A method for calculating the time-varying sensitivity of evaporative stress to influencing factors

Abstract

The present invention discloses a method for calculating the time-varying sensitivity of evaporative stress to influencing factors, and the method comprises the following steps: step 1, calculating the time series of evaporative stress index; step 2, calculating the abnormal component of the evaporative stress index without seasonal trend; step 3, obtaining the preceding influence sequence of the abnormal component of the evaporative stress index; step 4, calculating the abnormal component of the evaporative stress influencing factor without seasonal trend; step 5, establishing a memory dynamic linear model; step 6, determining the optimal expansion factor parameter of the model; step 7, calculating the time-varying sensitivity sequence. The method of the present invention effectively solves the problem of obtaining the instantaneous sensitivity change of evaporative stress within a short duration, and provides reliable theoretical and technical support for the study of the response mechanism of evaporative stress and timely drought warning.

Description

Technical Field

[0001] The invention belongs to the technical field of ecohydrological factor analysis, and in particular relates to a method for calculating the time-varying sensitivity of evaporation stress to influencing factors. Background Art

[0002] Evaporative stress is one of the main manifestations of water stress, and the evaporative stress index is defined as the ratio of actual evaporation to potential evaporation. The evaporative stress index can comprehensively reflect the balance between water, vegetation and climate. Studies have shown that because vegetation will reduce evaporative water consumption before the outbreak of drought, the evaporative stress index is highly sensitive to sudden drought and moderate drought, and can effectively predict the occurrence of these drought events. The continued development of evaporative stress leads to vegetation death and crop yield reduction. Therefore, understanding the development mechanism and related factors of evaporative stress is crucial for taking drought intervention measures in advance, protecting ecosystem stability and maintaining agricultural output. Under the drastic changes in water, vegetation and climate conditions, in-depth research on the development mechanism of evaporative stress and its sensitivity changes to different influencing factors is a scientific problem that needs to be urgently solved in ecohydrological research.

[0003] Regarding the technical methods for analyzing the sensitivity of dependent variables to the temporal changes of influencing factors, the more common technical methods are mostly based on the idea of ​​time-based comparison to explore the temporal changes. The difference is that the method of quantifying the sensitivity in each time period can use machine learning methods or algorithms to establish regression equations to estimate the sensitivity in each time period, and then compare the sensitivity of different time periods for evolution analysis. However, the sensitivity value obtained by this method is the average response in the time period, which fails to reflect the "instantaneous" or "dynamic" sensitivity. Therefore, it has limitations when studying the dynamic response of evaporation stress to influencing factors in short-duration events such as drought. The Chinese patent with publication number CN112883558A discloses a method for constructing a time-varying form of hydrological model parameters. The patent divides the historical period into multiple continuous sub-periods, and constructs a hydrological model in each sub-period, simulates the sensitivity of runoff changes to factors such as meteorological variables and underlying surface conditions in each sub-period, and explores the evolution of sensitivity in different periods. However, this method still obtains the average response of each sub-period, and has not yet proposed a method for determining the instantaneous sensitivity of hydrological phenomena such as evaporation stress to influencing factors. Summary of the invention

[0004] The object of the present invention is to provide a method for calculating the time-varying sensitivity of evaporative stress to influencing factors, so as to solve the above technical problems.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention discloses a method for calculating the time-varying sensitivity of evaporative stress to influencing factors, and the method comprises the following steps:

[0007] Step 1: Calculate the evaporation stress index time series: Obtain the actual evaporation time series ETa and the potential evaporation time series ETp of the study area, and calculate the evaporation stress index time series value ESI at time t according to formula (1): t , and then the evaporation stress index time series ESI is obtained;

[0008]

[0009] Where: ESI t is the time series value of the evaporation stress index at time t; ETa t is the actual evapotranspiration time series value at time t; ETp t is the time series value of potential evapotranspiration at time t;

[0010] Step 2: Calculate the deseasonal and detrended abnormal component of the evaporation stress index: Use the dynamic linear model DLM, set the input evaporation stress index time series ESI, do not introduce independent variables, and obtain the abnormal component of the evaporation stress index time series. The mathematical expression is as follows:

[0011] ESI=ESI l +ESI s +ESI r +v t (2)

[0012] Where: ESI is the time series of evaporation stress index; ESI l is the trend component of ESI; ESI s is the seasonal component of ESI; ESI r is the abnormal component of ESI; v t is the observation noise residual;

