A networking laser radar data assimilation method based on three-dimensional variation
By assimilating networked lidar data using a three-dimensional variational method, the uncertainty in PM2.5 forecasting in existing technologies has been resolved, achieving higher-precision pollutant forecasting.
Patent Information
- Application Number
- CN202411058937.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-02
- Publication Date
- 2025-11-11
- Estimated Expiration
- 2044-08-02
AI Technical Summary
In the current technology, the international mainstream numerical models still have a large degree of uncertainty in the forecast of PM2.5 in various regions of my country, especially during periods of heavy pollution, the forecast bias is large. This is mainly due to the uncertainty of emission sources, meteorological fields, initial conditions and the models themselves, as well as the lack of three-dimensional detection data and high temporal and spatial resolution data assimilation.
A three-dimensional variational method for networked LiDAR data assimilation is adopted. By performing quality control and preprocessing on the networked LiDAR data, calculating the background error covariance matrix and the objective function value, and using the iterative conjugate gradient method to calculate the minimum value, the three-dimensional data assimilation is achieved.
It has achieved data assimilation from two-dimensional to three-dimensional ground data, improving the accuracy and precision of pollutant forecasts and reducing forecast errors.
Smart Images
Figure CN118981584B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to atmospheric environmental science and lidar, specifically to a three-dimensional variational method for assimilation of networked lidar data. Background Technology
[0002] Frequent severe air pollution has significant impacts on human health, visibility, and climate. Therefore, implementing emergency prevention and control measures during periods of heavy pollution and promptly issuing early warnings and forecasts to the public are crucial steps in addressing the current serious air pollution problem.
[0003] Numerical air quality model-based forecasting is a crucial technique for addressing the current severe haze pollution problem. Numerical models simplify real atmospheric physical processes into ideal mathematical models, using meteorological and mathematical methods to simulate the transport, reaction, and removal of pollutants in the atmosphere both horizontally and vertically. However, current mainstream international numerical models still exhibit significant uncertainties in predicting PM2.5 levels across various regions of my country, particularly during periods of heavy pollution, with forecast biases reaching 30-60%. These errors are primarily due to uncertainties related to emission sources, meteorological fields, initial conditions, and the models themselves.
[0004] Data assimilation, as an important methodology for integrating models and observations in Earth system science strategy, has long been proven effective in improving forecast results in the meteorological field. Meteorological data assimilation has been implemented operationally in numerous meteorological forecasting centers both domestically and internationally. In recent years, the application of atmospheric pollutant data assimilation in air quality forecasting has also gained increasing attention and development. Although data assimilation can improve forecast accuracy to some extent, current atmospheric pollutant data assimilation is mainly based on the surface layer, lacking spatial multi-dimensional data assimilation. This is primarily due to the severe lack of three-dimensional pollutant detection data, the low data density, and insufficient temporal and spatial resolution to meet the data quality standards for data assimilation. For example, conventional data only includes ground-based detection, while radiosonde data has low temporal resolution and low point density. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention provides a data assimilation method capable of achieving three-dimensional data assimilation.
[0006] This invention provides a three-dimensional variational method for assimilation of networked lidar data, the specific process of which is as follows:
[0007] A. Perform quality control and preprocessing on the networked LiDAR data; first, query the measured LiDAR data within the current time period, then perform statistical feature checks on the LiDAR data to determine whether the data conforms to statistical laws, and finally convert the normal data into the data format required by the stereo assimilation system.
[0008] B. Calculate the background error covariance matrix; the background error covariance matrix is the product of the background error matrix and the background correlation coefficient matrix, where the background error is the difference between two sets of forecast fields at the same time, and the background correlation coefficient is calculated using the Gaussian model method.
[0009] C. Calculate the objective function value; using the background field data simulated by the model and the measured data of the networked lidar, the objective function value is calculated through a three-dimensional variational method.
[0010] D, Calculate the gradient value of the objective function; using the objective function value processed in the previous step, calculate the gradient value of the objective function.
[0011] E, calculate the minimum value of the objective function; using the objective function value and the minimum value of the objective function calculated in the previous two steps as inputs to the stepwise iterative method, the minimum value of the objective function is calculated through the iterative conjugate gradient process.
[0012] F, update the background field data; when the objective function of the previous step reaches the minimum value, the corresponding state variable is the optimal estimate, forming the final analysis field for networked lidar data assimilation.
[0013] Furthermore, the lidar data quality control specifically includes:
[0014] A. Obtain networked LiDAR data: Based on the latitude and longitude range covered by the model, find the number of networked LiDAR units in that area, and query all data for the required time period through the database.
[0015] B. LiDAR Data Quality Control: Deadweight Check, also known as Minimum Frequency Conversion Check. Deadweight occurs when the observed value remains unchanged for an extended period due to instrument malfunction or other reasons during transmission or recording, leading to inaccurate recordings. The detection method is as follows: Z represents the mean absolute difference in the intensity change of the echo signal, that is, the change in the intensity of adjacent echo signal data.
