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The changing frequency of extreme climate events generally has profound impacts on our living environment and decision-makers. Based on the daily temperature and precipitation data collected from 753 stations in China during 1961–2005, the geographically weighted regression (GWR) model is used to investigate the relationship between the index of frequency of extreme precipitation (FEP) and other climate extreme indices including frequency of warm days (FWD), frequency of warm nights (FWN), frequency of cold days (FCD), and frequency of cold nights (FCN). Assisted by some statistical tests, it is found that the regression relationship has significant spatial nonstationarity and the influence of each explanatory variable (namely, FWD, FWN, FCD, and FCN) on FEP also exhibits significant spatial inconsistency. Furthermore, some meaningful regional characteristics for the relationship between the studied extreme climate indices are obtained.

There is a general agreement that changes in the frequency or intensity of extreme climate events are likely to exert a much greater impact on nature and humanity than shifts in the mean value [

As for the relationship between some extreme climate indices, researchers generally assume that it is stationary over space and use an ordinary linear regression (OLR) model to analyze it. Nevertheless, it is known that an OLR model can only represent global relationship and it hardly takes into consideration the variations in relationships over space, in other words, the explicit incorporation of space or location has not been that commonly considered. In this context, there has been recently a surge focusing on the inclusion of spatial effects in climate models. A geographically weighted regression (GWR) model, which extends the traditional regression framework by allowing regression coefficients to vary with individual locations (spatial nonstationarity), is an effective method of utilizing spatial information to improve this issue [

China is strongly influenced by the East Asian monsoon [

The rest of the paper is organized as follows. Section

The experimental data sets used in this paper consist of daily maximum and minimum temperatures and daily precipitation observed at 753 meteorological stations in China from January 1, 1961 to December 31, 2005, which were offered by National Meteorological Information Center in China Meteorological Administration. Because the study must rely on reliable data, the missing data in each month should be no more than three days. Therefore, the data collected from the 504 stations (Figure

Stations for which data were available in China. (•) Stations used in this paper; (+) stations omitted due to excessive missing data.

Numerous temperature indices have been used in previous studies of climate events. Some indices involved arbitrary thresholds, such as the number of hot days exceeding 35°C and summer days exceeding 25°C. As indicated by Manton et al. [

As this study covers a broad region in China, climate indices chosen are based on the 10th and 90th percentiles. The extreme climate indices studied in this paper include FEP, FWD, FWN, FCD, and FCN whose definitions are described in detail in Table

Five extreme climate indices calculated based on daily temperature and precipitation data.

Indicator name | Indicator definition (unit: days) |
---|---|

FEP | Let |

FWD | Let |

FWN | Let |

FCD | Let |

FCN | Let |

The technique of linear regression estimates a parameter

An ordinary linear regression (OLR) model can be expressed by

In GWR model, the global regression coefficients are replaced by local parameters

The coefficient function vector

Although GWR is very appealing in analyzing spatial nonstationarity, from the statistical viewpoint, two critical questions still remain. One is the goodness-of-fit test, that is, a OLR model is compared to a GWR model to see which one provides the best fit. Usually, a GWR model can fit a given data set better than an OLR model. However, the simpler a model, the easier it can be applied and interpreted in practice. If a GWR model does not perform significantly better than an OLR model, it means that there is no significant drift in any of the model parameters. Thus, we will prefer an OLR model in practice. On the other hand, if a GWR model significantly outperforms an OLR model, we will be concerned with the second question, that is, whether each coefficient function estimate

To compare the goodness-of-fit of a GWR model and an OLR model, a simplified procedure is summarized as follows.

Formulate the hypothesis

Construct the test statistic

Test the hypothesis. The

In order to test whether each coefficient function estimate

For a given

Construct the test statistic

Test the hypothesis. The

In this part, we will carry out numerical experiments for the OLR model and GWR model. All programs are written in Matlab.

Based on the values of FWD, FWN, FCD, FCN, and FEP, Figure

Spatial distributions of the considered extreme climate indices ((a) FWD, (b) FWN, (c) FCD, (d) FCN, and (e) FEP) over the 504 stations in China.