[0013] Step 3: Obtain the preceding impact sequence of the abnormal component of the evaporation stress index: For the abnormal component ESI at time t r,t Value, get its value at previous time points to characterize memory effects, including ESI r The sequence of the preceding time interval ESI r,t-1 , ESI of the first two time intervals r,t-2 , ESI of the first three time intervals r,t-3 , ESI of the first four time intervals r,t-4 , ESI of the first five time intervals r,t-5 , these sequences, namely the pre-order impact sequences, are obtained by staggering the entire evaporation stress index time series, and then retaining the ESI r The valid data range of the sequence and the preceding sequence that affect the sequence overlaps is used as the valid research period data;

[0014] Step 4, calculate the seasonal and trend-free abnormal components of the evaporative stress influencing factors: the evaporative stress influencing factors include soil moisture SVM, saturated vapor pressure difference VPD and leaf area index LAI. The seasonal components are eliminated by subtracting the multi-year average climate state, and the long-term trend components are eliminated by subtracting the linear fitting to obtain the abnormal components of SVM, VPD and LAI;

[0015] The specific process is:

[0016] Calculation of seasonal components:

[0017]

[0018] Where: S(t) is the seasonal component; N is the total number of years in the time series; X i (t) is the data value at time point t in year i; X represents the evaporation stress influencing factor;

[0019] Calculation of trend component:

[0020] T(t)=a+bt (4)

[0021] Where: T(t) is the trend component, which is a linear fit with the X(t) sequence as the ordinate and the corresponding time t sequence as the ordinate, a and b are the intercept and slope obtained by linear fitting of X(t) respectively;

[0022] Get the abnormal component:

[0023] δX(t)=X(t)-S(t)-T(t) (5)

[0024] Where: δX(t) is the abnormal component of X(t);

[0025] Step 5, establish a memory dynamic linear model: Substitute the preceding influence sequence of ESI and ESI abnormal components obtained in the above steps, as well as the abnormal component sequence of svm, VPD, and LAI into the dynamic linear model to construct a memory dynamic linear model. The memory dynamic linear model takes into account the influence of its own preceding sequence in the development mechanism of evaporative stress, that is, the memory effect. The mathematical expression is as follows:

[0026] ESI=ESI l +ESI s +ESI r +v t (6)

[0027] ESI r,t =θ ESI1 ESI r,t-1 ~θ ESI5 ESI r,t-5+θ svm δsvm t +θ VPD δVPD t +θ LAI δLAI t +ε (7)

[0028] Wherein, formula (6) is the same as formula (2), indicating that the input dependent variable ESI of the memory dynamic linear model is the evaporation stress index time series, and the independent variable ESI r,t-1 、ESI r,t-2 、ESI r,t-3 、ESI r,t-4 、ESI r,t-5 ,δsvm t , δVPD t and δLAI t Time series as a driver; ESI r,t is the abnormal component of ESI at time t; ESI r,t-1 is the abnormal component of ESI at time t-1; θ ESI1 δESI t At time t, ESI r,t-1 Sensitivity coefficient; δsvm t , δVPD t and δLAI t are the abnormal components of soil moisture, saturated water vapor pressure deficit, and leaf area index at time t;

[0029] The memory dynamic linear model has the function of a dynamic linear model. First, it decomposes the original time series into trend components, seasonal components, and abnormal components, and then decomposes the regression component ESI. r,t The regression relationship between the model and the driving factors is established, and then the regression coefficient at each moment is obtained through the built-in Bayesian update method of the model, that is, θ svm ,θ VPD and θ LAI are ESI at time t r,t The output of the model is ESI, which is the sensitivity coefficient of the three variables. l 、ESI s 、ESI r ,θ ESI1 ~θ ESI5 and θ svm ,θ VPD and θ LAI time series;

[0030] Step 6: Determine the optimal expansion factor parameters of the model: By verifying the accuracy of the component decomposition process, the optimal expansion factor is selected. The steps are as follows:

[0031] Calculate the component sum of the memory dynamic linear model under different expansion factor γ parameters:

[0032]

[0033] Where: ESI (γ) is the sum of the three components obtained under the expansion factor γ, analogous to formula (6) and the input dependent variable ESI difference observation noise residual v t ; They are the trend component, seasonal component and abnormal component obtained under the expansion factor γ respectively;