[0016]
[0017] r is the correlation coefficient between adjacent radar echo signals, i.e., the degree of similarity of the echo waveforms:
[0018]
[0019] Here, A and B represent two echo signals.
[0020] Criterion: If consecutive data appears, and the Z-value between adjacent data is 0, and the corresponding r-value is 1, then the adjacent data is considered to be consecutive dead values.
[0021] C. LiDAR Data Preprocessing: The fine particulate matter (PM2.5) profile obtained directly from lidar inversion needs to be converted into a file in the Universal Binary Meteorological Data (BUFR) format required by the assimilation system. The following data formats were established: PTID, CLONH, CLATH, CSIGLEV, TPHR, TYPO, and COPOPM. Where: PTID represents the data ID, an auto-incrementing integer; CLONH and CLATH represent the longitude and latitude information of the current radar location, respectively; CSIGLEV represents the vertical layer information corresponding to the lidar data; TPHR represents the offset from the current simulation time; TYPO represents the data type ID number of the assimilation parameter PM2.5, currently fixed at 11; COPOPM represents the PM2.5 concentration information at the current spatial location of the current radar location.
[0022] Furthermore, the background error covariance matrix specifically includes:
[0023] A. Calculate the background error matrix: Use two different initial forecast times to forecast the same future time, and use the difference between the two sets of forecast fields as an approximation of the forecast error.
[0024] In this way, the background error covariance matrix B can be represented as a block diagonal matrix, which is usually obtained by the NMC (National Meteorological Center) method (Parish DF, Derber J., 1992). Its core is to use the difference between forecast values with different lead times at the same time as an approximation of the forecast error.
[0025]
[0026] Here, the subscripts i and l represent the grid point numbers in the horizontal and vertical directions, respectively. and This represents the forecast value of a certain element at a given time, with lead times of 24 hours and 12 hours respectively.
[0027] Among them, the background error covariance matrix of the chemical field variables in the statistical analysis mainly includes OC1, OC2, BC1, BC2, Sulfate, Sea salt1, and Dust1-2 in the GOCART model.
[0028] B. Calculate the background correlation coefficient matrix: Using the Gaussian model method, the background field correlation coefficient b(x, x0) between two points x and x0 is defined as a function of the distance dist(x-x0) between the two points. The specific calculation formula is as follows:
[0029]
[0030] C. Calculate the background error covariance matrix: Multiply the results of steps 3.1 and 3.2 to obtain the background error covariance matrix.
[0031] Furthermore, the calculation of the objective function value specifically includes:
[0032] A. Define the objective function:
[0033]
[0034] Among them, X a X is the analysis vector, or analysis field, representing the result of the model simulation after assimilation with observed data; that is, the final output value of the assimilation system. b For the forecast field or background field, it represents the unassimilated simulated values from the model simulation, which is a set of input values for the assimilation system. o The observed values represent the values observed by the instrument, and are also a set of input values for the assimilation system. Furthermore, B and O in the formula both represent error covariance matrices, where B is the background error covariance matrix and O is the observation error covariance matrix, representing the observation error. H represents the observation operator, indicating the transformation method or function from observed values to model values; the superscript "T" indicates transpose, and the superscript "-1" indicates the inverse matrix.
[0035] The first term on the right-hand side of the above formula is used to constrain the optimal parameters to make the model state as close as possible to the actual state. The second term is used to adjust the variables so that the model output is as close as possible to the continuous observations. The third term, Jc, represents a constant term, such as the changes caused by kinetic constants, water vapor constants, etc.
[0036] Define the analytical increment (ΔX)X=X a -X b The objective function is rewritten as:
[0037]
[0038] Assuming H is a linear operator, the objective function can be rewritten as follows:
[0039]
[0040] Define the observation increment as O = O0 - H Xb The objective function is finally rewritten as:
[0041]
[0042] Furthermore, the calculation of the minimum value of the objective function specifically includes:
[0043] After determining the objective function for data assimilation, the next task is to minimize the objective function. Minimization means changing the independent variables to minimize the function value. At this point, finding the minimum objective function under a series of external constraints is the solution for the cost function, also known as the loss function or error function.
