Climate mode dynamic downscaling method introducing dynamic SpectraNudging coefficient

Abstract

The invention relates to a climate mode dynamic downscaling method introducing a dynamic SpectraNudging coefficient. The climate mode dynamic downscaling method comprises the following steps: (1) calculating a difference value between a background field variable and a mode simulation variable; (2) constructing a SpectraNING coefficient which dynamically changes along with time and space: fitting a cubic function which changes along with a vertical height layer of a climate mode, performing Z-score standardization and proper constraint, and traversing each horizontal grid point and different time of the mode to obtain the SpectraNING coefficient which dynamically changes along with time and three-dimensional space; (3) determining the influence height of the SpectraNudging coefficient; (4) calculating the time tendency of the climate mode simulation variable; and (5) repeatedly executing the steps (1)-(4), and continuously integrating the mode until the preset Nudging time is ended. The method can meet the temporal and spatial variation characteristics, so that the simulation description of the wind field is more detailed.

Description

Technical Field

[0001] The invention relates to the technical field of climate evolution prediction, and in particular to a climate model dynamic downscaling method introducing a dynamic spectral nudging coefficient. Background Art

[0002] Climate models are an important means of understanding and predicting climate evolution. Affected by model errors, initial value errors, and boundary condition (external forcing) errors, the simulation errors of climate models will continue to accumulate and increase during long-term continuous integration, showing false changes independent of the internal variability of the climate system and external forcing (called "climate drift"), reducing the simulation ability of climate models. Studies have shown that in the Coupled Model Inter-comparison Project (CMIP), the simulation errors of different climate models for global monsoon precipitation and its changing trends are 70% and 18% respectively (Hsu et al. 2013), the simulation errors for annual precipitation and annual potential evapotranspiration in global arid areas are 74.9% and 29.7% respectively (Yu et al. 2024), and the simulation error for summer precipitation in East Asia is 0.8 mm / day (Qu et al. 2014). This shows that there is a large uncertainty in the simulation performance of climate models during long-term continuous integration. Continuously reducing the simulation errors and uncertainties of climate models during long-term integration processes is of great significance for a deeper understanding of the mechanism of climate change and accurate prediction of climate evolution.

[0003] The main ways to reduce the simulation error and uncertainty of climate models during long-term integration are: first, improve the climate model's ability to describe physical processes such as cloud-radiation processes, boundary layer processes, and land-atmosphere interactions, and reduce model errors; second, improve the accuracy of the initial and boundary conditions of the climate model; third, improve the simulation method, such as improving the model resolution, using multi-model, multi-driven field ensemble forecasts, and four-dimensional data assimilation methods based on Nudging. Studies have shown that the four-dimensional data assimilation method based on Nudging can reduce the false oscillation caused by the incoordination between the observation or reanalysis field and the climate model or the incoordination between the variables by introducing the observation or reanalysis field to correct the simulation results of the climate model during the continuous integration of the climate model (Zhang Zhifu 2008), thereby effectively suppressing the "climate drift" of the climate model during the long-term integration process (Storch et al. 2000). The core idea of ​​the four-dimensional data assimilation method based on Nudging is to add a weight term to the atmospheric motion equation so that the simulation results of the climate model are constantly approaching the observation or reanalysis field and the dynamic coordination between the simulated variables is achieved. The specific expression is:

[0004]

[0005] in, is the time tendency term of each simulated variable X in the climate model; M(X,t) is the forcing term of the climate model, including all physical and dynamic processes in the climate model; G(X)(X reana -X) is the weight item; is the Nudging coefficient of variable X (t e (X) represents the Nudging time scale of each simulated variable, in seconds, which determines the degree to which the model variable approaches the observation or reanalysis field; X reana Represents the background field (such as observation or reanalysis data) variables. This method has the advantages of small computational complexity and easy implementation in climate models, so it is widely used to reduce the simulation error and simulation uncertainty of climate models.

[0006] Nudging four-dimensional assimilation methods can be divided into observation nudging, grid nudging and spectral nudging. The former is for observational fields, while the latter two are for reanalysis data driving climate models. The difference between grid nudging and spectral nudging is that in equation (1) (X reana -X) is different. reana -X) is the difference between the climate model simulation variable and the background field, while in Spectral Nudging (X reana -X) is the remainder of the difference between the climate model simulated variable and the background field after spectral filtering through fast Fourier transform expansion. In the spectral nudging scheme, equation (1) can be further expressed as:

[0007]

[0008] in, is the spectral coefficient of variable X time orientation; is the spectral coefficient of the climate model forcing term; is the Nudging coefficient in the spectral space corresponding to the variable X; m and n are the truncated wave numbers in the latitudinal and longitudinal directions; x and y represent the latitudinal and longitudinal grids in the climate model, respectively; η represents the vertical height layer of the climate model; Indicates (X reana -X) spectral coefficients.

