A composite high temperature drought extreme event attribution method

Abstract

The application provides a composite high-temperature drought extreme event attribution method, relates to the technical fields of climate change, disaster prevention and statistical analysis, obtains observation precipitation data and observation temperature data of the same space-time scale, determines a space-time region needing to be subjected to composite high-temperature drought extreme event change attribution analysis according to a time period and a space range corresponding to the data, trims corresponding space longitude and latitude of the observation precipitation data and the observation temperature data according to selected space region longitude and latitude, trims a time dimension corresponding to the observation precipitation data and the observation temperature data according to a selected time range, aligns the trimming results of the observation precipitation data and the observation temperature data according to the time dimension, quantifies the contribution of three driving factors, i.e., precipitation change, temperature change and precipitation correlation change, in the composite high-temperature drought event change, realizes clearization of different sources of composite disaster return period change, is helpful to disaster prevention and reduction, and reduces the influence of climate change.

Description

Technical Field

[0001] This invention relates to the technical fields of climate change, disaster prevention and statistical analysis, and more specifically, to an attribution method for complex high-temperature and drought extreme events based on multivariate Taylor expansion. Background Technology

[0002] With continued global warming, severe droughts and heat waves have increased in many terrestrial regions worldwide in recent decades. Drought and heat waves are two major natural disasters affecting human production and life; they sometimes occur together, generally referred to as combined heat-drought extreme events. Combined heat-drought extreme events can have more severe impacts on ecosystems and human societies than individual events. Therefore, accurately assessing changes in combined heat-drought and dry events and their driving factors is crucial for improving our understanding of these events and mitigating their impacts.

[0003] The occurrence of combined dry-heat events is not only related to individual drought and heat wave events, but also to the correlation between precipitation and temperature, which is determined by the multivariate nature of the combined events. Therefore, changes in drought events, heat wave events, and the relationship between precipitation and temperature can be considered as three main factors driving changes in combined dry-heat events. Since the interdependence between variables is a key factor in characterizing combined extreme events, models based on the joint distribution of multivariate variables, such as copula and meta-gaussian models, are often used to simulate the occurrence of combined events. These joint distribution models not only meet the needs of describing the correlation properties of variables, but also allow for flexible marginal distribution forms in modeling to adapt to different meteorological and hydrological variables.

[0004] For example, an existing technology discloses a meteorological drought probabilistic forecasting method based on weather forecasting. First, basic data, including measured data of precipitation and average temperature, are collected. Then, a drought is defined, and a generalized Bayesian model is used to predict the probability of precipitation and temperature. Finally, a drought probabilistic early warning model based on the copula function is established, which improves the region's prevention of extreme hydrological events. However, it lacks quantitative means for the statistical changes in precipitation and temperature, and the overall change analysis is not comprehensive, lacks intuitiveness, and has poor disaster reduction and prevention effects. Summary of the Invention

[0005] To address the shortcomings of existing methods for preventing and managing complex high-temperature and drought extreme events, such as the lack of quantitative methods for statistical changes in precipitation and temperature, incomplete change analysis, and poor intuitiveness, this invention proposes a multivariate Taylor expansion-based attribution method for complex high-temperature and drought extreme events. This method quantifies the sources of the recurrence period of complex disasters based on the statistical characteristics of changes in precipitation and temperature, clarifying the different sources of changes in the recurrence period of complex disasters, which helps in disaster prevention and mitigation and reduces the impact of climate change.

[0006] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows:

[0007] An attribution method for complex high-temperature and drought extreme events, the method comprising the following steps:

[0008] S1. Use observed precipitation data and observed temperature data of the same spatiotemporal scale as input data;

[0009] S2. Based on the time periods and spatial ranges corresponding to the observed precipitation and temperature data in the input data, determine the spatiotemporal regions where attribution analysis of the changes in the composite high temperature and drought extreme events is required;

[0010] S3. Trim the spatial longitude and latitude of the observed precipitation data and observed temperature data according to the selected spatial region, and trim the time dimension of the observed precipitation data and observed temperature data according to the selected time range;

[0011] S4. Determine the set of spatial distributions corresponding to the data obtained from the cropping that need to be analyzed for the recurrence period of the combined high temperature and drought extreme events, and filter out the precipitation data within the set; determine the union of the selected time range and the time range for which the combined high temperature and drought change assessment needs to be performed, and crop the precipitation data for which the combined high temperature and drought change assessment needs to be performed;

[0012] S5. Align the cropped results of observed precipitation and temperature data according to the time dimension;

[0013] S6. Extract aligned observed precipitation and temperature data. Based on precipitation and temperature data with the same spatial location, identify the changes in driving factors of the composite high temperature and drought extreme events and conduct quantitative attribution analysis.

[0014] Preferably, the input data includes observed precipitation and observed temperature at the same spatiotemporal scale. The observed precipitation part includes observed precipitation data and its corresponding spatiotemporal dimensions, and the observed temperature part includes observed temperature data and its corresponding spatiotemporal dimensions. Based on the time dimension of “year-month-day” to “year-month-day” and the spatial range of [“longitude range”, “latitude range”] entered in string form, the spatiotemporal region for which composite event change attribution analysis needs to be performed is determined.