[0044] The minimum value of the objective function can be determined through a step-by-step iterative method. Define a new variable y = B. -1 X, then equation (16) becomes:
[0045] J = y T B T y+(HBy-0) T O -1 (HBy-0)+J c (17)
[0046] According to the chain rule in calculus, the gradients of the cost function J with respect to the background field x and the observation field y are respectively:
[0047] ▽ X J = B -1 X+H T O -1 (HX-0) (18)
[0048]
[0049] Equations (6) and (7) are simultaneously minimized through an iterative conjugate gradient process. To find the optimal result, the iterative steps are as follows:
[0050] Starting with the assumption:
[0051] x 0 =y 0 =0
[0052] Iteration step n:
[0053]
[0054] x n =x n-1 +αDir·x n
[0055] y n =y n-1 +αDir·y n
[0056] The above iterations continue until the maximum number of iterations is reached or the two gradients (18) and (19) reach the pre-given minimization condition. When the objective function reaches its minimum state, the corresponding state variable is the optimal estimate, forming the final analysis field for networked lidar data assimilation.
[0057] Beneficial effects
[0058] As can be seen from the above technical solution, the present invention provides a three-dimensional variational method for assimilation of networked lidar data. Compared with traditional data assimilation methods, the significant feature of the present invention is that, based on the three-dimensional data of networked lidar, the traditional three-dimensional variational method is extended from two-dimensional ground to three-dimensional space, realizing the assimilation function of the traditional assimilation system from two-dimensional ground to three-dimensional space, and using as much three-dimensional space measured data as possible to correct the model simulation results. Attached Figure Description
[0059] Figure 1 This is a flowchart of the data assimilation process for networked LiDAR systems.
[0060] Figure 2 It is a single-point test and verification of the assimilation system;
[0061] Figure 3 This is a time series comparison chart of assimilated and unassimilated results. Detailed Implementation
[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0063] Example 1
[0064] Combination Figure 1 A three-dimensional variational method for networked lidar data assimilation mainly includes the following steps:
[0065] Step 1: Perform quality control and preprocessing on the networked LiDAR data; first, query the measured LiDAR data within the current time period, then perform statistical feature checks on the LiDAR data to determine whether the data conforms to statistical laws, and finally convert the normal data into the data format required by the stereo assimilation system.
[0066] Step 2: Calculate the background error covariance matrix; the background error covariance matrix is the product of the background error matrix and the background correlation coefficient matrix, where the background error is the difference between two sets of forecast fields at the same time, and the background correlation coefficient is calculated using the Gaussian model method.
[0067] Step 3: Calculate the objective function value; using the background field data simulated by the model and the measured data of the networked lidar, calculate the objective function value through a three-dimensional variational method.
[0068] Step 4: Calculate the gradient value of the objective function; using the objective function value processed in the previous step, calculate the gradient value of the objective function.
[0069] Step 5: Calculate the minimum value of the objective function; using the objective function value and the minimum value of the objective function calculated in the previous two steps as inputs to the stepwise iterative method, the minimum value of the objective function is calculated through the iterative conjugate gradient process.
[0070] Step 6: Update the background field data; when the objective function of the previous step reaches its minimum value, the corresponding state variable is the optimal estimate, forming the final analysis field for networked lidar data assimilation.
[0071] Example 2
[0072] A three-dimensional variational method for assimilating networked lidar data, specifically including the following steps;
[0073] S1. Perform quality control and preprocessing on the networked lidar data; first, query the measured lidar data within the current time period, then perform statistical feature checks on the lidar data to determine whether the data conforms to statistical laws, and finally convert the normal data into the data format required by the stereo assimilation system.
[0074] S2. Calculate the background error covariance matrix; the background error covariance matrix is the product of the background error matrix and the background correlation coefficient matrix, where the background error is the difference between two sets of forecast fields at the same time, and the background correlation coefficient is calculated using the Gaussian model method.
[0075] S3. Calculate the objective function value; using the background field data simulated by the model and the measured data of the networked lidar, calculate the objective function value through a three-dimensional variational method;
[0076] S4. Calculate the gradient value of the objective function; using the objective function value processed in the previous step, calculate the gradient value of the objective function.
[0077] S5. Calculate the minimum value of the objective function; using the objective function value and the minimum value of the objective function calculated in the previous two steps as inputs to the stepwise iterative method, the minimum value of the objective function is calculated through the iterative conjugate gradient process;
[0078] S6. Update the background field data; when the objective function of the previous step reaches the minimum value, the corresponding state variable is the optimal estimate, forming the final analysis field for networked lidar data assimilation.
[0079] In this invention, the method for quality control and preprocessing of networked lidar data specifically includes the following steps;
[0080] A1. Obtain networked LiDAR data: Based on the latitude and longitude range covered by the model, find the number of networked LiDAR units in the area and query all data for the required time period through the database;
[0081] A2. LiDAR Data Quality Control: Deadpoint Check, also known as Minimum Frequency Conversion Check, is a test for the observation value that remains unchanged for a long time due to instrument failure or other reasons during transmission or recording, resulting in inaccurate recording. The detection method is as follows: Z is the mean absolute difference of the intensity change of the echo signal, which is the change in the intensity of adjacent echo signal data.