[0009] In summary, Grid Nudging does not consider the differences between climate model simulation variables and background field variables at different spectra, that is, it corrects the simulation results with the same intensity, ignoring the influence of medium and small-scale atmospheric motion in the climate model. Spectral Nudging takes into account the influence of different atmospheric scales and retains the remainder containing the main atmospheric fluctuation signal (Storch et al. 2000). Studies have shown that compared with Grid Nudging, Spectral Nudging can not only reduce false reflections at the lateral boundaries, but also eliminate the influence of the size and position of the simulation area in the climate model (Miguez-Machoet al. 2004). Some evaluation studies have also shown that Spectral Nudging is better than Grid Nudging in simulating precipitation and low-level circulation (Ma et al. 2016; Yang et al. 2019; Huang et al. 2021).

[0010] Studies have shown that one of the core factors affecting the simulation effect of the Spectral Nudging four-dimensional assimilation method is the selection of the Nudging coefficient. As can be seen from formula (1), if the Nudging coefficient is too large, the simulation results of the climate model will be forced by the background field and cannot develop freely, and the dynamic imbalance in the background field may be falsely amplified; if the Nudging coefficient is small, the background field will have a smaller impact on the simulation results of the climate model, which means that the simulation error of the climate model will be continuously amplified without constraint, making it easier to produce "climate drift" and reduce the simulation ability of the climate model. The results based on actual simulation experiments show that reducing the Nudging coefficient will not only increase the variability of the climate model simulation results, but also increase the simulation error (Bowden et al. 2012); the selection of the Nudging coefficient will affect the simulation ability of the climate model for the interannual climate variability (Pohl and Cretat 2014); using a smaller Nudging coefficient on the wind speed or temperature variables in the climate model can reduce the simulation error of the climate model for extreme precipitation in the Qinghai-Tibet Plateau (Huang et al. 2021). It should be noted that in the current climate model, the Nudging coefficient is assumed to be a constant that does not change with time and space, which means that the change of the simulation error of the climate model during the integration process is fixed in time and space due to the forcing of the background field. The existing studies using climate models to carry out dynamical downscaling simulations are also mainly designed by designing sensitivity tests of different Nudging coefficients to obtain the optimal simulation results. This may cause the following problems: First, due to the differences in the study period and study area, there are significant differences in the values ​​of the Nudging coefficient obtained in different studies, which leads to uncertainty in the conclusions of different studies; second, in the process of using climate models to carry out dynamical downscaling simulations, in order to obtain the optimal simulation results, it is necessary to repeatedly test the Nudging coefficient, which consumes computing resources; third, the simulation error of the climate model changes with time and space, and the assumption that the Nudging coefficient is a constant does not match this actual physical process. Some studies have also shown that different values ​​or distributions of the Nudging coefficient at vertical heights will have a significant impact on the simulation results of climate models. For example, the study by Storchet et al. (2000) showed that when using reanalysis data as background fields to drive climate models, in order to improve the simulation effect of climate models, it is recommended to use a larger Nudging coefficient in the upper atmosphere, while a smaller Nudging coefficient is recommended in the lower atmosphere.Schubert-Frisius et al. (2017) studied the effects of different types of profile structures of Nudging coefficients changing with height on the simulation performance of spectral nudging. The results showed that the use of a parabolic Nudging coefficient profile that increases quadratically with height will cause the correlation between the relative vorticity simulated by the climate model and the relative vorticity of the reanalysis data to decrease rapidly as the Nudging coefficient decreases; after using a platform-type Nudging coefficient profile with non-zero values ​​between two specific model layers and zero values ​​in other model layers, the large-scale correlation between the relative vorticity simulated by the climate model and the relative vorticity of the reanalysis data is the highest; the use of the default constant Nudging coefficient in the climate model has the worst simulation performance for relative vorticity. These studies mean that it may be unreasonable to assume that the Nudging coefficient is a constant in existing climate models, which may also be an important factor restricting the improvement of climate model simulation capabilities.