[0034] Compare the original time series ESI and calculate the evaluation index determination coefficient R 2 , used to evaluate the accuracy of the model, the calculation formula is:

[0035]

[0036] Among them, the mean of the original time series ESI for:

[0037]

[0038] Where: T is the length of the time series; is the ESI at time t (γ) value;

[0039] Step 7, calculate the time-varying sensitivity series: use the expansion factor γ with the largest determination coefficient determined in step 6 to run the memory dynamic linear model and obtain the output of the model, the sensitivity coefficient θ of the three variables at each moment svm ,θ VPD and θ LAI , that is, the time-varying sensitivity sequence is obtained; thus, the time-varying sensitivity sequence of evaporation stress to the influencing factors is determined.

[0040] Furthermore, the actual evapotranspiration time series ETa and the potential evapotranspiration time series ETp of the study area described in step 1 are obtained by downloading public data from the Internet or calculating actual meteorological data observations. If the time resolution of the acquired time series data is inconsistent, linear interpolation is used for upsampling or summation is used for downsampling to unify the time resolution.

[0041] Furthermore, the dynamic linear model DLM in step 2 contains a parameter expansion factor γ, and the value of γ is 0.999.

[0042] Furthermore, the soil moisture svm, saturated vapor pressure difference VPD and leaf area index LAI data in step 4 are generally obtained by downloading public data from the Internet or by actual observation and calculation.

[0043] Furthermore, leaf area index LAI data are obtained from the global land surface satellite GLASS data website, and soil moisture SVM data, temperature and dew point temperature data are obtained from the European Centre for Medium-Range Weather Forecasts network, where the temperature and dew point temperature data are used to calculate the saturated water vapor pressure difference VPD data series through the Clausius-Clapeyron relationship.

[0044] The beneficial effect of the present invention is that the method of the present invention can determine the time-varying sensitivity sequence of evaporative stress to influencing factors by establishing a memory dynamic linear model including a memory effect, thereby analyzing the changes in the response of evaporative stress to influencing factors under a changing environment, and then exploring the impact mechanism of evaporative stress. The method of the present invention effectively solves the problem of obtaining the instantaneous sensitivity changes of evaporative stress within a short duration, and provides reliable theoretical and technical support for the study of evaporative stress response mechanism and timely drought warning.

[0045] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram comparing instantaneous sensitivity and average sensitivity;

[0047] Figure 2 is a flow chart of the method of the present invention;

[0048] Figure 3 It is a schematic diagram of the decomposition of time series components;

[0049] Figure 4 To obtain the schematic diagram of the preceding order influence sequence by using the staggered arrangement method;

[0050] Figure 5 This is a time-varying sensitivity sequence diagram obtained in Example 1. DETAILED DESCRIPTION

[0051] The present invention discloses a method for calculating the time-varying sensitivity of evaporative stress to influencing factors, and the principle on which the method is based is as follows:

[0052] When studying the impact and causal relationship between hydrological and meteorological variables, it is usually necessary to remove seasonal and long-term trends to extract abnormal components for factorial analysis because similar seasonal patterns and long-term trends will lead to "overfitting" of variable relationships. The dynamic linear model (DLM) can effectively remove the interference of seasonal cycle patterns and long-term trends by decomposing the evaporation stress index time series into seasonal components, trend components and abnormal components, thereby more accurately revealing the actual association between meteorological variables. In addition, when conducting sensitivity analysis between variables, traditional methods can only obtain the average response of the dependent variable to the independent variable over a period of time, that is, the average sensitivity. This static analysis cannot reflect the complex time-varying characteristics between variables. The unique advantage of DLM is that it can capture the dynamic change characteristics of variable relationships, that is, time-varying sensitivity. Specifically, DLM can not only decompose the time series, but also establish a dynamic regression relationship between the decomposed abnormal components and the relevant influencing factors of the input. DLM uses the Bayesian update method to estimate the regression coefficient, which means that the model can be adjusted according to the newly observed data at each time point. Bayesian updating provides a recursive statistical inference method that can adjust model parameters based on the observed data at the current time point so that the regression coefficient (i.e., sensitivity) of the model can change over time. This method allows the model to reflect the latest sensitivity changes at each time point, i.e., instantaneous sensitivity, such as Figure 1 shown.

