Snow multi-mode integration method based on TC covariance

Abstract

The invention discloses an accumulated snow multi-mode integration method based on TC covariance, and the method comprises the following steps: (1) employing atmosphere forced data to drive different land surface modes of CLM, Noah and Noah-MP, and carrying out the simulation of accumulated snow in different land surface modes; (2) based on a TC covariance method, calculating variances and covariances of accumulated snow simulation in different regions in different modes, and calculating weights of different modes in different regions according to the variances and the covariances; and step (3), according to the calculated accumulated snow weights simulated in different areas in different modes, performing accumulated snow multi-mode integration. According to the invention, errors caused by multi-mode integration of a single mode in an area with large errors can be reduced, and the precision of multi-mode snow accumulation simulation is improved.

Description

Technical Field

[0001] The present invention relates to the field of snow cover multi-model integration, and more particularly to a snow cover multi-model integration method based on TC covariance. Background Art

[0002] There are many methods for combining models. The simplest approach is the ensemble average method, which completely ignores model performance and presents model results as an arithmetic mean. This method can improve model simulation results to a certain extent, but it makes it difficult to fully utilize available information. In 2003, Barnston et al. proposed combining data by assigning equal weights to all model forecast samples, effectively combining them using the arithmetic mean. Hagdorn tested this method in 2005, demonstrating that the ensemble forecasts obtained using this method were comparable to those obtained from any single model ensemble sample. Many researchers in China have also used this method for integration. In 2007, Xu Chonghai et al. used the ensemble average method to integrate the results of 22 coupled ocean-atmosphere simulations participating in the IPCC Fourth Assessment and analyzed the performance of climate simulations over East Asia. Currently, multi-model ensembles are widely used for temperature, typhoons, surface radiation, and precipitation, achieving excellent results.

[0003] The second method for combining models is weight allocation. This approach combines multiple models by determining weights, where the weights are determined by the performance of a particular model. The key lies in defining a metric for model performance, typically based on past and present observations. In 1999, Su Bingkai applied the optimal weighted combination method to the study of summer precipitation forecast integration. He used precipitation forecast scores and anomaly correlation coefficients to maximize the utilization of information provided by various models. The results showed that this method can effectively reduce the influence of environmental factors on individual model predictions. In 2000, Chen Guiying proposed a method for integrating data using historical forecast evaluation parameters as weights, using the ratio of the square of the forecast score of each participating method to the sum of the squares of the forecast scores as the weight coefficient. In 2008, Ma Qing et al. used a multivariate regression method to integrate data, using n products as regression factors and the corresponding observed values ​​as integration variables. The integration process was performed by finding the mathematical expression that best represents the relationship between them. In 2010, Chen Chaohui et al. introduced a multivariate linear regression and correlation weighting method to study multimodel integration. In 2015, Huang Si combined multi-model ensemble forecasting with multiple linear regression ensemble methods to reduce uncertainty in air quality forecasts. In 2016, Feng Huimin integrated temperature data from four numerical models using four methods: simple arithmetic averaging, bias-removed ensemble averaging, weighted bias-removed ensemble, and multi-model super ensemble. The results showed that the bias-removed ensemble averaging and weighted bias-removed ensemble performed the best.

[0004] In general, simple arithmetic averaging is simple and easy to implement at the grid scale, but it doesn't fully utilize the available information. Combining models by weighting often relies on the past or present relationship between simulated and observed values ​​to establish a mathematical model. Weights determined in this way are less reliable when there are only a few observation sites. Model simulation results vary at each grid point, so comparing models to determine weights independently of true values ​​is a viable approach. Summary of the Invention

[0005] To this end, the technical problem to be solved by the present invention is to provide a multi-model integration method for snow accumulation based on TC covariance, reduce the error caused by multi-model integration of a single model in areas with large errors, and improve the accuracy of multi-model simulation of snow accumulation.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] A snow cover multi-model integration method based on TC covariance includes the following steps:

[0008] Step (1) using atmospheric forcing data to drive the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model respectively, and combining surface parameter data such as soil texture, vegetation cover, and topography to simulate snow cover in different land surface models;

[0009] Step (2), using the TC covariance method, calculate the variance and covariance of snow cover simulated by different models in different regions in step (1), and calculate the weights of different land surface models in different regions based on the variance and covariance;

[0010] Step (3): Perform multi-model integration of snow cover based on the snow cover weights simulated by different models in different regions calculated in step (2).

[0011] In the above-mentioned TC covariance-based snow cover multi-model integration method, in step (1), the atmospheric forcing data include the near-surface air temperature, air pressure, specific humidity, wind speed, precipitation and solar radiation data of the China Meteorological Administration's Land Data Assimilation System CLDAS; the surface parameter data include soil texture data, vegetation cover data, topography data and other surface parameters required for land surface model simulation.

[0012] The above-mentioned snow cover multi-model integration method based on TC covariance is used to simulate snow cover in three different land surface models as follows:

[0013] CLM land surface model simulation: Using a long series of atmospheric forcing data and integrated surface parameter data, a long series of CLM land surface model spin-ups is conducted to obtain stable initial values ​​for the CLM model. These initial values ​​are then used to simulate three snow variables: snow depth, snow cover, and snow water equivalent (SWE) for at least five years.

[0014] Noah Land Surface Model Simulation: Using a long series of atmospheric forcing data and ensemble surface parameter data, a long series of Noah Land Surface Model spin-ups is conducted to obtain stable initial values ​​for the Noah Model. Simulations of three snow variables, snow depth, snow cover, and snow water equivalent, are then conducted using these initial values ​​for at least five years.