[0011] In summary, the size and vertical structure of the spectral nudging coefficient are the key factors affecting the simulation performance of climate models. However, in the current climate models, the spectral nudging coefficient is assumed to be a constant that does not change with time or space, which is inconsistent with the actual physical process that the simulation error of the climate model changes continuously with time and space, restricting the improvement of the simulation performance of the climate model.

[0012] Therefore, the present invention attempts to consider the temporal and spatial variation characteristics of the difference between the climate model simulation field and the background field, establish a spectral nudging coefficient that changes dynamically with time and space, and couple it to the climate model to provide a scientific basis for improving the climate model. Summary of the invention

[0013] The technical problem to be solved by the present invention is to provide a climate model dynamic downscaling method that introduces a dynamic spectral nudging coefficient and can meet the characteristics of temporal and spatial variations.

[0014] In order to solve the above problems, a climate model dynamic downscaling method introducing a dynamic spectral nudging coefficient is provided in the present invention, comprising the following steps:

[0015] ⑴ Calculate the difference between background field variables and model simulation variables

[0016] First, the background field X of each variable in the background field at two adjacent moments reana (x,y,η,t) and X reana (x,y,η,t+ΔT) is interpolated to different integration moments X of the climate model reana (x,y,η,t),X reana(x,y,η,t+Δt)...X reana (x, y, η, t + ΔT); where x and y represent the latitudinal and longitudinal grids in the climate model, respectively; η represents the vertical height layer of the climate model; t represents the integration time of the climate model; ΔT is the time resolution of the background field; Δt is the time integration step of the climate model; X represents different simulation variables;

[0017] Then calculate the background field X of each simulation variable at different times according to the following formula reana The difference between (x,y,η,t+Δt) and the model simulation field X(x,y,η,t+Δt) is denoted as F(x,y,η,t+Δt):

[0018] F(x,y,η,t+Δt)=X reana (x,y,η,t+Δt)-X(x,y,η,t+Δt)

[0019] Finally, the spherical function is used as the basis function to perform the generalized Fourier series expansion on the above formula:

[0020]

[0021] in, It represents the difference between the spectral coefficients of the background field and the model simulation field at different times and different three-dimensional grid points of each simulated variable; m and n are the truncated wave numbers in the latitudinal and longitudinal directions;

[0022] ⑵Construct Spectral Nudging coefficients that change dynamically over time and space

[0023] At the current time t+Δt and at each horizontal grid point, the least squares method is first used to fit Cubic function of the vertical height layer η of the climate model:

[0024]

[0025] Among them, a, b, c and d are cubic functions The coefficient of

[0026] Then the fitted function Perform Z-score standardization:

[0027]

[0028] in, for The standardized value of for The average value of for The standard deviation of

[0029] Then use the following formula By making appropriate constraints, we can obtain the spectral nudging coefficients of the dynamics of each simulation variable.

[0030]

[0031] in, yes The dynamic Nudging coefficient obtained after appropriate constraints; β is the amplification factor, which is used to adjust the multiple of the Nudging coefficient to be enlarged or reduced over time and space; is the default constant for the mode, set to 0.0003;

[0032] Finally, the process in this step is repeated until all grid points at the model level and different times are traversed, thereby obtaining the spectral nudging coefficient that changes dynamically with time and three-dimensional space;

[0033] ⑶Determine the influence height of Spectral Nudging coefficient:

[0034] Determine the dynamic Nudging coefficient by setting whether Nudging is within the boundary layer and whether Nudging is above a specified altitude layer Whether to act within the boundary layer or below the specified model altitude layer, thereby controlling the dynamic Nudging coefficient of each simulation variable The altitude range affected;

[0035] ⑷Calculate the time trend of climate model simulation variables:

[0036] Using the dynamic Nudging coefficients of each simulation variable Calculate the weight of each simulation variable Then add the forcing term to the climate model Finally, the Matsuno time integration scheme is used to integrate and calculate the time tendency value of each simulation variable:

[0037]

[0038] in, is the spectral coefficient of each simulated variable time orientation; is the spectral coefficient of the climate model forcing term;

[0039] ⑸ Repeat steps ⑴~⑷ to continuously accumulate points for the mode until the preset Nudging duration ends.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] 1. The Nudging coefficient determined by the present invention based on the difference between the background field and the climate model simulation field changes dynamically not only in three-dimensional space but also in time. Therefore, the present invention is more complete in theory.