[0053] As one of the main manifestations of water stress, evaporative stress is usually expressed as the ratio of actual evapotranspiration to potential evapotranspiration, i.e., the evaporative stress index. There is a self-reinforcing mechanism of "dry to dry" in the development mechanism of evaporative stress, which is a stress continuation effect, that is, in areas with poor regional evaporation conditions (water deficit, sparse vegetation, etc.), the water stress in the previous stage will have a lasting impact on the next stage. This is because when water is limited, plants reduce water loss and evaporation by closing their stomata, which leads to a decrease in water vapor content in the atmosphere, further exacerbating the regional water deficit. Due to this "self-reinforcing" mechanism, evaporative stress exhibits a significant memory effect over time.

[0054] In order to capture this memory effect, the present invention proposes a memory dynamic linear model. This model not only takes into account the abnormal component of the evaporation stress index, but also incorporates the abnormal component of the previous time point, which can improve the fitting accuracy of the model and more comprehensively capture the impact of driving factors on the development mechanism of evaporation stress. Compared with traditional methods of exploring sensitivity, the memory dynamic linear model can provide a sensitivity analysis that is updated at each time point, that is, time-varying sensitivity. Through this model, the instantaneous response of the dependent variable to the independent variable can be obtained at each moment of the time series, and the evolution law of sensitivity under a changing environment can be further analyzed. This method can improve the ability to understand complex hydrological processes, especially in the case of drought or water shortage, and provide an important reference for water resources management and agricultural irrigation decision-making.

[0055] The method of the present invention specifically comprises the following steps: Figure 2 As shown:

[0056] Step 1: Calculate the evaporation stress index time series: Obtain the actual evaporation time series ETa and the potential evaporation time series ETp of the study area, which are generally obtained by downloading public data from the Internet or calculating actual meteorological data observations. If the time resolution of the acquired time series data is inconsistent, upsampling is performed by linear interpolation or downsampling is performed by calculating the sum to unify the time resolution. The evaporation stress index time series value ESI at time t is calculated according to formula (1): t , and then the evaporation stress index time series ESI is obtained;

[0057]

[0058] Where: ESI t is the time series value of the evaporation stress index at time t; ETa t is the actual evapotranspiration time series value at time t; ETp t is the time series value of potential evapotranspiration at time t.

[0059] Step 2: Calculate the deseasonalized and detrended abnormal components of the evaporation stress index: When analyzing the influence relationship between meteorological variables, similar seasonal cycle patterns and long-term evolution trends will lead to overfitting and mask the true correlation. Therefore, it is necessary to remove the seasonal component and trend component to more accurately reveal the actual correlation between meteorological variables. The dynamic linear model (DLM) can decompose the evaporation stress index time series into seasonal component, trend component and abnormal component, such as Figure 3As shown. In DLM, by inputting the time series of dependent variables and independent variables, the model can extract the seasonal component, trend component and abnormal component of the dependent variable, and analyze the linear regression relationship between the abnormal component and the independent variable. Here, DLM is used to set the input evaporation stress index time series, without introducing independent variables, and the abnormal component of the evaporation stress index time series can be obtained. The mathematical expression is as follows:

[0060] ESI=ESI l +ESI s +ESI r +v t (2)

[0061] Where: ESI is the time series of evaporation stress index; ESI l is the trend component of ESI; ESI s is the seasonal component of ESI; ESI r is the abnormal component of ESI; v t is the observed noise residual, which is the error when DLM performs variable decomposition.

[0062] DLM contains a parameter - the expansion factor γ. The value of γ is usually between 0.97 and 1.00. A smaller γ will lead to more significant fluctuations in local trends and seasonal components. Here, in order to ensure the stability of the two, we set γ to 0.999.

[0063] Step 3: Obtain the preceding impact sequence of the abnormal component of the evaporation stress index: For the abnormal component ESI at time t r,t Values, you need to obtain its values ​​at previous time points to characterize memory effects, including ESI r The sequence of the preceding time interval ESI r,t-1 , ESI of the first two time intervals r,t-2 , ESI of the first three time intervals r,t-3 , ESI of the first four time intervals r,t-4 , ESI of the first five time intervals r,t-5 ,like Figure 4 As shown in the figure, these sequences, namely the pre-order impact sequences, are obtained by staggering the entire evaporation stress index time series, and then retaining the ESI r The valid data range of the sequence and the preceding sequence overlaps, which is used as the valid research period data.