[0015] Noah-MP land surface model simulation: Using a long sequence of atmospheric forcing data and ensemble surface parameter data, a long sequence of Noah-MP land surface model spin-up is carried out to obtain stable initial values ​​of the Noah-MP model. Combined with this initial value, the Noah-MP land surface model is used to simulate three snow variables: snow depth, snow cover, and snow water equivalent for no less than 5 years.

[0016] In the above-mentioned TC covariance-based snow cover multi-model integration method, in step (2), the weight calculation of different land surface models in different regions includes the following steps:

[0017] Step (2-1), respectively calculate the variance and covariance of snow cover simulated by three different land surface models: CLM land surface model, Noah land surface model and Noah-MP land surface model;

[0018] Step (2-2): Calculate the random errors of the three different land surface model simulations based on the variances and covariances of the three different land surface model simulation results calculated in step (2-1);

[0019] Step (2-3): Based on the random error calculated in (2-2), the weight of the simulated snow cover of each land surface model is calculated using the least squares method.

[0020] In the above TC covariance-based snow cover multi-model integration method, in step (2-1), the variance is calculated as:

[0021] The calculation formula of covariance is:

[0022] In formula (4), σ 2 i represents the variance of snow cover simulated by the three land surface models, β 2 i Represents the multiplicative deviation coefficient relative to the true value, σ 2θ represents the snow cover simulated by the three land surface models, represents the error of the three data sets; in formula (5), σ ij represents the covariance of snow cover simulated by the land surface model, β i β j Represents the product of the coefficient of deviation between two data sets, Represents the product of snow cover between two datasets.

[0023] In the above multi-model integration method of snow cover based on TC covariance, in step (2-2), the random errors simulated by three different land surface models are calculated as follows:

[0024]

[0025] In formula (6) to formula (8), and represent the random errors of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; 2 X , σ 2 Y and σ 2 Z represent the variances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; XY , σ XZ and σ YZ are the covariances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, Represents the covariance product of the two data sets CLM and Noah, Represents the covariance product of the two data sets CLM and Noah-MP, Represents the covariance product of the Noah and Noah-MP datasets.

[0026] In the above-mentioned TC covariance-based snow cover multi-model integration method, in steps (2-3), the weights of the three different land surface models are calculated as follows:

[0027]

[0028] In formulas (9) to (11), ω CLM3.5 is the weight of the CLM land surface model, ω Noah is the weight of the Noah land surface model, ω No[h-MP is the weight of the Noah-MP land surface model; and represent the random errors of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively.

[0029] In the above-mentioned snow cover multi-model integration method based on TC covariance, in step (3), the calculation method for multi-model integration based on the weight calculation result is:

[0030] CLDAS TC =ω CLM3.5 CLDAS CLM3.5 +ω Noah CLDAS Noah +ω Noah-MP CLDAS Noah-MP (12);

[0031] Where, CLDAS TC The multi-model integrated snow cover simulated by the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model; CLDAS CLM3.5 、CLDAS Noah and CLDAS Noah-MP represent the snow cover simulated by the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model respectively; ω CLM3.5 They represent the weights of the CLM land surface model, the Noah land surface model and the Noah-MP land surface model respectively.

[0032] In the above-mentioned TC covariance-based snow cover multi-model integration method, in step (1), the atmospheric forcing data include the near-surface air temperature, air pressure, specific humidity, wind speed, precipitation and solar radiation data of the China Meteorological Administration's Land Data Assimilation System (CLDAS); the surface parameter data include soil texture data, vegetation cover data, topography data and other surface parameters required for land surface model simulation;

[0033] The snow simulation methods of three different land surface models are as follows:

[0034] CLM land surface model simulation: Using a long series of atmospheric forcing data and integrated surface parameter data, a long series of CLM land surface model spin-ups is conducted to obtain stable initial values ​​for the CLM model. These initial values ​​are then used to simulate three snow variables: snow depth, snow cover, and snow water equivalent (SWE) for at least five years.

[0035] Noah Land Surface Model Simulation: Using a long series of atmospheric forcing data and ensemble surface parameter data, a long series of Noah Land Surface Model spin-ups is conducted to obtain stable initial values ​​for the Noah Model. Simulations of three snow variables, snow depth, snow cover, and snow water equivalent, are then conducted using these initial values ​​for at least five years.

[0036] Noah-MP land surface model simulation: Using a long series of atmospheric forcing data and ensemble surface parameter data, a long series of Noah-MP land surface model spin-ups is conducted to obtain stable initial values ​​for the Noah-MP model. These initial values ​​are then used to simulate the three snow variables of snow depth, snow cover, and snow water equivalent in the Noah-MP land surface model for at least five years.

[0037] In step (2), the weight calculation of different land surface modes in different areas includes the following steps:

[0038] Step (2-1), respectively calculate the variance and covariance of snow cover simulated by three different land surface models: CLM land surface model, Noah land surface model and Noah-MP land surface model;

[0039] The calculation formula of variance is:

[0040] The calculation formula of covariance is:

[0041] In formula (4), σ 2 i represents the variance of snow cover simulated by the three land surface models, β 2 i Represents the multiplicative deviation coefficient relative to the true value, σ 2 θ represents the snow cover simulated by the three land surface models, represents the error of the three data sets; in formula (5), σ ij represents the covariance of snow cover simulated by the land surface model, β i β j Represents the product of the coefficient of deviation between two data sets, Represents the product of snow cover between two datasets;

[0042] Step (2-2): Calculate the random errors of the three different land surface model simulations based on the variances and covariances of the three different land surface model simulation results calculated in step (2-1);

[0043]

