydraulic structures.

In Figure 6, the overall result of the difference between the observations and the raw RCM products as well as the BCRCM products with the eight tested distribution types is shown for all day precipitation (upper panel) and extreme precipitation (greater than 99 percent, lower panel) Were used as mean absolute errors (MAEs) for 60 meteorological stations in South Korea. The MAE results for all precipitation show that the E-E, E-G and G-V distributions are superior to the rest distributions, while the G-U distributions show slightly higher errors than those three distributions (see the upper panel of FIG. 6). However, all of the tested distribution types except for the G-U distribution yield unreasonably large outliers for the river values in South Korea. For extreme precipitation above 99 percent, G-U is dominant over the remaining distributions with no odds.

Similar to the MAE in FIG. 7, the RMSEs of all precipitation data show that the E-G distribution is a good alternative, but that the G-U distribution is the only distribution that does not produce anomalies. On the other hand, the RMSE (over 99 percent) of extreme precipitation shows that the G-U distribution can be the best alternative without any abnormalities.

In FIG. 8, the mean values of extreme precipitation observations as well as BCRCM data for past time (1979-2005) and future time (2006-2055) were compared to show the overall performance of the applied distribution types. The G-U distribution shows the best performance. As can be seen in Figure 8 (f) showing the G-U distribution, the median of the mean precipitation for the RCM data (indicated by the horizontal dotted line) is approximately equal to the median for the observed data. In contrast, the remaining distribution models show overestimated or underestimated estimates. Otherwise, the generation of outliers for the mean statistics is visible. Furthermore, all tested distribution types except the G-U distribution produce outliers for future extreme precipitation affected by climate change (ie, RCP 4.5 and 8.5).

Mean values of observed extreme precipitation (greater than 99 percent) are plotted spatially in Figure 9 throughout South Korea. Spatial illustrations show that the southern and northern regions of South Korea have relatively higher extreme values than central regions. The differences between the extreme mean precipitation of the observed values and the extreme mean precipitation of the BCRCM from the tested distribution types (ie, RCM-Obs) for the observation period (1979-2005) are shown in FIG. In addition, differences between the extreme mean precipitation of the BCRCM from the tested distribution types (ie, RCM-Obs) for future scenario time 2006-2055 with extreme mean precipitation of observations and RCP 4.5 and RCP 8.5 11 and 12, respectively.

In Figure 10, the difference in mean extreme precipitation over the observation period is a measure of performance measurement and should be closer to zero for better performance.

As shown in the previous results, the G-U distribution shows the minimum difference between the observations and the BCRCM outputs. The western and eastern sides of the southern region show that the mean extrema of the BCRCM from the G-U distribution is slightly lower than the observations.

RCP 4.5 as in FIG. 11 shows that the change in average extreme values is significantly different between each tested distribution type. The E, G, U, and E-E distributions show a decrease in extreme precipitation in the future up to 2055, while the remaining four distributions show an increase in extreme precipitation. This suggests that the selection of an appropriate distribution plays a very important role in gauging future changes in extreme precipitation. In the G-U distribution, the left southern and northern regions show a high increase, while the right and middle regions show no or slight increase. These spatial features of future mean extreme precipitation for RCP 4.5 show similar habits for RCP 8.5 as shown in FIG.

<Summary and Conclusion>

Appropriate side correction plays a crucial role in the correct assessment of climate change impacts, especially for extreme precipitation events. The purpose of this study is to test the mixed distribution types compared to the conventional non-mixed distribution types for proper side correction of GCM or RCM data. The present inventors have evaluated the performance of the quintiles (QM), especially for extreme precipitation. Furthermore, we have applied it to future climate scenarios to see how much difference can be formed for the choice of the probability distribution model with the deconcentration with adopted distribution types.

The results show that the G-U (Gamma-Gumbel) mixed distribution is the best alternative to produce an observational distribution pattern without producing anomalies. Since extreme events in South Korea originate from a variety of sources, such as tropical cyclones (typhoons) and monsoon rainfall, these results are consistent with "Shin et al. (2015a)" Share the conclusion. Accurate reproduction of historical distribution characteristics suggests a reliable assessment of future climate patterns, especially for water-related disasters.

In conclusion, the results of this study demonstrate that time-based statistics of daily precipitation from climate models are significantly and consistently improved only by intensity-based statistical deviation correction techniques.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but many variations and modifications may be made without departing from the spirit and scope of the invention. Be clear to the technician. Accordingly, the true scope of protection of the present invention should be construed according to the following claims, and all technical ideas within the scope of the same should be construed as being included in the scope of the present invention.

Claims (6)

A method for correcting an error of extreme precipitation data of a climate model by executing an algorithm (software program) for correcting an error of precipitation data of a predetermined climate model mounted on a computer,
a) establishing a climate scenario of global climate model (GCM) or regional climate model (RCM) outputs by execution of the algorithm;
(b) using the quantile mapping (QM) to calibrate the deviation of the global climate model (GCM) or regional climate model (RCM) Adjusting a probability distribution of the variable;
c) testing models of a plurality of mixture distribution functions for evaluation of climate change impacts based on a probability distribution of the parameters of the adjusted regional climate model (RCM);
d) estimating parameters of the mixed distribution function models using a meta-heuristic maximum likelihood (MHML) technique;
e) comparing the result data obtained by the model of the mixed distribution function showing the graph characteristic closest to the Observation Data (Obs.) graph characteristic with respect to the extreme precipitation among the plurality of mixed distribution function models tested, Performing shift correction based on the estimated parameters; And
and f) correcting the error of the extreme precipitation data of the climate model by reflecting the result of the deviation correction to the extreme precipitation data of the climate model.
The method according to claim 1,
The climate scenario of the Global Climate Model (GCM) or Regional Climate Model (RCM) products in step a) above is a method of correcting errors in extreme precipitation data of a global climate model using a mixed distribution type consisting of a basic (historical) .
The method according to claim 1,
Wherein the probability distribution (y) of the observed data in step b) is defined by the following equation:

here,

Represents the inverse of the cumulative distribution function for the observed data,

Represents the cumulative distribution function of the RCM calculation.
The method according to claim 1,
Wherein the mixed distribution function in the step c) is defined by the following mathematical relation: a method of correcting the error of extreme precipitation data of a global climate model using a mixed distribution type.

here,

Is the parameter set of the jth density elements,

Is the jth mixing part or weight.

Is a nonnegative value that is not greater than 1, and h is the number of hybrid types applied.
The method according to claim 1,
Wherein the estimator of the parameter is determined by maximizing the likelihood function in step d).
The method according to claim 1,
A method for correcting errors in extreme precipitation data of a global climate model using a mixed distribution type, wherein the deviation correction is performed using a GU (Gamma-Gumbel) mixture distribution in step e).

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