[0015] Preferably, in step S3, when cropping the spatial longitude corresponding to the observed precipitation data and observed temperature data according to the selected spatial region, all longitude information in the observed precipitation data and observed temperature data is read, and the longitude vector of any one of the observed precipitation data and observed temperature data is represented by a vector. It is represented as:

[0016]

[0017] in, Represents the longitude vector of either observed precipitation data or observed temperature data. It is the value of any longitude from either the observed precipitation data or the observed temperature data. p The total length of either the observed precipitation data or the observed temperature data along the longitude direction. i =1,2,…, p ;

[0018] Read the longitude range of the selected spatial region using vector coordinates. It is represented as:

[0019]

[0020] By selecting longitude ranges that exist in both observed precipitation and observed temperature data and fall within the selected spatial region's latitude and longitude, the spatial longitudes corresponding to the cropped observed precipitation and temperature data are obtained. These longitudes are then represented by vectors. It is represented as: ;

[0021] When cropping the spatial dimensions corresponding to observed precipitation and temperature data according to the selected spatial region's latitude and longitude, all latitude information from the observed precipitation and temperature data is read. Let the latitude vector of any one of the observed precipitation and temperature data be represented by a vector... It is represented as:

[0022]

[0023] in, Represents the latitude vector of either the observed precipitation data or the observed temperature data. It is the value of any latitude from the observed precipitation data and observed temperature data. q The total length of either the observed precipitation data or the observed temperature data along the longitude direction. j =1,2,…, q ;

[0024] Read the latitude range of the selected spatial region using vector coordinates. It is represented as:

[0025]

[0026] By selecting a latitude range that exists in both observed precipitation and observed temperature data and falls within the selected spatial region, the spatial latitudes corresponding to the cropped observed precipitation and temperature data are obtained. These latitudes are then used as vectors. It is represented as: .

[0027] Preferably, the method for determining the set of spatial distributions corresponding to the data for the recurrence period of the combined high-temperature and drought extreme events is as follows: taking a vector , The set of elements contained , Calculate the set , Cartesian product S: This yields the set of spatial distributions corresponding to the data for which the recurrence period of the composite event needs to be determined.

[0028] Preferably, in step S6, the changing trend of the driving factors of the composite high temperature and drought extreme events is estimated using the Sen slope, and the Mann-Kendall trend test method is used to determine whether the trend is significant.

[0029] Preferably, the attribution analysis process for combined high-temperature and drought extreme events is as follows:

[0030] S61. Using the Normal Quantile Transform (NQT) method, a precipitation time series of length n is transformed. and a temperature time series of length n These were respectively converted into standardized precipitation index (SPI) time series for the corresponding research period. Standardized Temperature Index (STI) time series ;

[0031] S62. Will and By incorporating a two-dimensional meta-Gaussian model and the equation for calculating the recurrence interval of extreme events, the recurrence intervals of drought and heat wave events over the entire time series are estimated. The correlation coefficient between the Standardized Precipitation Index (SPI) and the Standardized Temperature Index (STI) ;

[0032] The equation for the recurrence period of extreme events is expressed as:

[0033]

[0034] in, , , These are the recurrence periods of drought events, heat wave events, and combined high-temperature and drought events, respectively. and These are the threshold values ​​for the standardized indices corresponding to drought and heat wave events; Let the cumulative distribution function and correlation coefficient of the standard normal distribution be respectively: The cumulative distribution function of the bivariate normal distribution;

[0035] S63. The entire time series Using this as a benchmark, the partial derivatives of the combined time with respect to drought return period, heat return period, and precipitation-temperature relationship are calculated by substituting the total differential equation for the return period of the combined event. ;

[0036] S64. Divide the time series of the Standardized Precipitation Index (SPI) and the Standardized Temperature Index (STI) into two equal time periods, period 1 and period 2. The time of period 1 is represented as follows: The time period for time period 2 is represented as Among them, the precipitation time series and temperature time series in time period 1 are respectively and The precipitation and temperature time series in time period 2 are respectively and ;

[0037] S65. [The sentence appears to be incomplete and lacks context.] and Substituting the equation for the return period of extreme events, we obtain the drought return period in period 1. Heatwave recurrence period Correlation coefficient between precipitation and temperature Recurrence period of joint events ; in time period 2 and Substituting the equation for the return period of extreme events, we obtain the drought return period in period 2. Heatwave recurrence period Correlation coefficient between precipitation and temperature Recurrence period of joint events ;

[0038] S66. Calculate the changes in the return period of joint events, the return period of drought, the return period of heat waves, and the correlation between precipitation and temperature during the two time periods, time period 1 and time period 2.

[0039] S67. Based on the combined changes in time return period, drought return period, heat wave return period, and the correlation between precipitation and temperature, calculate the absolute contribution of each variable. and relative contribution .

[0040] Here, the sources of the recurrence period of compound disasters are quantified based on the statistical characteristics of precipitation and temperature changes. This clarifies the different sources of changes in the recurrence period of compound disasters, which helps in disaster prevention and mitigation and reduces the impact of climate change.