[0044] In formula (6) to formula (8), and represent the random errors of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; 2 X , σ 2 Y and σ 2 Zrepresent the variances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; XY , σ XZ and σ YZ are the covariances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, Represents the covariance product of the two data sets CLM and Noah, Represents the covariance product of the two data sets CLM and Noah-MP, Represents the covariance product of the Noah and Noah-MP datasets;

[0045] In step (2-3), based on the random error calculated in step (2-2), the weight of snow cover simulated by each land surface model is calculated using the least squares method. The weights of the three different land surface models are calculated as follows:

[0046]

[0047] In formulas (9) to (11), ω CLM3.5 is the weight of the CLM land surface model, ω Noah is the weight of the Noah land surface model, ω No[h-MP is the weight of the Noah-MP land surface model;

[0048] In step (3), the calculation method for multi-mode integration based on the weight calculation results is:

[0049] CLDAS TC =ω CLM3.5 CLDAS CLM3.5 +ω Noah CLDAS Noah +ω Noah-MP CLDAS Noah-MP (12);

[0050] Where, CLDAS TC The multi-model integrated snow cover simulated by the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model; CLDAS CLM3.5 、CLDAS Noah and CLDAS Noah-MP They represent the snow cover simulated by the CLM land surface model, the Noah land surface model and the Noah-MP land surface model respectively.

[0051] The technical solution of the present invention achieves the following beneficial technical effects:

[0052] The present invention proposes a multi-model ensemble assimilation method for snow cover based on TC covariance. The method uses the TC covariance method to calculate the weights of snow cover simulated by the CLM, Noah, and Noah-MP land surface models in different regions. The multi-model simulated snow cover is then integrated based on the weights of the different models to obtain the integrated snow cover. The method uses the TC covariance method to weight the snow cover simulated by the different models, fully accounting for the errors of the different models in different regions. This method achieves the integration of the multi-model simulated snow cover, reduces the errors caused by the multi-model integration in areas with large errors caused by a single model, and effectively improves the accuracy of the multi-model snow cover simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 Technical roadmap of the snow cover multi-model integration method based on TC covariance in the embodiment of the present invention;

[0054] Figure 2 Comparison diagram of each mode weight calculated by the traditional arithmetic mean method (a: CLM mode; b: Noah mode; c: Noah-MP mode) and the mode weight calculated based on the TC covariance method (d: CLM mode; e: Noah mode; f: Noah-MP mode) in an embodiment of the present invention;

[0055] Figure 3 The daily deviation time series of snow depth of GLDAS, ERA5_Land, and CLDAS_TC during the snow accumulation period from 2015 to 2019 in the embodiment of the present invention;

[0056] Figure 4 The daily root mean square error time series of snow depth of GLDAS, ERA5_Land, and CLDAS_TC during the snow accumulation period from 2015 to 2019 in the embodiment of the present invention;

[0057] Figure 5 The daily correlation coefficient time series of snow depth of GLDAS, ERA5_Land, and CLDAS_TC during the snow accumulation period from 2015 to 2019 in the embodiment of the present invention;

[0058] Figure 6 The daily deviation time series of snow depth of GLDAS, ERA5_Land, and CLDAS_TC during the snowmelt period from 2015 to 2019 in the embodiment of the present invention;

[0059] Figure 7 The daily root mean square error time series of snow depth of GLDAS, ERA5_Land, and CLDAS_TC during the snowmelt period from 2015 to 2019 in the embodiment of the present invention;

[0060] Figure 8The daily correlation coefficient time series of snow depth of GLDAS, ERA5_Land, and CLDAS_TC during the snowmelt period from 2015 to 2019 in the embodiment of the present invention;

[0061] Figure 9 The snow depth partition hit rate of GLDAS, ERA5_Land, and CLDAS_TC during the snow accumulation period from 2015 to 2019 in the embodiment of the present invention;

[0062] Figure 10 Snow depth zoning false alarm rates of GLDAS, ERA5_Land, and CLDAS_TC during the snow accumulation period from 2015 to 2019 in the embodiment of the present invention;

[0063] Figure 11 Snow depth zoning TS scores of GLDAS, ERA5_Land, and CLDAS_TC during the 2015-2019 snow accumulation period in the embodiment of the present invention;

[0064] Figure 12 TS scores for snow depth zones of GLDAS, ERA5_Land, and CLDAS_TC during the snowmelt period from 2015 to 2019 in the embodiments of the present invention. DETAILED DESCRIPTION

[0065] This embodiment takes the snow cover information collected by Fengyun satellites as an example to further illustrate the snow cover multi-mode integration method based on TC covariance of the present invention.

[0066] 1. Overall technical route

[0067] Figure 1 This embodiment presents a technical approach for a multi-model integration of snow cover based on TC covariance. This approach primarily involves simulations using the CLM land surface model, the Noah land surface model, the Noah-MP land surface model, snow cover simulation weight calculation, and multi-model integration. The CLM 3.5 land surface model, which features biogeophysical, hydrological, and biogeochemical processes; the Noah model, which depicts snow accumulation, sublimation, ablation, and heat exchange processes; and the Noah-MP land surface model, which features a multi-parameterization scheme for snow cover, runoff, and soil moisture. Using CLDAS-V2.0 surface parameters such as temperature, pressure, humidity, wind, precipitation, solar radiation, soil texture, and vegetation cover type as input, the method achieves snow cover simulations using the CLM, Noah, and NoahMP land surface models after decades of spin-up cycles. The TC covariance method is then used to calculate the model errors in different regions based on the simulated snow cover from these three models, and these errors are then combined for multi-model integration.

[0068] 2. China Meteorological Administration Land Surface Data Assimilation System

[0069] The China Meteorological Administration Land Data Assimilation System (CLDAS) was developed by Shi Chunxiang's research team at the National Meteorological Information Center of the China Meteorological Administration. The CLDAS-V2.0 atmospheric driving data mainly includes temperature, pressure, wind speed, humidity, precipitation, and incident ground solar shortwave radiation.