[0042] 2. The present invention uses different Nudging coefficients for the meridional wind and zonal wind in the climate model, which makes the simulation of the wind field more detailed and can be widely used in numerical simulation of weather and climate; climate resource assessment; agriculture, environment, and ecological evaluation, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The specific implementation modes of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0044] Figure 1 It is a flow chart of the present invention.

[0045] Figure 2 3 and 4, which are the deviation spatial distributions of temperature (a, b) and precipitation (c, d) over the Qinghai-Tibet Plateau simulated by the original method (a, c) and the new method (b, d) in the embodiments of the present invention.

[0046] Figure 3 Root mean square error (RMSE), mean relative error (MRE), and spatial similarity index (SSIM) of temperature (a) and precipitation (b) on the Qinghai-Tibet Plateau simulated by different experiments in the embodiments of the present invention. DETAILED DESCRIPTION

[0047] like Figure 1 As shown in FIG. 1 , a dynamic downscaling method for a climate model that introduces a dynamic spectral nudging coefficient includes the following steps:

[0048] ⑴ Calculate the difference between background field variables and model simulation variables

[0049] Since the time resolution of the background field is ΔT and the time integration step of the climate model is Δt, there is a significant difference in the resolution between the two. Therefore, the background field X of each variable (such as wind speed, temperature, geopotential height, water vapor) at two adjacent moments is calculated. reana (x,y,η,t) and X reana (x,y,η,t+ΔT) is interpolated to different integration moments X of the climate model reana (x,y,η,t),X reana (x,y,η,t+Δt)...X reana(x, y, η, t + ΔT); where x and y represent the latitudinal and longitudinal grids in the climate model, respectively; η represents the vertical height layer of the climate model; t represents the integration time of the climate model; ΔT is the time resolution of the background field; Δt is the time integration step of the climate model; X represents different simulation variables (such as wind speed, temperature, specific humidity, and potential height).

[0050] Calculate the background field X of each simulation variable at different times reana The difference between (x,y,η,t+Δt) and the model simulation field X(x,y,η,t+Δt) is denoted as F(x,y,η,t+Δt):

[0051] F(x,y,η,t+Δt)=X reana (x,y,η,t+Δt)-X(x,y,η,t+Δt) (3)

[0052] Referring to formula (2), taking the spherical function as the basis function, generalized Fourier series expansion is performed on formula (3):

[0053]

[0054] in, It represents the difference between the spectral coefficients of the background field and the model simulation field at different times and different three-dimensional grid points of each simulated variable; m and n are the truncated wave numbers in the latitudinal and longitudinal directions.

[0055] ⑵Construct Spectral Nudging coefficients that change dynamically over time and space (vertical height layers)

[0056] At the current time t+Δt and at each horizontal grid point, the least squares method is first used to fit the equation (4): Cubic function of the vertical height layer η of the climate model:

[0057]

[0058] Among them, a, b, c and d are cubic functions The coefficient of

[0059] Then the fitted function Perform Z-score standardization:

[0060]

[0061] in, for The standardized value of for The average value of for The standard deviation of

[0062] Then use the following formula to By making appropriate constraints, we can obtain the spectral nudging coefficients of the dynamics of each simulation variable.

[0063]

[0064] in, yes The dynamic Nudging coefficient obtained after appropriate constraints; β is the amplification factor, which is used to adjust the multiple of the Nudging coefficient to be enlarged or reduced over time and space; is the default constant for the mode, set to 0.0003;

[0065] Finally, the process in this step is repeatedly executed until all grid points at the mode level and different times are traversed, thereby obtaining the spectral nudging coefficients that change dynamically with time and three-dimensional space.

[0066] It should be noted that although is a function of three-dimensional space, but considering that the climate model is integrated over time, the It changes dynamically with time and three-dimensional space.

[0067] ⑶Determine the influence height of Spectral Nudging coefficient:

[0068] Determine the dynamic Nudging coefficient by setting whether Nudging is within the boundary layer and whether Nudging is above a specified altitude layer Whether to act within the boundary layer or below the specified model altitude layer, thereby controlling the dynamic Nudging coefficient of each simulation variable The height range affected.

[0069] ⑷Calculate the time trend of climate model simulation variables:

[0070] The dynamic Nudging coefficient of each simulation variable Substitute into formula (2) to calculate the weight of each simulation variable Then, further, superimposed on the forcing term of the climate model Finally, the Matsuno time integration scheme is used to integrate formula (2) to calculate the time tendency value of each simulation variable:

[0071]

[0072] in, is the spectral coefficient of each simulated variable time orientation; is the spectral coefficient of the climate model forcing term.

