Application Of Drought Index Based On Copula Function Model And FDA Method

Drought is one of the extreme natural disasters,and it is easy to cause incalculable losses to agriculture and ecosystems.Unlike natural disasters,drought has a larger impact and its consequences are difficult to measure.So far,there is no consistent definition of drought.In addition,the causes of drought are also extremely complex.The interweaving of temperature,precipitation,wind speed,radiation and other factors makes drought events difficult to quantify.Many characteristic variables of drought have complex non-linear relationships,which makes it difficult to build drought assessment models.Academia still has not found a perfect way to explain the drought events,and the research on drought is still in the developing stage.Firstly,based on the daily precipitation and temperature data of Henan Shangcai,Chongqing Tongnan and Heilongjiang Fuyuan from 1978 to 2017,the SPI,SPEI indices based on the monthly scale and EDI based on the daily scale are calculated.Compared with the drought monitoring in the last ten years,the identification of drought events by EDI index is similar to that by SPI and SPEI.In terms of the severity of drought,the EDI index is heavier than that by SPEI index,which is similar to that by SPEI index.In view of the advantages of EDI itself,EDI is finally taken as the main drought index studied in this paper.Secondly,according to the classification of drought grade of EDI index,the drought duration D and drought intensity S are extracted from the run-length theory.The marginal distribution functions of D and S are fitted,and the results show that the marginal distribution of Henan,Chongqing and Heilongjiang are lognormal distribution.In view of the strong correlation between D and S,this paper establishes a two-dimensional Copula function model of drought duration D and drought intensity S,and finally determines that the joint distribution functions of the three places are Frank copula functions.By analyzing the co-occurrence period and co-occurrence period,the paper finds that the incidence of drought events with high intensity and long duration is very low;when the same degree of drought duration D and drought intensity S increases,the co-occurrence period increases faster than the co-occurrence period,which is consistent with the fact.Finally,the effective drought index EDI was analyzed by functional data,and the Fourier function was used as the fitting base.In order to avoid curve over-fitting,the linear differential operator of the curve is used to smooth the curve,and the optimal penalty coefficients of the three regions are selected by cross-validation method.Finally,the change trend of EDI is extracted and the value of EDI is predicted by using the method of principal component analysis and prediction of functional data.It is concluded that the EDI index of Henan and Chongqing are better predicted by analyzing the drought data,which can identify drought relatively accurately,while the drought identification effect of Heilongjiang is general.