[0070] Among them, the temperature, pressure, humidity and wind driving data are mainly obtained by using the multi-grid variational analysis method, integrating the temperature, pressure, humidity and wind observation data of more than 2,400 national automatic stations and more than 40,000 regional automatic stations of the China Meteorological Administration with the ECMWF numerical forecast / ERA-Interim reanalysis products; the precipitation driving data are obtained by using the multi-grid variational analysis method, downscaling method and rain and snow identification method, integrating the precipitation observation data of more than 2,400 national automatic stations and nearly 70,000 regional automatic stations of the China Meteorological Administration with CMOPRH precipitation / EMSIP precipitation / MERRA2 precipitation; the radiation driving data are based on the DISORT radiation transfer model, with ozone, atmospheric precipitable water and surface air pressure in the GFS numerical analysis product as the dynamic input parameters of the radiation transfer model, and are formed by inverting the full-disk nominal map data of the FY2 geostationary satellite VIS channel. When the FY2 satellite is not available, the hybrid estimated station radiation data is fused with the ERA5 radiation data.

[0071] 3. CLM3.5, Noah, and Noah-MP land surface models

[0072] CLM3.5 incorporates new parameterization improvements to CLM3.0, enabling coupling with the LPJ model to simulate vegetation dynamics, enabling dynamic representation of vegetation in the land surface model. CLM includes up to five snow layers and ten unequally spaced soil layers. To represent the complexity of the land surface within the climate model grid, CLM employs a subgridding technique to account for underlying surface heterogeneity. Each CLM grid contains four possible land cover types: glaciers, wetlands, lakes, and vegetation. Within the vegetation layer, vegetation is categorized into different functional types based on their biophysical and chemical properties, for a total of 16 vegetation types. Each PFT solves its own hydrological and energy balance relationships and integrates them within each grid. Biophysical processes simulated in CLM3.5 include the interaction between shortwave and longwave radiation and the vegetation canopy and soil; momentum and turbulent fluxes in the soil and canopy; heat transfer between the soil and snow layer; hydrological processes in the canopy, soil, and snow layers; physiological changes in plant leaf stomata and photosynthesis.

[0073] The Noah land surface model was developed from the OSU-LSM (Oregon State University / Land Surface Model) and was officially named Noah in 2000. The soil moisture is calculated using the Richard equation and takes into account four soil layers, namely 0-10cm, 10cm-40cm, 40-100cm, and 100cm-200cm. After years of continuous improvement, the Noah land surface model has been widely used in the comprehensive simulation of land surface processes and in many foreign land surface data assimilation systems, such as the US Global Land Data Assimilation System GLDAS and the North American Land Data Assimilation System NLDAS. Figure 3 Noah characterizes the accumulation and ablation of snow, simulating the exchange of energy, momentum, and water between land and air based on a physical parameterization scheme. It also simulates snow accumulation, sublimation, melting, and heat exchange. The snow parameterization scheme in Noah was developed by Koren V et al. based on the NCEP climate model's snow cover and permafrost parameterization scheme. Snow depth is affected by snow water equivalent, snow density, snow surface temperature, and soil surface temperature, and is calculated from the snow water equivalent and snow density.

[0074] The Community Noah Land Surface Model with Multi-Parameterization Options (NOAH-MP) is a further development of the Noah land surface model. Unlike the Noah model, NOAH-MP separates vegetation from the land surface, revising the overall model framework and improving the energy balance of vegetation-covered areas, snow cover, frozen ground and infiltration, and soil moisture-groundwater interactions. Furthermore, the model offers thousands of parameterization scheme combinations for various physical process options, such as dynamic vegetation, runoff, and groundwater, allowing users to configure parameterization schemes according to their needs. The number of soil layers in NOAH-MP remains the same as in the Noah model, remaining four. This model is currently used in the NCAR High-Resolution Land Data Assimilation System (HRLDAS v3.6) and the China Meteorological Administration's Land Surface Data Assimilation System (CLDAS-V2.0). This paper uses the default Noah-MP scheme, with the specific parameterization combinations shown in Table 1. Regarding snow accumulation, the Noah model considers the soil and canopy as a whole. When the snow is thick, a large amount of energy is stored on the snow surface, causing the snow to melt and the surface temperature and soil temperature to drop. To address this problem, Noah-MP adopts a three-layer snow accumulation physics model and snow interception model, dividing the snow cover into three layers to represent the processes of infiltration, retention and refreezing in the snow, as well as energy transfer.

[0075] Table 1 Selection of Noah-MP parameterization schemes

[0076] Parameterized options Parameterized Scheme Dynamic vegetation Off (use leaf area index and maximum vegetation fraction) Canopy stomatal resistance Ball-Berry scheme Soil moisture factor on stomatal resistance Noah (using soil moisture) Runoff and groundwater Considering groundwater TOPMODEL Surface drag coefficient Noah's original plan Supercooled water No iteration Frozen soil permeability Linear, more permeable Radiative transfer Improved second-rate approximation Snow surface albedo CLASS Division of rain and snow Jordan (1991) used 2.5°C Lower boundary of soil temperature The bottom heat flux is zero, that is, no heat flux exchange Snow accumulation and soil temperature time plan Semi-secluded

[0077] 4. Multi-mode integration method based on TC covariance

[0078] The TC method is based on the following three assumptions: First, the errors in the three datasets are independent of each other. Second, the errors in the three datasets are independent of the true value. Third, the errors are stable and do not change over time.