[0073] ⑸ Repeat steps ⑴~⑷ to continuously accumulate points for the mode until the preset Nudging duration ends.

[0074] In order to verify whether the method of the present invention can improve the model's ability to simulate the temperature and precipitation of the Qinghai-Tibet Plateau, two sets of numerical experiments were set up. Old experiment: using the model default Nudging coefficient; New experiment: using the dynamic Nudging coefficient obtained by the method of the present invention, respectively simulating the temperature and precipitation of the Qinghai-Tibet Plateau in the summer of 1998.

[0075] Figure 2 The temperature and precipitation errors of the Qinghai-Tibet Plateau simulated by the two experiments were compared. The results show that compared with the original method (Old) experiment, the precipitation error of the western Qinghai-Tibet Plateau simulated by the method of the present invention (New experiment) is significantly reduced.

[0076] Figure 3 The root mean square error (RMSE), mean relative error (MRE) and spatial similarity index (SSIM) of the temperature and precipitation simulated in the Qinghai-Tibet Plateau by different experiments were further compared. The results show that compared with the original method, the errors of the temperature and precipitation simulated by the proposed method are reduced, and the spatial similarity index is higher.

[0077] Therefore, the above results show that the simulation effect of climate models can be improved by using the method of the present invention.

Claims

1. A climate model dynamic downscaling method that introduces a dynamic spectral nudging coefficient comprises the following steps: ⑴ Calculate the difference between background field variables and model simulation variables First, the background field X of each variable in the background field at two adjacent moments reana (x,y,η,t) and X reana (x,y,η,t+ΔT) is interpolated to different integration moments X of the climate model reana (x,y,η,t),X reana (x,y,η,t+Δt)...X reana (x, y, η, t + ΔT); x and y represent the latitudinal and longitudinal grids in the climate model, respectively; η represents the vertical height layer of the climate model; t represents the integration time of the climate model; ΔT is the time resolution of the background field; Δt is the time integration step of the climate model; X represents different simulation variables; Then calculate the background field X of each simulation variable at different times according to the following formula reana The difference between (x,y,η,t+Δt) and the model simulation field X(x,y,η,t+Δt) is denoted as F(x,y,η,t+Δt): F(x,y,η,t+Δt)=X reana (x,y,η,t+Δt)-X(x,y,η,t+Δt) Finally, the spherical function is used as the basis function to perform the generalized Fourier series expansion on the above formula: in, It represents the difference between the spectral coefficients of the background field and the model simulation field at different times and different three-dimensional grid points of each simulated variable; m and n are the truncated wave numbers in the latitudinal and longitudinal directions; ⑵Construct Spectral Nudging coefficients that change dynamically over time and space At the current time t+Δt and at each horizontal grid point, the least squares method is first used to fit Cubic function of the vertical height layer η of the climate model: Among them, a, b, c and d are cubic functions The coefficient of Then the fitted function Perform Z-score standardization: in, for The standardized value of for The average value of for The standard deviation of Then use the following formula By making appropriate constraints, we can obtain the SpectralNudging coefficients of the dynamics of each simulation variable. in, yes The dynamic Nudging coefficient obtained after appropriate constraints; β is the amplification factor, which is used to adjust the multiple of the Nudging coefficient to be enlarged or reduced over time and space; is the default constant for the mode, set to 0.0003; Finally, the process in this step is repeated until all grid points at the model level and different times are traversed, thereby obtaining the spectral nudging coefficient that changes dynamically with time and three-dimensional space; ⑶Determine the influence height of Spectral Nudging coefficient: Determine the dynamic Nudging coefficient by setting whether Nudging is within the boundary layer and whether Nudging is above a specified altitude layer Whether to act within the boundary layer or below the specified model altitude layer, thereby controlling the dynamic Nudging coefficient of each simulation variable The altitude range affected; ⑷Calculate the time trend of climate model simulation variables: Using the dynamic Nudging coefficients of each simulation variable Calculate the weight of each simulation variable Then add the forcing term to the climate model Finally, the Matsuno time integration scheme is used to integrate and calculate the time tendency value of each simulation variable: in, is the spectral coefficient of each simulated variable time orientation; is the spectral coefficient of the climate model forcing term; ⑸ Repeat steps ⑴~⑷ to continuously accumulate points for the mode until the preset Nudging duration ends.

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