[0064] Step 4, calculate the seasonal and trend-free abnormal components of the evaporative stress influencing factors: The evaporative stress influencing factors include soil moisture SVM, saturated water vapor pressure difference VPD and leaf area index LAI. The relevant data are generally obtained by downloading public data from the Internet or by actual observation and calculation. Specifically, the leaf area index LAI data can be obtained from the global land surface satellite GLASS data website, and the soil moisture SVM data, temperature and dew point temperature data can be obtained from the European Center for Medium-Term Weather Forecasts network, where the temperature and dew point temperature data are used to calculate the saturated water vapor pressure difference VPD data series through the Clausius-Clapeyron relationship. The seasonal component is eliminated by subtracting the multi-year average climate state, and the long-term trend component is eliminated by subtracting the linear fit, so as to obtain the abnormal components of SVM, VPD and LAI.

[0065] Different from step 2, this step deals with the factors affecting evaporative stress (including svm, VPD and LAI), that is, external driving factors. The dependent variable evaporative stress index time series processed in step 2 is used to obtain the abnormal component series by removing the seasonal and trend components. The previous impact series, that is, the internal driving factors, are further obtained through step 3 as the independent variables representing the "memory effect". Due to the strong collinearity between the previous impact series and the dependent variable, the abnormal components obtained using DLM can be regarded as "pure abnormal" regression components. However, for the abnormal components of external driving factors, if the same method (removing trend and seasonality) is used, too many trend components may be eliminated, and the observation noise residual v will also be eliminated. t . Since the fluctuation of residuals also has a potential impact on the dependent variable, the residuals need to be retained when dealing with these external driving factors. To this end, the seasonal component is removed by subtracting the multi-year average climate state, and the long-term trend component is removed by subtracting the linear fit, so as to obtain the abnormal component of the external driving factors of the retained residuals. The specific process is as follows:

[0066] Calculation of seasonal components:

[0067]

[0068] Where: S(t) is the seasonal component; N is the total number of years in the time series; X i (t) is the data value at time point t in year i; X represents the evaporation stress influencing factor;

[0069] Calculation of trend component:

[0070] T(t)=a+bt (4)

[0071] Where: T(t) is the trend component, which is a linear fit with the X(t) sequence as the ordinate and the corresponding time t sequence as the ordinate, a and b are the intercept and slope obtained by linear fitting of X(t) respectively;

[0072] Get the abnormal component:

[0073] δX(t)=X(t)-S(t)-T(t) (5)

[0074] Where: δX(t) is the abnormal component of X(t).

[0075] Step 5, establish a memory dynamic linear model: Substitute the previous influence sequence of ESI and ESI abnormal component obtained in the above steps, as well as the abnormal component sequence of svm, VPD, and LAI into the dynamic linear model to construct a memory dynamic linear model. The memory dynamic linear model takes into account the influence of its own previous sequence in the development mechanism of evaporative stress, that is, the influence of memory effect, which is due to the existence of "self-enhancement" in the development process of evaporative stress.

[0076] cycle, the evaporation stress caused by water limitation in the previous stage will force the water-isolating vegetation to close the stomata to reduce transpiration water loss. The reduction of transpiration water vapor entering the atmosphere will further lead to atmospheric water deficit, aggravating the water stress in the next period. Therefore, compared with the traditional dynamic linear model, the development mechanism of evaporation stress is incorporated into the memory effect of the previous sequence, and it is named the memory dynamic linear model. The mathematical expression is as follows:

[0077] ESI=ESI l +ESI s +ESI r +v t (6)

[0078] ESI r,t =θ ESI1 ESI r,t-1 ~θ ESI5 ESI r,t-5 +θ svm δsvm t +θ VPD δVPD t +θ LAI δLAI t +ε (7)

[0079] Wherein, formula (6) is the same as formula (2) in step 2, indicating that the input dependent variable ESI of the memory dynamic linear model is the original time series of evaporation stress index, and the independent variable ESI r,t-1 、ESI r,t-2 、ESI r,t-3 、ESI r,t-4 、ESI r,t-5,δsvm t , δVPD t and δLAI t Time series as a driver. ESI r,t is the abnormal component of ESI at time t, obtained through step 2; ESI r,t-1 is the abnormal component of ESI at time t-1 (i.e., the previous time interval); θ ESI1 δESI t At time t, ESI r,t-1 Sensitivity coefficient; δsvm t , δVPD t and δLAI t They are the abnormal components of soil moisture, saturated vapor pressure deficit, and leaf area index at time t, respectively, obtained through step 4.