[0079] θ X =α X +β X θ+r X (1);

[0080] θ Y =α Y +β Y θ+r Y (2);

[0081] θ Z =α Z +β Z θ+r Z (3);

[0082] In formula (1) to formula (3), α X , β Y and α Z Represents the additive deviation coefficient of the three data sets relative to the true value, β X , β Y and β Z represents the systematic error of the three data sets; r X 、r Y and r Z represents additive noise with a mean of 0, θ X ,θ Y ,θ Z represents the simulated values ​​of the three data sets, and θ represents the observed values.

[0083] The TC method can be divided into the difference method and the covariance method. The difference method requires that one of the three data sets be selected as the reference data in advance, and the other two data sets be converted proportionally to obtain a new data set. The error variance is estimated by averaging the cross-multiplication differences between the three data sets. The difference between the covariance method and the difference method is that there is no need to select the reference data in advance and to convert the data proportionally. This embodiment uses the TC covariance method to obtain the variance of the random error of the data. The variance and covariance formulas of the pattern data are as follows:

[0084]

[0085] In formula (4), σ 2 irepresents the variance of snow cover simulated by the three land surface models, β 2 i Represents the multiplicative deviation coefficient relative to the true value, σ 2 θ represents the snow cover simulated by the three land surface models, represents the error of the three data sets; in formula (5), σ ij represents the covariance of snow cover simulated by the land surface model, β i β j Represents the product of the coefficient of deviation between two data sets, Represents the product of snow cover between two datasets.

[0086] The calculation formula for random errors of different data sets is as follows:

[0087]

[0088] In formula (6) to formula (8), and represent the random errors of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; 2 X , σ 2 Y and σ 2 Z represent the variances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; XY , σ XZ and σ YZ are the covariances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, Represents the covariance product of the two data sets CLM and Noah, Represents the covariance product of the two data sets CLM and Noah-MP, Represents the covariance product of the Noah and Noah-MP datasets.

[0089] The weight of each land surface model data is obtained by the least squares method. The weight calculation formula is as follows:

[0090]

[0091] In formulas (9) to (11), ω CLM3.5 is the weight of the CLM land surface model, ω Noah is the weight of the Noah land surface model, ω No[h-MP is the weight of the Noah-MP land surface model.

[0092] Multi-mode fusion is performed according to the weights of different modes to obtain the result of multi-mode fusion.

[0093] CLDAS TC =ω CLM3.5 CLDAS CLM3.5 +ω Noah CLDAS Noah +ω Noah-MP CLDAS Noah-MP (12);

[0094] Where, CLDAS TC The multi-model integrated snow cover simulated by the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model; CLDAS CLM3.5 、CLDAS Noah and CLDAS Noah-MP They represent the snow cover simulated by the CLM land surface model, the Noah land surface model and the Noah-MP land surface model respectively.

[0095] Figure 10 The weights for the CLM, Noah, and Noah-MP models calculated using the arithmetic mean and TC covariance methods are shown. The weights calculated using the arithmetic mean method in the first row are the same for all models and regions. The second row shows the weights for the CLM, Noah, and NoahMP models in different regions. This shows that the TC covariance method accounts for model errors individually, resulting in different weights for the three models in different regions.

[0096] 5. Evaluation Metrics

[0097] The assessment of snow depth is mainly divided into two aspects: qualitative and quantitative assessment. The qualitative assessment mainly looks at the spatial distribution of snow depth and compares it with the spatial distribution of snow depth observations at the China Meteorological Administration's snow depth stations. The quantitative assessment is mainly based on the observation data of snow depth stations, and evaluates the snow accumulation period (January, November, and December each year) and the snowmelt period (February, March, and April each year). The main calculations include deviation, root mean square error, correlation coefficient, hit rate, false alarm rate, and TS score. The thresholds of hit rate, false alarm rate, and TS score are based on the snowfall grade standard. Light snow refers to a ground snow depth of 0.5 to 3 cm, moderate snow refers to a ground snow depth of 3 to 5 cm, and heavy snow refers to a ground snow depth greater than 5 cm.

[0098]

[0099] The above formulas represent the deviation, root mean square error and correlation coefficient respectively, where N is the total number of samples, Sim i is the analog value, Obs i is the observed value, and are the averages of the simulated and observed values, respectively.

[0100]

[0101] Among them, hits is the number of samples that are hit (shreshs represents the threshold, ground represents the observed snow depth at the station, snow represents the snow depth grid product, ground≥shreshs and snow≥shreshs), miss is the number of samples with missed reports (ground≥shreshs and snow<shreshs), and false is the number of false alarm samples (ground<shreshs and snow≥shreshs).

[0102] The value of the probability of detection (POD) is between 0 and 1. The closer it is to 1, the higher the probability of detection (POD), and the better the snow depth product. The value of the false alarm rate (FAR) is between 0 and 1. The closer it is to 0, the lower the false alarm rate. The TS score comprehensively evaluates the impacts of hits, false alarms, and missed reports. The value range is also between 0 and 1. The closer it is to 1, the better the snow depth product.

[0103] 6. Result Analysis

[0104] Record the snow cover result obtained by using the method of this embodiment as "CLDAS_TC", and compare it with the international similar products GLDAS of the United States and ERA5_Land of Europe, as well as CAS of the Chinese Academy of Sciences. The result analysis is as described below.

[0105] Figure 2 The pattern weights calculated by the arithmetic mean method (a: CLM model; b: Noah model; c: Noah-MP model) and the TC covariance method (d: CLM model; e: Noah model; f: Noah-MP model) for CLM3.5, Noah, and Noah-MP in a certain area are given. It can be seen that the weights of each pattern in the arithmetic mean method are the same in this area. The pattern weights calculated by the TC covariance method fully consider the variances and covariances of the patterns at different grid points, can reflect the differences of different patterns at different grid points in this area, and thus reduce the systematic errors brought by multi-model integration.

