# Characteristics of Extreme Value Statistics of Annual Maximum Monthly Precipitation in East Asia Calculated Using an Earth System Model of Intermediate Complexity

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data and Methods

#### 2.1. Earth System Model

^{14}C annual tree ring data were used. The greenhouse gases considered were CO

_{2}, CH

_{4}, and N

_{2}O.

#### 2.2. Target Grid

#### 2.3. Analysis Method

_{i}represents an annual maximum monthly precipitation in interval i, and μ

_{i}and β

_{i}represent location and scale of x. The L-moment method [19] was used to estimate the population parameter, and precipitation within the return level was estimated for each of the 117 samples.

#### 2.4. Data

## 3. Current Climate Reproducibility

## 4. Results and Discussion

#### 4.1. 100-Year Climatological Annual Maximum Monthly Precipitation

^{−1}, equivalent to 24 mm·month

^{−1}. Therefore, the 100-year climatological mean of the annual maximum monthly precipitation did not change much in the target grid.

^{−1}until 5200 BP. Subsequently, the 100-year climatological mean decreased until 2000 BP. Following large variations around 2000 BP, the 100-year climatological mean remained at 9. 1 mm·day

^{−1}until present, albeit with unprecedented large variations. The variations on a 10,000-year time scale probably correspond to the retreat of polar ice sheets, whereby the climatological zonal mean air temperature decreased after 9500 BP in the high-latitude region but not in the mid-latitude region (Figure 2c).

#### 4.2. Estimated Annual Maximum Monthly Precipitation with a Return Level of 100 Years

^{−1}) can be seen in Figure 5b. The skewness and kurtosis values of the data distribution were 0.05 and −0.19, representing a near-normal distribution. Moreover, Bartlett’s test was performed to detect the deviation from normality, further confirming the normal distribution (p < 0.01).

#### 4.3. Autocorrelation

#### 4.4. Wavelet Analysis

^{−1}) in 5200 BP with significance at a 95% confidence level only observed before and after 5200 BP (Figure 7d). This corresponds to the minimum of the estimated annual maximum monthly precipitation with a return level of 100 years in Figure 7a. The other local maxima of the average power spectrum in 7800 BP, 6800 BP, and 2200 BP occurred when the estimated annual maximum monthly precipitation with a return level of 100 years exhibited fluctuation with respect to local values. These fluctuations increased the amplitude and, thus, the average power spectrum.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The target grid (thick blue box) at 135.0° east (E) and 36.0° north (N) in the grid system (thin blue lines) within the Loch-Vecode-Ecbilt-Clio-agism (LOVECLIM) model.

**Figure 2.**(

**a**) Time series of temperature anomalies reconstructed from a proxy of ice cores and of those simulated with LOVECLIM in Greenland during the Holocene. Thick and thin orange lines denote reconstructed and LOVECLIM results, respectively. (

**b**) Time series of mean temperature anomalies in the Northern Hemisphere simulated with LOVECLIM. (

**c**) Same as in (

**b**) but represented separately for high (60–90° N) and mid (30–60° N), and low latitudes (0–30° N). An anomaly was defined as a deviation from the latest 1000 year mean temperatures. The light-blue shading denotes predominant climatic events. This figure was drawn on the basis of Figure 3 in [14] (CC BY).

**Figure 3.**Comparison of climatological mean precipitation between observation at Maizuru (135.32° E, 35.45° N) and LOVECLIM simulation.

**Figure 4.**(

**a**) Time series of 100-year climatological mean of the annual maximum monthly precipitation in the Holocene simulated with LOVECLIM. (

**b**) Same as in (

**a**) but the ratio of the 100 year maximum of the annual maximum monthly precipitation to the 100-year climatological mean.

**Figure 5.**(

**a**) Histogram and (

**b**) quantile–quantile map of the estimated annual maximum monthly precipitation with a return level of 100 years for each 100-year interval for the Holocene under the assumption of a Gumbel distribution. Red lines denote the normal distribution estimated on the basis of the histogram statistics.

**Figure 6.**Autocorrelation of the time series of the estimated annual maximum monthly precipitation with a return level of 100 years for each 100-year interval for the Holocene. The light-blue shading represents the significance interval at a 95% confidence level.

**Figure 7.**Wavelet analysis of time series of the estimated annual maximum monthly precipitation with a return level of 100 years. The Morlet function was used as the other wavelet. (

**a**) Time series of the original estimated annual maximum monthly precipitation with a return level of 100 years (black line) and the inverse transformed values (gray) from wavelet analysis. (

**b**) Wavelet power spectrum. (

**c**) Global wavelet spectrum (black) with a confidence level of 95% (black broken line). The gray solid line denotes the red noise power spectrum, while the gray dotted line denotes the 95% confidence level. (

**d**) Average power scaled every 8–16 centuries. The horizontal broken line denotes the 95% confidence level.

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**MDPI and ACS Style**

Nakaegawa, T.; Kobashi, T.; Kamahori, H.
Characteristics of Extreme Value Statistics of Annual Maximum Monthly Precipitation in East Asia Calculated Using an Earth System Model of Intermediate Complexity. *Atmosphere* **2020**, *11*, 1273.
https://doi.org/10.3390/atmos11121273

**AMA Style**

Nakaegawa T, Kobashi T, Kamahori H.
Characteristics of Extreme Value Statistics of Annual Maximum Monthly Precipitation in East Asia Calculated Using an Earth System Model of Intermediate Complexity. *Atmosphere*. 2020; 11(12):1273.
https://doi.org/10.3390/atmos11121273

**Chicago/Turabian Style**

Nakaegawa, Tosiyuki, Takuro Kobashi, and Hirotaka Kamahori.
2020. "Characteristics of Extreme Value Statistics of Annual Maximum Monthly Precipitation in East Asia Calculated Using an Earth System Model of Intermediate Complexity" *Atmosphere* 11, no. 12: 1273.
https://doi.org/10.3390/atmos11121273