As shown in Figure

In order to make clear the relationship among these extreme climate indices in 504 stations in China so that some useful information can be provided to decision-makers to help them to deduce the disaster caused by extreme weather, a GWR model was fitted by considering FEP as the response variable

When we apply a fixed Gaussian function, the minimum score of (

Because Wheeler [

Correlation coefficients of the independent variables, that is, FWD, FWN, FCD, and FCN.

FWD | FWN | FCD | FCN | |
---|---|---|---|---|

FWD | 1.0000 | 0.3862 | 0.3453 | 0.1836 |

FWN | 1.0000 | 0.1318 | 0.1329 | |

FCD | 1.0000 | 0.4174 | ||

FCN | 1.0000 |

Correlation coefficients of the GWR coefficient estimates, that is,

1.0000 | −0.4068 | −0.1734 | −0.5044 | 0.0828 | |

1.0000 | 0.0491 | −0.3281 | −0.0366 | ||

1.0000 | −0.4295 | 0.6309 | |||

1.0000 | −0.6375 | ||||

1.0000 |

As shown in Tables

After conducting the goodness-of-fit test, the computed

Prediction error (PE) of the responsible variable, FEP, for ordinary linear regression (OLR) and geographically weighted regression (GWR) over the 504 stations in China.

Furthermore, the statistical significance tests for the variations of the coefficient functions are carried out. The obtained results show that all the regression coefficient estimates

Global stationarity for regression relationship | Significance for | Significance for | Significance for | Significance for | Significance for |
---|---|---|---|---|---|

0 | 0 | 0.0018 | 0 |

In order to visualize these spatial inconsistencies, Figure

Geographic distributions of the estimated GWR coefficient functions ((a)

Figure

As Figure

From Figure

As for

On the basis of the above analysis, some regional characteristics for the relationship between the studied extreme climate indices can be observed. In western China, FEP increases with the increase of FCD, while it decreases with the increase of FWD, FWN, and FCN. In southern China, FEP increases with the increase of FCN, while it decreases with the increase of FWD, FWN, and FCD. In the northern part of northeast China, FEP increases with the increase of FCD and FCN, while it decreases with the increase of FWD and FWN. The impacts of FCN and FCD on the FEP are roughly the opposite over almost all China.

Based on the Chinese daily temperature and precipitation data collected at 753 meteorological stations from 1961 to 2005, the relationship among the numbers of days that experience extreme temperature or precipitation events (i.e., FEP, FWD, FWN, FCD, and FCN) is investigated by a GWR model and their spatial distributions in China. The main conclusions can be summarized as follows.

FWD, FWN, FCD, FCN and FEP exhibit different spatial variations. There are larger values about 24–29 times per year for FWD mainly in northeast China. In the north of the Yangtze River, FWN has larger values of 24–35 times per year. FCD has larger values about 18–26 times per year in most part of China but northwest China. As for FCN, most of China has larger values about 18–28 times except for the south. Except in some stations in southern Xinjiang and Tibet, FEP has larger values of 17–33 times per year.

With respect to how FWD, FWN, FCD, and FCN affect FEP, the GWR model is significantly superior to the OLR model at the significance level 0.05. Furthermore, the statistical tests indicate that the influence of each explanatory variable (viz., FWD, FWN, FCD, and FCN) on FEP has spatial inconsistency.

Some regional features are detected for the relationship between the studied extreme climate indices. In western China, FCD has a positive effect on FEP, which is contrary to that of FWD, FWN, and FCN. However, it is just the opposite in southern China. The effects of FCD as well as FCN on FEP are positive in the northern part of Northeast China, while those of FWD and FWN are negative. Meanwhile, FCN and FCD have the opposite influence on FEP over most of China.

This work is supported by the National Natural Science Foundation of China (Grant nos. 60675013, 10531030) and the National Basic Research Program of China (973 Program) (Grant no. 2007CB311002).