[0106] Figures 3 to 5The biases, root mean square errors, and correlation coefficients of GLDAS, ERA5_Land, and CLDAS_TC are presented for the snow cover period from 2015 to 2019. The biases show that both ERA5_Land and GLDAS exhibit positive biases, with ERA5_Land exhibiting the largest bias, ranging from 0 to 0.025 m, followed by GLDAS, with a bias between 0 and 0.02 m. CLDAS_TC has the lowest bias, ranging from -0.005 to 0.003 m. From the root mean square error, it can be seen that ERA5_Land has the largest root mean square error, which is basically between 0.01-0.082m, followed by GLDAS, with a root mean square error basically between 0.01 and 0.07m. The smallest root mean square error is CLDAS_TC, with a root mean square error basically between 0.002 and 0.04m. From the correlation coefficient, it can be seen that the correlation coefficient of ERA5_Land is relatively low, basically between 0.2 and 0.8, followed by GLDAS, which is basically between 0.2 and 0.82, and CLDAS_TC has the best correlation coefficient of 0.3 to 0.9.

[0107] Figures 6 to 8 The biases, root mean square errors, and correlation coefficients of GLDAS, ERA5_Land, and CLDAS_TC for the snowmelt period from 2015 to 2019 are presented. The biases show that both ERA5_Land and GLDAS exhibit positive biases, with ERA5_Land exhibiting the largest bias, ranging from 0.02 to 0.0225 m, followed by GLDAS, with a bias between 0 and 0.02 m. CLDAS_TC exhibits the lowest bias, ranging from -0.012 to 0.002 m. From the root mean square error, it can be seen that ERA5_Land has the largest root mean square error, basically between 0.02-0.13m, followed by GLDAS, with a root mean square error basically between 0.01 and 0.09m. The smallest root mean square error is CLDAS_TC, with a root mean square error basically between 0.0 and 0.04m. From the correlation coefficient, it can be seen that the correlation coefficient of ERA5_Land is higher than that of GLDAS in April 2017 and March and April 2019, and is basically lower than that of GLDAS in other time periods. The best effect is CLDAS_TC, with a correlation coefficient as high as 0.9.

[0108] Figure 9 and Figure 10The hit rates and false alarm rates of GLDAS, ERA5_Land, CAS, and CLDAS_TC for light snow, moderate snow, and heavy snow in Northeast China, Xinjiang, and the Qinghai-Tibet Plateau during the snow accumulation period from 2015 to 2019 were calculated. The hit rates and false alarm rates for the Northeast region show that the hit rates of the four products are high at different snowfall levels, while the false alarm rates are low. ERA5_Land and CAS have the highest hit rates, followed by GLDAS, and finally CLDAS_TC. The corresponding false alarm rates are similar, with ERA5_Land and CAS having the highest false alarm rates, followed by GLDAS, and finally CLDAS_TC. For Xinjiang, CAS has the highest hit rate, followed by ERA5_Land and CLDAS_TC, while GLDAS has the lowest hit rate. For the corresponding false alarm rates, CAS has the highest false alarm rate, followed by ERA5_Land and GLDAS. CLDAS_TC has the lowest false alarm rate. Looking at the Qinghai-Tibet Plateau, during light and moderate snowfall, ERA5_Land and CAS have the highest hit rates, followed by GLDAS, with CLDAS_TC having the lowest hit rate. A similar pattern holds for false alarm rates: ERA5_Land and CAS have the highest false alarm rates, followed by GLDAS, with CLDAS_TC having the lowest. During heavy snowfall, ERA5_Land has the highest hit rate, followed by CLDAS_TC and CAS, with GLDAS having the lowest hit rate. Regarding false alarm rates, ERA5_Land has the highest false alarm rate, followed by GLDAS and CAS, with CLDAS_TC having the lowest hit rate. In summary, CLDAS_TC has a low hit rate during light and moderate snowfall, but also the lowest false alarm rate. The other three products, while having high hit rates, also have high false alarm rates. This may be because CLDAS_TC uses IMS snow cover information when fusion, and IMS snow cover is relatively low, especially in terrain areas.

[0109] Figure 11The TS scores for GLDAS, ERA5_Land, CAS, and CLDAS_TC were calculated for light, moderate, and heavy snow in Northeast China, Xinjiang, and the Qinghai-Tibet Plateau during the snow cover period from 2015 to 2019. In Northeast China, CLDAS_TC had the highest TS score of 0.86 for light snow, followed by GLDAS (0.8). ERA5_Land and CAS had similar TS scores, both around 0.75. For moderate snow, CLDAS_TC still had the highest TS score, reaching 0.79. ERA5_Land had a higher TS score than GLDAS, which in turn had a higher TS score than CAS. For heavy snow, ERA5_Land had the highest TS score (0.698), slightly higher than CLDAS_TC (0.693), followed by GLDAS (0.653). In Xinjiang, under light snow conditions, CLDAS_TC has the highest TS score, reaching 0.807, followed by GLDAS (0.66) and ERA5_Land (0.635). The TS score of CAS is slightly lower than that of ERA5_Land. From the perspective of moderate snow, CLDAS_TC still has the highest TS score, reaching 0.799. Under moderate snow conditions, the TS score of ERA5_Land is higher than that of GLDAS, and the TS score of CAS is higher than that of GLDAS. Heavy snow is basically similar to moderate snow, and is slightly lower in magnitude. From the Qinghai-Tibet Plateau, it can be seen that under light snow, the TS score of CLDAS_TC is The TS score of CLDAS_TC was the highest (0.398), followed by GLDAS (0.182), while ERA5_Land and CAS were similar, at 0.125 and 0.131, respectively. During moderate snowfall, CLDAS_TC had the highest TS score (0.349), followed by GLDAS (0.1), while ERA5_Land and CAS were similar, at 0.069 and 0.066, respectively. During heavy snowfall, CLDAS_TC had the highest TS score (0.332), followed by GLDAS (0.06), while ERA5_Land and CAS were similar, at 0.057 and 0.045, respectively.