[0041] Preferably, the calculation expression for the change in the return period of the joint event described in step S66 is: ;

[0042] The formula for calculating the variation in drought return period is: ;

[0043] The formula for calculating the recurrence interval of heat waves is: ;

[0044] The formula for calculating the change in the correlation between precipitation and temperature is: .

[0045] Preferably, the absolute contribution of each variable is calculated. The expressions are as follows:

[0046] ;

[0047] in, and These represent the changes in the return period of drought and the changes in the return period of the compound disasters it causes, respectively. and These represent the changes in the return period of heat waves and the changes in the return period of the compound disasters they cause, respectively. and These represent changes in the correlation between precipitation and temperature, and changes in the recurrence period of the resulting compound disasters, respectively.

[0048] Calculate relative contribution The expressions are as follows:

[0049]

[0050] in, These represent the relative contributions of changes in precipitation, temperature, and the correlation between precipitation and temperature to the change in the recurrence period of dry-heat combined disasters.

[0051] Preferably, the method further includes: visualizing the precipitation types of the entire space based on the results of attribution analysis, and drawing a watershed diagnostic map of complex high temperature and drought extreme events.

[0052] Here, during the visualization process, the same observation time and precipitation time can be automatically matched, avoiding the complicated manual adjustment process.

[0053] Preferably, the watershed diagnostic map of the combined high temperature and drought extreme event includes: a spatial map of the changing trends of driving factors, a spatial map of the changing return period of the combined event, a spatial map of the contribution of the combined event, and a watershed diagnostic map of the combined event;

[0054] The watershed diagnostic map of the combined high temperature and drought extreme events shows the joint distribution within time period 1 and time period 2, the occurrence of drought, high temperature and combined high temperature and drought events in this watershed over time, the recurrence period of the combined events and the contribution of each factor over time.

[0055] The watershed diagnostic map of combined high-temperature and drought extreme events can visually link the joint distribution, extreme events, and factor contributions at the watershed scale. It can analyze the overall changes in the watershed from the perspective of joint distribution, as well as specifically analyze the changes in extreme events and the causes of these changes within a certain time period.

[0056] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0057] This application proposes an attribution method for complex high-temperature and drought extreme events. First, it acquires observed precipitation and temperature data at the same spatiotemporal scale. Based on the corresponding time periods and spatial ranges of the observed precipitation and temperature data, it determines the spatiotemporal regions for attribution analysis of changes in complex high-temperature and drought extreme events. Then, it trims the spatial longitude and latitude corresponding to the observed precipitation and temperature data according to the selected spatial region, and trims the time dimension corresponding to the observed precipitation and temperature data according to the selected time range. The trimmed results of the observed precipitation and temperature data are aligned according to the time dimension, quantifying the contributions of three driving factors—precipitation change, temperature change, and changes in precipitation correlation—to the changes in complex high-temperature and drought events. This clarifies the different sources of changes in the recurrence period of complex disasters, contributing to disaster prevention and mitigation, and reducing the impact of climate change. Attached Figure Description

[0058] Figure 1 This is a schematic diagram illustrating the overall process of the composite high-temperature and drought extreme event attribution method proposed in Embodiment 1 of the present invention.

[0059] Figure 2 A detailed block diagram illustrating the attribution of the complex high-temperature and drought extreme events proposed in Embodiment 2 of the present invention;

[0060] Figure 3 This represents the watershed diagnostic map for the combined high temperature and drought extreme events proposed in Embodiment 3 of the present invention. Detailed Implementation

[0061] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0062] To better illustrate this embodiment, some parts of the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions;

[0063] It is understandable to those skilled in the art that some well-known details may be omitted from the accompanying drawings.

[0064] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0065] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0066] Example 1

[0067] This embodiment proposes a composite attribution method for extreme high-temperature and drought events. The overall flowchart of the method is shown below. Figure 1 As shown, it includes the following steps:

[0068] S1. Use observed precipitation data and observed temperature data of the same spatiotemporal scale as input data;

[0069] S2. Based on the time periods and spatial ranges corresponding to the observed precipitation and temperature data in the input data, determine the spatiotemporal regions where attribution analysis of the changes in the composite high temperature and drought extreme events is required;

[0070] S3. Trim the spatial longitude and latitude of the observed precipitation data and observed temperature data according to the selected spatial region, and trim the time dimension of the observed precipitation data and observed temperature data according to the selected time range;

[0071] S4. Determine the set of spatial distributions corresponding to the data obtained from the cropping that need to be analyzed for the recurrence period of the combined high temperature and drought extreme events, and filter out the precipitation data within the set; determine the union of the selected time range and the time range for which the combined high temperature and drought change assessment needs to be performed, and crop the precipitation data for which the combined high temperature and drought change assessment needs to be performed;

[0072] S5. Align the cropped results of observed precipitation and temperature data according to the time dimension;

[0073] S6. Extract aligned observed precipitation and temperature data. Based on precipitation and temperature data with the same spatial location, identify the changes in driving factors of the composite high temperature and drought extreme events and conduct quantitative attribution analysis.