[0080] The memory dynamic linear model has the function of a dynamic linear model. First, it decomposes the original time series into trend components, seasonal components, and abnormal components, and then decomposes the regression component ESI. r,t The regression relationship between the model and the driving factors is established, and then the regression coefficient at each moment is obtained through the built-in Bayesian update method of the model, that is, θ svm ,θ VPD and θ LAI are ESI at time t r,t The output of the model is ESI l 、ESI s 、ESI r ,θ ESI1 ~θ ESI5 and θ svm ,θ VPD and θ LAI time series.

[0081] Step 6, determine the optimal expansion factor parameters of the model: Regarding the adjustment of the expansion factor γ parameter (usually in the range of 0.97 to 1.00), unlike the use of DLM for data preparation in step 2, the dynamic linear model considering the memory effect is used here to obtain accurate regression relationships and time-varying sensitivity coefficient sequences. Therefore, it is necessary to adjust different expansion factor parameters to obtain different model output results. The optimal expansion factor can be selected by verifying the accuracy of the component decomposition process. The steps are as follows:

[0082] Calculate the component sum of the memory dynamic linear model under different expansion factor γ parameters:

[0083]

[0084] Where: RSI (γ)is the sum of the three components obtained under the expansion factor γ, analogous to formula (6) and the input dependent variable ESI difference observation noise residual v t ; They are the trend component, seasonal component and abnormal component obtained under the expansion factor γ respectively;

[0085] Compare the original time series ESI and calculate the evaluation index determination coefficient R 2 , used to evaluate the accuracy of the model, the calculation formula is:

[0086]

[0087] Among them, the mean of the original time series ESI for:

[0088]

[0089] Where: T is the length of the time series; is the ESI at time t (γ) value.

[0090] Step 7, calculate the time-varying sensitivity series: Use the expansion factor γ with the largest determination coefficient determined in step 6 to run the memory dynamic linear model, and you can get the output of the model, the sensitivity coefficients θ of the three variables at each moment svm ,θ VPD and θ LAI , that is, the time-varying sensitivity sequence is obtained. Thus, the time-varying sensitivity sequence of evaporation stress to the influencing factors is determined.

[0091] Embodiment 1

[0092] This embodiment is an application example of the above method.

[0093] This embodiment selects the Chinese region as the study area. China, located in East Asia (73°33′-135°05′E, 3°51′-53°33′N), has a vast land area of ​​about 9.6 million square kilometers, with diverse climate and vegetation types. Over the past two decades, China's average temperature has risen by 0.24°C every decade, exceeding the global average warming rate of 0.2°C per decade. Against the backdrop of global warming, coupled with active greening efforts, the regional leaf area index has increased significantly by 7.7%. This growth rate leads the world. Despite this, the downward trend in surface soil moisture is worrying, with a rate of 0.08% per decade. Faced with significant terrestrial environmental changes and the impact of human activities, China's hydrological, vegetation and climatic conditions have changed significantly, making it a hot spot for studying the interactions and influencing mechanisms between eco-hydrological factors. Combined with meteorological observation data in China, the evaporation stress index in China is calculated and its time-varying sensitivity to soil moisture SVM, saturated vapor pressure difference VPD and leaf area index LAI is calculated to improve the problem that sensitivity research is not instantaneous and specific enough.

[0094] By downloading the actual evapotranspiration time series ETa and the potential evapotranspiration time series ETp with hourly time resolution in the study area from 2001 to 2020, the data were obtained from the European Centre for Medium-Range Weather Forecasts network. In order to ensure the consistency of the time resolution of related influencing factors for the convenience of analysis, the data were downsampled to an 8-day time resolution by calculating the sum of each hour within 8 days. The evaporation stress index time series ESI in the Chinese region was obtained by calculating the ratio of ETa and ETp. The values ​​of this series fluctuate continuously between 0.70 and 0.73.

[0095] Calculate the deseasonalized and detrended anomaly component of ESI using DLM r The value of the sequence fluctuates continuously between 0.48 and 0.59, and the ESI r The time series of the first 1 to 5 time intervals of the sequence, after this process, the ESI is retained r The valid data range for the sequence and interval time series overlap.