[0110] These results indicate that during the snowy period, CLDAS_TC performs best in Northeast China and Xinjiang. ERA5_Land's TS score is slightly lower than GLDAS in light snow, but outperforms GLDAS in moderate and heavy snow. Over the Qinghai-Tibet Plateau, CLDAS_TC remains the most effective, with GLDAS slightly outperforming ERA5_Land. ERA5_Land and CAS perform roughly equivalently.

[0111] Figure 12The TS scores of GLDAS, ERA5_Land, CAS, and CLDAS_TC were calculated for light, moderate, and heavy snow in Northeast China, Xinjiang, and the Qinghai-Tibet Plateau during the snowmelt period from 2015 to 2019. In Northeast China, CLDAS_TC had the highest TS score for light snow, reaching 0.813, followed by ERA5_Land (0.614). The TS scores of GLDAS and CAS were similar, both around 0.7. For moderate snow, CLDAS_TC still had the highest TS score, reaching 0.79. For moderate snow, ERA5_Land's TS score was similar to GLDAS, both higher than CAS. For heavy snow, CLDAS_TC still had the highest TS score (0.72), followed by ERA5_Land (0.645) and GLDAS (0.628). CAS had a relatively low TS score (0.518). In Xinjiang, under light snow conditions, CLDAS_TC has the highest TS score, reaching 0.783, followed by GLDAS (0.587) and ERA5_Land (0.568). CAS has a slightly lower TS score than ERA5_Land. From the perspective of moderate snow, CLDAS_TC still has the highest TS score, reaching 0.778. CAS has a slightly higher TS score than ERA5_Land, while GLDAS is relatively lower. Heavy snow is similar to moderate snow, and is slightly lower in value. From the Qinghai-Tibet Plateau, it can be seen that under light snow, CLDAS_TC has the highest TS score (0.778). 0.333), followed by GLDAS (0.169), and ERA5_Land slightly lower than CAS, with similar scores of 0.132 and 0.158, respectively. During moderate snowfall, CLDAS_TC had the highest TS score (0.407), followed by GLDAS (0.11), and ERA5_Land was also slightly lower than CAS, with scores of 0.064 and 0.105, respectively. During heavy snowfall, CLDAS_TC had the highest TS score (0.435), followed by GLDAS (0.093), and ERA5_Land slightly lower than CAS, with scores of 0.048 and 0.139, respectively. These results indicate that during the snowmelt period, CLDAS_TC is the most effective, followed by GLDAS, with ERA5_Land having a slightly lower TS score than CAS.

Claims

1. A snow cover multi-model integration method based on TC covariance, characterized by: The steps include: Step (1) using atmospheric forcing data to drive the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model respectively, combined with surface parameter data, to simulate snow cover in the three different land surface models; Step (2), using the TC covariance method, calculate the variance and covariance of snow cover simulated by different models in different regions in step (1), and calculate the weights of different land surface models in different regions based on the variance and covariance; Step (3): Perform multi-model integration of snow cover based on the snow cover weights simulated by different models in different regions calculated in step (2).

2. The snow cover multi-model integration method based on TC covariance according to claim 1 is characterized in that: In step (1), the atmospheric forcing data include the near-surface air temperature, air pressure, specific humidity, wind speed, precipitation and solar radiation data from the China Meteorological Administration's Land Data Assimilation System (CLDAS); the surface parameter data include soil texture data, vegetation cover data and terrain data.

3. The snow cover multi-model integration method based on TC covariance according to claim 1 is characterized in that: In step (1), the snow simulation methods for three different land surface models are as follows: CLM land surface model simulation: Using a long series of atmospheric forcing data and integrated surface parameter data, a long series of CLM land surface model spin-ups is conducted to obtain stable initial values ​​for the CLM model. These initial values ​​are then used to simulate three snow variables: snow depth, snow cover, and snow water equivalent (SWE) for at least five years. Noah Land Surface Model Simulation: Using a long series of atmospheric forcing data and ensemble surface parameter data, a long series of Noah Land Surface Model spin-ups is conducted to obtain stable initial values ​​for the Noah Model. Simulations of three snow variables, snow depth, snow cover, and snow water equivalent, are then conducted using these initial values ​​for at least five years. Noah-MP land surface model simulation: Using a long sequence of atmospheric forcing data and ensemble surface parameter data, a long sequence of Noah-MP land surface model spin-up is carried out to obtain stable initial values ​​of the Noah-MP model. Combined with this initial value, the Noah-MP land surface model is used to simulate three snow variables: snow depth, snow cover, and snow water equivalent for no less than 5 years.

4. The snow cover multi-model integration method based on TC covariance according to claim 1 is characterized in that: In step (2), the weight calculation of different land surface modes in different areas includes the following steps: Step (2-1), respectively calculate the variance and covariance of snow cover simulated by three different land surface models: CLM land surface model, Noah land surface model and Noah-MP land surface model; Step (2-2): Calculate the random errors of the three different land surface model simulations based on the variances and covariances of the three different land surface model simulation results calculated in step (2-1); Step (2-3): Based on the random error calculated in (2-2), the weight of the simulated snow cover of each land surface model is calculated using the least squares method.