[0074] The input data includes observed precipitation and observed temperature data at the same spatiotemporal scale. In this embodiment, both the observed precipitation and observed temperature data are NC files. The observed precipitation NC file includes the observed precipitation data and its corresponding spatiotemporal dimensions, while the observed temperature NC file includes the observed temperature data and its corresponding spatiotemporal dimensions. The `load_dataset` function of the Python third-party library `xarray` is used to read a single input .nc file and extract the corresponding precipitation data and spatiotemporal dimensions (time, latitude, and longitude). Based on the time dimension of "year-month-day" to "year-month-day" and the spatial range of ["longitude range", "latitude range"] input in string form, the spatiotemporal region for which composite event change attribution analysis needs to be performed is determined.

[0075] In step S3, when cropping the spatial longitude corresponding to the observed precipitation data and observed temperature data according to the selected spatial region, all longitude information in the observed precipitation data and observed temperature data is read. Let the longitude vector of any one of the observed precipitation data and observed temperature data be represented by a vector... It is represented as:

[0076]

[0077] in, Represents the longitude vector of either observed precipitation data or observed temperature data. It is the value of any longitude from either the observed precipitation data or the observed temperature data. p The total length of either the observed precipitation data or the observed temperature data along the longitude direction. i =1,2,…, p ;

[0078] Read the longitude range of the selected spatial region using vector coordinates. It is represented as:

[0079]

[0080] By selecting longitude ranges that exist in both observed precipitation and observed temperature data and fall within the selected spatial region's latitude and longitude, the spatial longitudes corresponding to the cropped observed precipitation and temperature data are obtained. These longitudes are then represented by vectors. It is represented as: ;

[0081] When cropping the spatial dimensions corresponding to observed precipitation and temperature data according to the selected spatial region's latitude and longitude, all latitude information from the observed precipitation and temperature data is read. Let the latitude vector of any one of the observed precipitation and temperature data be represented by a vector... It is represented as:

[0082]

[0083] in, Represents the latitude vector of either the observed precipitation data or the observed temperature data. It is the value of any latitude from the observed precipitation data and observed temperature data. q The total length of either the observed precipitation data or the observed temperature data along the longitude direction. j =1,2,…, q ;

[0084] Read the latitude range of the selected spatial region using vector coordinates. It is represented as:

[0085]

[0086] By selecting a latitude range that exists in both observed precipitation and observed temperature data and falls within the selected spatial region, the spatial latitudes corresponding to the cropped observed precipitation and temperature data are obtained. These latitudes are then used as vectors. It is represented as: .

[0087] The method for determining the set of spatial distributions corresponding to the data required for the recurrence period of combined high-temperature and drought extreme events is as follows: take a vector. , The set of elements contained , Calculate the set , Cartesian product S: This yields a set of spatial distributions corresponding to the data for which composite event recurrence intervals need to be determined. Then, using the broadcast interface of NumPy functions in xarray, the .sel method is used to filter out data from the set. Precipitation data within the set was used, and the broadcast interface of NumPy functions in xarray was used to filter the data using the .sel method. The precipitation data within the region is processed, and the above two clipping methods are applied to the target data. The clipping results are then aligned according to the time dimension.

[0088] In step S6, the changing trend of the driving factors of the combined high-temperature and drought extreme events is estimated using the Sen slope, and the Mann-Kendall trend test is used to determine whether this trend is significant. This mainly includes: calculating the trend of precipitation changes and determining whether the precipitation changes are significant; calculating the trend of temperature changes and determining whether the temperature and precipitation changes are significant; using a 30-year sliding window, calculating the precipitation-temperature correlation coefficient within different time periods of the sliding window, and determining the changing trend and significance of the precipitation-temperature correlation coefficient based on the Sen slope and the Mann-Kendall trend test.

[0089] Example 2

[0090] In this embodiment, cropped precipitation and temperature data are taken. Based on precipitation and temperature data with the same spatial location, changes in the complex drought-heat wave event are identified and attributed. Figure 2 This is a flowchart illustrating the attribution of complex high-temperature and drought extreme events. The process of attribution analysis for complex high-temperature and drought extreme events is as follows:

[0091] S61. Using the Normal Quantile Transform (NQT) method, a precipitation time series of length n is transformed. and a temperature time series of length n These were respectively converted into standardized precipitation index (SPI) time series for the corresponding research period. Standardized Temperature Index (STI) time series ;

[0092] Standardized Precipitation Index (SPI) and Standardized Temperature Index (STI) are commonly used indicators to describe the severity of extreme precipitation and temperature events. The standardized indices are typically derived from the raw data using the Normal Quantile Transform (NQT) method.

[0093]

[0094] in, and These represent the raw precipitation and temperature data, respectively. and These represent the empirical cumulative distribution functions of precipitation and temperature estimated from the location using Weibull plotting, respectively; and These represent the time series of standardized precipitation index and standardized temperature index, respectively. It represents the inverse function of the cumulative distribution function of the standard normal distribution.