[0096] The leaf area index data LAI from 2001 to 2020 was obtained from the global land surface satellite GLASS data website, and the surface soil moisture data SVM, temperature and dew point temperature data were obtained from the European Centre for Medium-Range Weather Forecasts network. The temperature and dew point temperature data were used to calculate the saturated vapor pressure difference VPD data series through the Clausius-Clapeyron relationship. The traditional method of subtracting the multi-year average climate state to eliminate the seasonal component and subtracting the linear fitting to eliminate the long-term trend component was used to obtain the abnormal components of SVM, VPD, and LAI.

[0097] The ESI, the preceding influence sequence of the abnormal component of ESI, and the abnormal component sequences of svm, VPD, and LAI obtained in the above steps are substituted into the dynamic linear model to construct a memory dynamic linear model. The expansion factor γ parameter is set to 0.98, 0.99, and 0.999 respectively. The trend component, seasonal component, and abnormal component of ESI are decomposed by the model under different parameters. The three components are summed and the determination coefficient R is calculated by comparing with the original time series. 2 The results are 0.87, 0.92, and 0.93 respectively. 2 The maximum γ value is 0.999. The memory dynamic linear model is run to further obtain the time-varying sensitivity sequence of the evaporation stress index time series ESI to the abnormal component series of SVM, VPD, and LAI. The length of this sequence is consistent with the length of the input variable, which is the real "instantaneous" sensitivity. The obtained sensitivity series of SVM, VPD, and LAI fluctuate in the range of 1.0 to 1.8, -0.055 to -0.020, and -0.005 to 0.015, respectively. Figure 5 shown.

[0098] By calculating the "instantaneous" sensitivity sequence of evaporation stress to influencing factors, the effect of analyzing the sensitivity change law over a short period of time can be achieved.