5. The snow cover multi-model integration method based on TC covariance according to claim 4 is characterized in that: In step (2-1), the variance is calculated as: The calculation formula of covariance is: In formula (4), σ 2 i represents the variance of snow cover simulated by the three land surface models, β 2 i Represents the multiplicative deviation coefficient relative to the true value, σ 2 θ represents the snow cover simulated by the three land surface models, represents the error of the three data sets; in formula (5), σ ij represents the covariance of snow cover simulated by the land surface model, β i β j Represents the product of the coefficient of deviation between two data sets, Represents the product of snow cover between two datasets.

6. The snow cover multi-model integration method based on TC covariance according to claim 4 is characterized in that: In step (2-2), the random errors simulated by the three different land surface models are calculated as follows: In formula (6) to formula (8), and represent the random errors of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; 2 X , σ 2 Y and σ 2 Z represent the variances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; XY , σ XZ and σ YZ are the covariances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, Represents the covariance product of the two data sets CLM and Noah, Represents the covariance product of the two data sets CLM and Noah-MP, Represents the covariance product of the Noah and Noah-MP datasets.

7. The snow cover multi-model integration method based on TC covariance according to claim 4 is characterized in that: In steps (2-3), the weights of the three different land surface models are calculated as follows: In formulas (9) to (11), ω CLM3.5 is the weight of the CLM land surface model, ω Noah is the weight of the Noah land surface model, ω Noah-MP is the weight of the Noah-MP land surface model; and represent the random errors of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively.

8. The snow cover multi-model integration method based on TC covariance according to claim 1 is characterized in that: In step (3), the calculation method for multi-mode integration based on the weight calculation results is: CLDAS TC =ω CLM3.5 CLDAS CLM3.5 +ω Noah CLDAS Noah +ω Noah-MP CLDAS Noah-MP (12); Where, CLDAS TC The multi-model integrated snow cover simulated by the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model; CLDAS CLM3.5 、CLDAS Noah and CLDAS Noah-MP represent the snow cover simulated by the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model respectively; ω CLM3.5 They represent the weights of the CLM land surface model, the Noah land surface model and the Noah-MP land surface model respectively.

9. The snow cover multi-model integration method based on TC covariance according to claim 1 is characterized in that: In step (1), the atmospheric forcing data include the surface air temperature, pressure, specific humidity, wind speed, precipitation and solar radiation data from the China Meteorological Administration's Land Data Assimilation System (CLDAS); the surface parameter data include soil texture data, vegetation cover data and topography data; In step (1), the snow simulation methods for three different land surface models are as follows: CLM land surface model simulation: Using a long series of atmospheric forcing data and integrated surface parameter data, a long series of CLM land surface model spin-ups is conducted to obtain stable initial values ​​for the CLM model. These initial values ​​are then used to simulate three snow variables: snow depth, snow cover, and snow water equivalent (SWE) for at least five years. Noah Land Surface Model Simulation: Using a long series of atmospheric forcing data and ensemble surface parameter data, a long series of Noah Land Surface Model spin-ups is conducted to obtain stable initial values ​​for the Noah Model. Simulations of three snow variables, snow depth, snow cover, and snow water equivalent, are then conducted using these initial values ​​for at least five years. Noah-MP land surface model simulation: Using a long series of atmospheric forcing data and ensemble surface parameter data, a long series of Noah-MP land surface model spin-ups is conducted to obtain stable initial values ​​for the Noah-MP model. These initial values ​​are then used to simulate the three snow variables of snow depth, snow cover, and snow water equivalent in the Noah-MP land surface model for at least five years. In step (2), the weight calculation of different land surface modes in different areas includes the following steps: Step (2-1), respectively calculate the variance and covariance of snow cover simulated by three different land surface models: CLM land surface model, Noah land surface model and Noah-MP land surface model; The calculation formula of variance is: The calculation formula of covariance is: In formula (4), σ 2 i represents the variance of snow cover simulated by the three land surface models, β 2 i Represents the multiplicative deviation coefficient relative to the true value, σ 2 θ represents the snow cover simulated by the three land surface models, represents the error of the three data sets; in formula (5), σ ij represents the covariance of snow cover simulated by the land surface model, β i β j Represents the product of the coefficient of deviation between two data sets, Represents the product of snow cover between two datasets; Step (2-2): Calculate the random errors of the three different land surface model simulations based on the variances and covariances of the three different land surface model simulation results calculated in step (2-1); In formula (6) to formula (8), and represent the random errors of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; 2 X , σ 2 Y and σ 2 Z represent the variances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, respectively; XY , σ XZ and σ YZ are the covariances of the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model, Represents the covariance product of the two data sets CLM and Noah, Represents the covariance product of the two data sets CLM and Noah-MP, Represents the covariance product of the Noah and Noah-MP datasets; Step (2-3), based on the error calculated in (22), the weight of the simulated snow cover of each land surface model is calculated using the least squares method; In formulas (9) to (11), ω CLM3.5 is the weight of the CLM land surface model, ω Noah is the weight of the Noah land surface model, ω Noah-MP is the weight of the Noah-MP land surface model; In step (3), the calculation method for multi-mode integration based on the weight calculation results is: CLDAS TC =ω CLM3.5 CLDAS CLM3.5 +ω Noah CLDAS Noah +ω Noah-MP CLDAS Noah-MP (12); Where, CLDAS TC The multi-model integrated snow cover simulated by the CLM land surface model, the Noah land surface model, and the Noah-MP land surface model; CLDAS CLM3.5 、CLDAS Noah and CLDAS Noah-MP They represent the snow cover simulated by the CLM land surface model, the Noah land surface model and the Noah-MP land surface model respectively.

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