[0095] S62. Will and By incorporating a two-dimensional meta-Gaussian model and the equation for calculating the recurrence interval of extreme events, the recurrence intervals of drought and heat wave events over the entire time series are estimated. The correlation coefficient between the Standardized Precipitation Index (SPI) and the Standardized Temperature Index (STI) ;

[0096] Among them, the two-dimensional meta-Gaussian model is often used to describe the relationship between two distributions:

[0097]

[0098] in, , These represent the mean and variance of the SPI for a specific period. , These represent the mean and variance of the STI for a specific period. This represents the correlation coefficient between SPI and STI.

[0099] According to the meta-Gaussian model, the probability of drought events Probability of heat wave events Probability of dry-thermal complex events They can be represented as follows:

[0100]

[0101] in, The cumulative distribution function represents the standard normal distribution; The correlation coefficient is The cumulative distribution function (BNCDF) of the bivariate normal distribution. and This determines the thresholds for drought and heat wave events.

[0102] Probability of dry heat events Probability of drought events Probability of heat wave events Relationship with precipitation and temperature This process can be described as a joint decision, or in the form of... The equation represents:

[0103]

[0104] The equations for calculating the recurrence period of extreme events are expressed as follows:

[0105]

[0106] in, , , These are the recurrence periods of drought events, heat wave events, and combined high-temperature and drought events, respectively. and These are the threshold values ​​for the standardized indices corresponding to drought and heat wave events; Let the cumulative distribution function and correlation coefficient of the standard normal distribution be respectively: The cumulative distribution function of the bivariate normal distribution;

[0107] S63. The entire time series Using this as a benchmark, the partial derivatives of the combined time with respect to drought return period, heat return period, and precipitation-temperature relationship are calculated by substituting the total differential equation for the return period of the combined event. The total differential is expressed as:

[0108]

[0109] The partial derivatives of the joint event recurrence period with respect to each driving factor are:

[0110]

[0111]

[0112]

[0113] Here, in the meta-gaussian model, the cumulative probability function (BNCDF) of the binary joint normal distribution is used. It is used to describe the probability of occurrence and recurrence period of a compound event. Its partial derivatives with respect to the three control variables have analytical solutions, as detailed below:

[0114] (1) BNCDF pair partial derivatives for:

[0115]

[0116] in, and Let the probability density function and correlation coefficient of the standard normal distribution be respectively: The probability density function of a bivariate normal distribution.

[0117] (2) BNCDF pair The partial derivatives can be expressed as:

[0118]

[0119] (3) BNCDF pair The partial derivatives can be expressed as:

[0120]

[0121] Among them, a fixed pattern was used. The proof is as follows:

[0122]

[0123] S64. Divide the time series of the Standardized Precipitation Index (SPI) and the Standardized Temperature Index (STI) into two equal time periods, period 1 and period 2. The time of period 1 is represented as follows: The time period for time period 2 is represented as Among them, the precipitation time series and temperature time series in time period 1 are respectively and The precipitation and temperature time series in time period 2 are respectively and ;

[0124] S65. [The sentence appears to be incomplete and lacks context.] and Substituting the equation for the return period of extreme events, we obtain the drought return period in period 1. Heatwave recurrence period Correlation coefficient between precipitation and temperature Recurrence period of joint events ; in time period 2 and Substituting the equation for the return period of extreme events, we obtain the drought return period in period 2. Heatwave recurrence period Correlation coefficient between precipitation and temperature Recurrence period of joint events ;

[0125] S66. Calculate the changes in the return period of joint events, the return period of drought, the return period of heat waves, and the correlation between precipitation and temperature during the two time periods, time period 1 and time period 2.

[0126] The expression for calculating the change in the return period of joint events is: ;

[0127] The formula for calculating the variation in drought return period is: ;

[0128] The formula for calculating the recurrence interval of heat waves is: ;

[0129] The formula for calculating the change in the correlation between precipitation and temperature is: .

[0130] S67. Based on the combined changes in time return period, drought return period, heat wave return period, and the correlation between precipitation and temperature, calculate the absolute contribution of each variable. and relative contribution .

[0131] Calculate the absolute contribution of each variable. The expressions are as follows:

[0132] ;

[0133] in, and These represent the changes in the return period of drought and the changes in the return period of the compound disasters it causes, respectively. and These represent the changes in the return period of heat waves and the changes in the return period of the compound disasters they cause, respectively. and These represent changes in the correlation between precipitation and temperature, and changes in the recurrence period of the resulting compound disasters, respectively.

[0134] In this embodiment, the effect of three driving factors on the return period of the joint event is quantified by multivariate Taylor expansion. Size of contribution:

[0135]

[0136] in, and These represent the changes in the return period of drought and the changes in the return period of the compound disasters it causes, respectively. and These represent the changes in the return period of heat waves and the changes in the return period of the compound disasters they cause, respectively. and These represent changes in the correlation between precipitation and temperature, and changes in the recurrence period of the resulting compound disasters, respectively.