[0099] Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred arrangement scheme, a person skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for calculating the time-varying sensitivity of evaporative stress to influencing factors, characterized in that: The method comprises the following steps: Step 1: Calculate the evaporation stress index time series: Obtain the actual evaporation time series ETa and the potential evaporation time series ETp of the study area, and calculate the evaporation stress index time series value ESI at time t according to formula (1): t , and then the evaporation stress index time series ESI is obtained; Where: ESI t is the time series value of the evaporation stress index at time t; ETa t is the actual evapotranspiration time series value at time t; ETp t is the time series value of potential evapotranspiration at time t; Step 2: Calculate the deseasonal and detrended abnormal component of the evaporation stress index: Use the dynamic linear model DLM, set the input evaporation stress index time series ESI, do not introduce independent variables, and obtain the abnormal component of the evaporation stress index time series. The mathematical expression is as follows: YES = YES l +ESI s +ESI r +v t (2) Where: ESI is the time series of evaporation stress index; ESI l is the trend component of ESI; ESI s is the seasonal component of ESI; r is the abnormal component of ESI; v t is the observation noise residual; Step 3: Obtain the preceding impact sequence of the abnormal component of the evaporation stress index: For the abnormal component ESI at time t r，t Value, get its value at previous time points to characterize memory effects, including ESI r The sequence of the preceding time interval ESI r，t-1 , ESI of the first two time intervals r，t-2 , ESI of the first three time intervals r，t-3 , ESI of the first four time intervals r，t-4 , ESI of the first five time intervals r，t-5 , these sequences, namely the pre-order impact sequences, are obtained by staggering the entire evaporation stress index time series, and then retaining the ESI r The valid data range of the sequence and the preceding sequence that affect the sequence overlaps is used as the valid research period data; Step 4, calculate the seasonal and trend-free abnormal components of the evaporative stress influencing factors: the evaporative stress influencing factors include soil moisture SVM, saturated vapor pressure difference VPD and leaf area index LAI. The seasonal components are eliminated by subtracting the multi-year average climate state, and the long-term trend components are eliminated by subtracting the linear fitting to obtain the abnormal components of SVM, VPD and LAI; The specific process is: Calculation of seasonal components: Where: S(t) is the seasonal component; N is the total number of years in the time series; X i (t) is the data value at time point t in year i; X represents the evaporation stress influencing factor; Calculation of trend component: T(t)=a+bt (4) Where: T(t) is the trend component, which is a linear fit with the X(t) sequence as the ordinate and the corresponding time t sequence as the ordinate, a and b are the intercept and slope obtained by linear fitting of X(t) respectively; Get the abnormal component: δX(t)=X(t)-S(t)-T(t) (5) Where: δX(t) is the abnormal component of X(t); Step 5, establish a memory dynamic linear model: Substitute the preceding influence sequence of ESI and ESI abnormal components obtained in the above steps, as well as the abnormal component sequence of svm, VPD, and LAI into the dynamic linear model to construct a memory dynamic linear model. The memory dynamic linear model takes into account the influence of its own preceding sequence in the development mechanism of evaporative stress, that is, the memory effect. The mathematical expression is as follows: YES = YES l +ESI s +ESI r +v t (6) ESI r，t =θ ESI1 ESI r，t-1 ~θ ESI5 ESI r，t-5 +θ svm δsvm t +θ VPD ΔVPD t +θ LAI δLAI t +e (7) Wherein, formula (6) is the same as formula (2), indicating that the input dependent variable ESI of the memory dynamic linear model is the evaporation stress index time series, and the independent variable ESI r，t-1 、ESI r，t-2 、ESI r，t-3 、ESI r，t-4 、ESI r，t-5 ,δsvm t , δVPD t and δLAI t Time series as a driver; ESI r，t is the abnormal component of ESI at time t; ESI r，t-1 is the abnormal component of ESI at time t-1; θ ESI1 δESI t At time t, ESI r，t-1 Sensitivity coefficient; δsvm t , δVPD t and δLAI t are the abnormal components of soil moisture, saturated water vapor pressure deficit, and leaf area index at time t; The memory dynamic linear model has the function of a dynamic linear model. First, it decomposes the original time series into trend components, seasonal components, and abnormal components, and then decomposes the regression component ESI. r，t The regression relationship between the model and the driving factors is established, and then the regression coefficient at each moment is obtained through the built-in Bayesian update method of the model, that is, θ svm ,θ VPD and θ LAI are ESI at time t r，t The output of the model is ESI, which is the sensitivity coefficient of the three variables. l 、ESI S 、ESI r ,θ ESI1 ~θ ESI5 and θ svm ,θ VPD and θ LAI time series; Step 6: Determine the optimal expansion factor parameters of the model: By verifying the accuracy of the component decomposition process, the optimal expansion factor is selected. The steps are as follows: Calculate the component sum of the memory dynamic linear model under different expansion factor γ parameters: Where: ESI (γ) is the sum of the three components obtained under the expansion factor γ, analogous to formula (6) and the input dependent variable ESI difference observation noise residual v t ; They are the trend component, seasonal component and abnormal component obtained under the expansion factor γ respectively; Compare the original time series ESI and calculate the evaluation index determination coefficient R 2 , used to evaluate the accuracy of the model, the calculation formula is: Among them, the mean of the original time series ESI for: Where: T is the length of the time series; is the ESI at time t (γ) value; Step 7, calculate the time-varying sensitivity series: use the expansion factor γ with the largest determination coefficient determined in step 6 to run the memory dynamic linear model and obtain the output of the model, the sensitivity coefficient θ of the three variables at each moment Svm ,θ VPD and θ LAI , that is, the time-varying sensitivity sequence is obtained; thus, the time-varying sensitivity sequence of evaporation stress to the influencing factors is determined.

2. The method for calculating the time-varying sensitivity of evaporative stress to influencing factors according to claim 1, characterized in that: The actual evapotranspiration time series ETa and the potential evapotranspiration time series ETp of the study area described in step 1 are obtained by downloading public data from the Internet or calculating actual meteorological data observations. If the time resolution of the acquired time series data is inconsistent, linear interpolation is used for upsampling or summation is used for downsampling to unify the time resolution.

3. The method for calculating the time-varying sensitivity of evaporative stress to influencing factors according to claim 1, characterized in that: The dynamic linear model DLM described in step 2 contains a parameter expansion factor γ, and the value of γ is 0.

999.

4. The method for calculating the time-varying sensitivity of evaporative stress to influencing factors according to claim 1, characterized in that: The soil moisture svm, saturated vapor pressure difference VPD and leaf area index LAI data in step 4 are generally obtained by downloading public data from the Internet or by actual observation and calculation.

5. The method for calculating the time-varying sensitivity of evaporative stress to influencing factors according to claim 4, characterized in that: The leaf area index LAI data were obtained from the global land surface satellite GLASS data website, and the soil moisture SVM data, temperature and dew point temperature data were obtained from the European Center for Medium-Range Weather Forecasts network. The temperature and dew point temperature data were used to calculate the saturated water vapor pressure difference VPD data series through the Clausius-Clapeyron relationship.

Images