[0137] Calculate relative contribution The expressions are as follows:

[0138]

[0139] in, These represent the relative contributions of changes in precipitation, temperature, and the correlation between precipitation and temperature to the change in the recurrence period of dry-heat combined disasters.

[0140] Here, the sources of the recurrence period of compound disasters are quantified based on the statistical characteristics of precipitation and temperature changes. This clarifies the different sources of changes in the recurrence period of compound disasters, which helps in disaster prevention and mitigation and reduces the impact of climate change.

[0141] Example 3

[0142] In this embodiment, the method further includes: visualizing the precipitation types across the entire space based on the attribution analysis results, and drawing a watershed diagnostic map of the complex high-temperature and drought extreme event. During visualization, identical observation times and precipitation times are automatically correlated, avoiding cumbersome manual adjustments. The watershed diagnostic map of the complex high-temperature and drought extreme event includes: a spatial map of driving factor change trends, a spatial map of complex event return periods, a spatial map of complex event contributions, and a watershed diagnostic map of the complex event.

[0143] In the watershed diagnostic map of the combined high temperature and drought extreme event, from top to bottom, the data represent the joint distribution within time period 1 and time period 2, the occurrence of drought in this watershed throughout the entire time series, the changes in high temperature and combined high temperature and drought events over time, the recurrence period of the combined event, and the changes in the contribution of each factor over time.

[0144] The watershed diagnostic map of combined high-temperature and drought extreme events can visually link the joint distribution, extreme events, and factor contributions at the watershed scale. It can analyze the overall changes in the watershed from the perspective of joint distribution, as well as specifically analyze the changes in extreme events and the causes of these changes within a certain time period.

[0145] Example 3

[0146] This embodiment mainly focuses on the method proposed in this invention, and provides an operational description for a practical platform, including the following operations:

[0147] S1. File Input: Using the Dataset function of the open-source Python library netcdf and the load_mfdataset function of xarray, precipitation and temperature data are read from the .nc file to extract the corresponding precipitation measurement data and spatiotemporal dimensions (time, latitude and longitude). Based on the time period "year-month-day" to "year-month-day" and the spatial range ["longitude range", "latitude range"] input in string form, the spatiotemporal region for which composite high-temperature drought recurrence change attribution needs to be performed is determined.

[0148] S2. Data processing: (1) Spatiotemporal analysis was performed using Python third-party libraries xarray and dask. The main contents are as follows: extract the dimensional information of precipitation and temperature, and trim the spatial dimension of precipitation and temperature data according to the latitude and longitude of the selected spatial region; trim the temporal dimension of precipitation and temperature data according to the input time range; and align the precipitation and temperature data. (2) Using Python's numpy and scipy libraries, statistical methods were used to perform attribution analysis on the combined drought and heat wave events at the same location.

[0149] S3. Precipitation Data Visualization: This step primarily utilizes the Python third-party libraries geopandas and cartopy to visualize the attribution results data. When drawing spatial maps, the `plt.subplots` function in Matplotlib is used to set the appropriate sub-canvas size; the `ccrs.PlateCarree()` function in cartopy is used to call the `geoaxes` object in Matplotlib to control its projection type; and the `ax.pcolormesh` method is used to draw the spatial map. The `ax.gridlines` method is used to draw latitude and longitude grid lines, the `fig.add_axes` method is used to add subplots to control the position of the colorbar, the `fig.colorbar` method is used to set the position of the colorbar, the `cbar.set_ticks` method is used to set the tick mark position, and tick labels are used to display the content. Finally, the `savefig` method of `matplotlib.figure.Figure` is used to save the drawn spatial map to the specified path. When drawing watershed diagnostic maps, the third-party library seaborn is required.

[0150] For visualization, the visualization steps for classifying and classifying the complex high-temperature drought in summer in China from 1901 to 2000 are analyzed as follows:

[0151] S1. Store the precipitation observation data (NetCDF file) and temperature observation data (NetCDF file) required for watershed map drawing in the selected folder, and define the variables path_precipitation and path_temperature respectively and store the corresponding paths. Read and merge these files using the xarray.open_mfdataset and geopandas.read_file functions; manually input the spatiotemporal range.

[0152] S2. Spatiotemporal range clipping was performed using Python third-party libraries xarray and numpy. Then, composite attribution of high-temperature drought was performed on precipitation and temperature data using Python's numpy and scipy libraries.

[0153] (1) Use xarray.dataset to extract precipitation data and observation data. Use the broadcast interface of numpy functions in xarray and filter the precipitation data in set S using the .sel method;

[0154] (2) Based on the union of the input precipitation time range and the time range for which complex high temperature and drought changes need to be judged, the precipitation data is cropped using the .isel method;

[0155] (3) Extract the cropped temperature and precipitation data and perform attribution analysis on the changes in the combined high temperature and drought event. First, use numpy.cov and scipymultivariate_normal to construct the joint distribution of precipitation and temperature. Then, calculate the difference in statistical parameters (recurrence period, correlation coefficient) between the two time periods. After that, use the math library and numpy library to calculate the partial derivative results based on the constructed joint distribution. Based on the above two results, calculate the relative values.

[0156] (4) Use the apply_func broadcast method in xarray and the for loop in Python to repeat the above process for data at different spatial locations to obtain data for visualization;

[0157] S3. Use the Python third-party libraries Mpl_toolkits and Matplotlib to draw spatial plots and diagnostic plots:

[0158] (1) Set the map's projection mode to PlateCarree using the cartopy.crs.ccrs method of cartopy;

[0159] (2) Use the plt.subplots function in the third-party visualization library Matplotlib to set the size of the canvas to be plotted, and use the cartopy.set_extent method to set the latitude and longitude spatial region to be plotted;

[0160] (3) The ax.pcolormesh method draws the spatial map corresponding to the classification. If the trend of change is significant, the plt.scatter method is used to draw marker points in the areas of significant change.

[0161] (4) Create latitude and longitude labels using the gridlines method in geoaxes and the cticker.LongitudeFormatter() method in the third-party library cartopy;

[0162] (5) Use the fig.add_axes method to add sub-graphs that control the position of the colorbar, use the cbar.set_ticks method to set the tick positions, and use tick labels to display the content;

[0163] (6) Use the `savefig` method of `matplotlib.figure.Figure` to save the plotted precipitation data visualization to the specified path;

[0164] (7) At the watershed scale, several watersheds are used as visualization cases, and joint distribution maps are drawn using seabornjointgrid. The plot method and fill_between method in matplotlib are used to plot the changes in composite events. Finally, the diagnostic plot is saved to the specified path using the savefig method of matplotlib.figure.Figure.

[0165] like Figure 3 As shown in the diagnostic diagram, from left to right, the combined distributions within time period 1 and time period 2 represent the total time series; the changes in drought, high temperature, and combined high temperature and drought events in this watershed over time; and the changes in the recurrence period of combined events and the contributions of each factor over time.

[0166] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. An attribution method for complex high-temperature and drought extreme events, characterized in that, The method includes the following steps: S1. Use observed precipitation data and observed temperature data of the same spatiotemporal scale as input data; S2. Based on the time periods and spatial ranges corresponding to the observed precipitation and temperature data in the input data, determine the spatiotemporal regions where attribution analysis of the changes in the composite high temperature and drought extreme events is required; S3. Trim the spatial longitude and latitude of the observed precipitation data and observed temperature data according to the selected spatial region, and trim the time dimension of the observed precipitation data and observed temperature data according to the selected time range; S4. Determine the set of spatial distributions corresponding to the data obtained from the cropping that need to be analyzed for the recurrence period of the combined high temperature and drought extreme events, and filter out the precipitation data within the set; determine the union of the selected time range and the time range for which the combined high temperature and drought change assessment needs to be performed, and crop the precipitation data for which the combined high temperature and drought change assessment needs to be performed; S5. Align the cropped results of observed precipitation and temperature data according to the time dimension; S6. Extract aligned observed precipitation and temperature data. Based on spatially similar precipitation and temperature data, identify changes in the driving factors of composite high-temperature and drought extreme events and conduct quantitative attribution analysis. The process of attribution analysis for complex high-temperature and drought extreme events is as follows: S61. Using the Normal Quantile Transform (NQT) method, a precipitation time series of length n is transformed. and a temperature time series of length n These were respectively converted into standardized precipitation index (SPI) time series for the corresponding research period. Standardized Temperature Index (STI) time series ; S62. Will and By incorporating a two-dimensional meta-Gaussian model and the equation for calculating the recurrence interval of extreme events, the recurrence intervals of drought and heat wave events over the entire time series are estimated. The correlation coefficient between the Standardized Precipitation Index (SPI) and the Standardized Temperature Index (STI) ; The equation for the recurrence period of extreme events is expressed as: in, , , These are the recurrence periods of drought events, heat wave events, and combined high-temperature and drought events, respectively. and These are the threshold values ​​for the standardized indices corresponding to drought and heat wave events; Let the cumulative distribution function and correlation coefficient of the standard normal distribution be respectively: The cumulative distribution function of the bivariate normal distribution; S63. The entire time series Using this as a benchmark, the partial derivatives of the combined time with respect to drought return period, heat return period, and precipitation-temperature relationship are calculated by substituting the total differential equation for the return period of the combined event. ; S64. Divide the time series of the Standardized Precipitation Index (SPI) and the Standardized Temperature Index (STI) into two equal time periods, period 1 and period 2. The time of period 1 is represented as follows: The time period for time period 2 is represented as Among them, the precipitation time series and temperature time series in time period 1 are respectively and The precipitation and temperature time series in time period 2 are respectively and ; S65. [The sentence appears to be incomplete and lacks context. It seems to be referring to time period 1.] and Substituting the equation for the return period of extreme events, we obtain the drought return period in period 1. Heatwave recurrence period Correlation coefficient between precipitation and temperature Recurrence period of joint events ; in time period 2 and Substituting the equation for the return period of extreme events, we obtain the drought return period in period 2. Heatwave recurrence period Correlation coefficient between precipitation and temperature Recurrence period of joint events ; S66. Calculate the changes in the return period of joint events, the return period of drought, the return period of heat waves, and the correlation between precipitation and temperature during the two time periods, time period 1 and time period 2. S67. Based on the combined changes in time return period, drought return period, heat wave return period, and the correlation between precipitation and temperature, calculate the absolute contribution of each variable. and relative contribution .

2. The attribution method for complex high-temperature and drought extreme events according to claim 1, characterized in that, The input data includes observed precipitation and observed temperature at the same spatiotemporal scale. The observed precipitation part includes observed precipitation data and its corresponding spatiotemporal dimensions, and the observed temperature part includes observed temperature data and its corresponding spatiotemporal dimensions. Based on the time dimension of "year-month-day" to "year-month-day" and the spatial range of ["longitude range", "latitude range"] entered in string form, the spatiotemporal region for which composite event change attribution analysis needs to be performed is determined.

3. The attribution method for complex high-temperature and drought extreme events according to claim 2, characterized in that, In step S3, when cropping the spatial longitude corresponding to the observed precipitation data and observed temperature data according to the selected spatial region, all longitude information in the observed precipitation data and observed temperature data is read. Let the longitude vector of any one of the observed precipitation data and observed temperature data be represented by a vector... It is represented as: in, Represents the longitude vector of either observed precipitation data or observed temperature data. It is the value of any longitude from either the observed precipitation data or the observed temperature data. p The total length of either the observed precipitation data or the observed temperature data along the longitude direction. i =1,2,…, p ; Read the longitude range of the selected spatial region using vector coordinates. It is represented as: By selecting longitude ranges that exist in both observed precipitation and observed temperature data and fall within the selected spatial region's latitude and longitude, the spatial longitudes corresponding to the cropped observed precipitation and temperature data are obtained. These longitudes are then represented by vectors. It is represented as: ; When cropping the spatial dimensions corresponding to observed precipitation and temperature data according to the selected spatial region's latitude and longitude, all latitude information from the observed precipitation and temperature data is read. Let the latitude vector of any one of the observed precipitation and temperature data be represented by a vector... It is represented as: in, Represents the latitude vector of either the observed precipitation data or the observed temperature data. It is the value of any latitude from the observed precipitation data and observed temperature data. q The total length of either the observed precipitation data or the observed temperature data along the longitude direction. j =1,2,…, q ; Read the latitude range of the selected spatial region using vector coordinates. It is represented as: By selecting a latitude range that exists in both observed precipitation and observed temperature data and falls within the selected spatial region, the spatial latitudes corresponding to the cropped observed precipitation and temperature data are obtained. These latitudes are then used as vectors. It is represented as: .

4. The attribution method for composite high-temperature and drought extreme events according to claim 3, characterized in that, The method for determining the set of spatial distributions corresponding to the data required for the recurrence period of combined high-temperature and drought extreme events is as follows: take a vector. , The set of elements contained , Calculate the set , Cartesian product S: This yields the set of spatial distributions corresponding to the data for which the recurrence period of the composite event needs to be determined.

5. The attribution method for complex high-temperature and drought extreme events according to claim 1, characterized in that, In step S6, the changing trend of the driving factors of the combined high temperature and drought extreme events is estimated using the Sen slope, and the Mann-Kendall trend test method is used to determine whether the trend is significant.

6. The attribution method for complex high-temperature and drought extreme events according to claim 1, characterized in that, The calculation expression for the change in the return period of the joint event mentioned in step S66 is as follows: ; The formula for calculating the variation in drought return period is: ; The formula for calculating the recurrence interval of heat waves is: ; The formula for calculating the change in the correlation between precipitation and temperature is: .

7. The attribution method for complex high-temperature and drought extreme events according to claim 6, characterized in that, Calculate the absolute contribution of each variable. The expressions are as follows: ； in, and These represent the changes in the return period of drought and the changes in the return period of the compound disasters it causes, respectively. and These represent the changes in the return period of heat waves and the changes in the return period of the compound disasters they cause, respectively. and These represent changes in the correlation between precipitation and temperature, and changes in the recurrence period of the resulting compound disasters, respectively. Calculate relative contribution The expressions are as follows: in, These represent the relative contributions of changes in precipitation, temperature, and the correlation between precipitation and temperature to the change in the recurrence period of dry-heat combined disasters.

8. The attribution method for complex high-temperature and drought extreme events according to claim 6, characterized in that, The method also includes: visualizing the precipitation types of the entire space based on the results of attribution analysis, and drawing a watershed diagnostic map of complex high temperature and drought extreme events.

9. The attribution method for complex high-temperature and drought extreme events according to claim 8, characterized in that, The aforementioned watershed diagnostic map of the combined high temperature and drought extreme event includes: a spatial map of the changing trends of driving factors, a spatial map of the changing return period of the combined event, a spatial map of the contribution of the combined event, and a watershed diagnostic map of the combined event. The watershed diagnostic map of the combined high temperature and drought extreme event shows the joint distribution within time period 1 and time period 2, the occurrence of drought, high temperature, and combined high temperature and drought events in this watershed over time throughout the entire time series, the changing return period of the combined event, and the changing contribution of each factor over time.

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