[0082]
[0083] r is the correlation coefficient between adjacent radar echo signals, i.e., the degree of similarity of the echo waveforms;
[0084]
[0085] Where A and B represent two echo signals;
[0086] Criterion: If continuous data appears, and the Z=0 between adjacent data and the corresponding r=1, then the adjacent data is judged to be a continuous dead value;
[0087] A3. LiDAR Data Preprocessing: The fine particulate matter (PM2.5) profile obtained directly from lidar inversion needs to be converted into a file in the Universal Binary Meteorological Data (BUFR) format required by the assimilation system. The following data format has been established: PTID, CLONH, CLATH, CSIGLEV, TPHR, TYPO, COPOPM, where: PTID represents the data ID, which is an auto-incrementing integer; CLONH and CLATH represent the longitude and latitude information of the current radar location, respectively; CSIGLEV represents the vertical layer information corresponding to the lidar data; TPHR represents the offset from the current simulation time; TYPO represents the data type ID number of the assimilation parameter PM2.5, which is currently fixed at 11; COPOPM represents the PM2.5 concentration information of the current radar at the current spatial location.
[0088] In this invention, the step of calculating the background error covariance matrix specifically includes the following steps;
[0089] B1. Calculate the background error matrix: Two sets of different initial forecast times are used to forecast the same future time. The difference between the two sets of forecast fields is used as an approximate value of the forecast error. Among them, the background error covariance matrix of the chemical field variables in the statistical analysis mainly includes OC1, OC2, BC1, BC2, Sulfate, Sea salt1, and Dust1-2 in the GOCART model.
[0090] B2. Calculate the background correlation coefficient matrix: Using the Gaussian model method, the background field correlation coefficient b(x, x0) between two points x and x0 is defined as a function of the distance dist(x-x0) between the two points. The specific calculation formula is as follows;
[0091]
[0092] B3. Calculate the background error covariance matrix: Multiply the results of steps 3.1 and 3.2 to obtain the background error covariance matrix.
[0093] In this invention, calculating the objective function value specifically includes the following steps;
[0094] C1. Define the objective function:
[0095]
[0096] Among them, X a The analysis vector, or analysis field, represents the result of the model simulation after assimilation with observed data; that is, the final output value of the assimilation system, X. b Forecast field or background field, representing the unassimilated simulated values from the model simulation, and O is a set of input values for the assimilation system. o The observed values represent the values observed by the instrument, and are also a set of input values for the assimilation system. In addition, B and O in the formula both represent error covariance matrices, where B is the background error covariance matrix and O is the observation error covariance matrix, which represents the observation error. H represents the observation operator, which represents the transformation method or function from the observed values to the model values. The superscript "T" indicates transpose, and the superscript "-1" indicates the inverse matrix.
[0097] The first term on the right side of the above formula is used to constrain the optimal parameters to make the model state as close as possible; the second term is used to adjust the variables so that the model output is as close as possible to the continuous observation value; and the third term Jc represents the constant term, such as the changes caused by the dynamic constant, water vapor constant, etc.
[0098] C2. Define the analytical increment (ΔX) X = X a -X b The objective function is rewritten as:
[0099]
[0100] Assuming H is a linear operator, the objective function can be rewritten as follows:
[0101]
[0102] Define the observation increment as O = O0 - H Xb The objective function is finally rewritten as:
[0103]
[0104] In this invention, calculating the minimum value of the objective function specifically includes the following steps;
[0105] D1. After determining the objective function for data assimilation, the next task is to minimize the objective function. Minimization means changing the independent variable to minimize the function value. At this point, solving for the minimization of the objective function under a series of external constraints is the solution for the cost function, or loss function or error function.
[0106] The minimum value of the objective function can be determined through a step-by-step iterative method. A new variable y = B is defined. -1 X, then the expression becomes:
[0107] J = y T B T y+(HBy-0) T O -1 (HBy-0)+J c
[0108] According to the chain rule in calculus, the gradients of the cost function J with respect to the background field x and the observation field y are respectively:
[0109]
[0110] The system of equations is minimized simultaneously through an iterative process of conjugate gradients. To find the optimal result, the iterative steps are as follows:
[0111] Starting with the assumption:
[0112] x 0 =y 0 =0
[0113] Iteration step n:
[0114]
[0115] x n =x n-1 +αDir·x n
[0116] yn =y n-1 +αDir·y n
[0117] The above iterations continue until the maximum number of iterations is reached or the two gradients meet the pre-defined minimization condition.
[0118] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified.
[0119] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A method for data assimilation of networked lidar based on three-dimensional variation, characterized in that, Specifically, it includes the following steps; S1. Perform quality control and preprocessing on the networked lidar data; the quality control and preprocessing methods include: A1. Obtain networked LiDAR data: Based on the latitude and longitude range covered by the model, find the number of networked LiDAR units in the area and query all data for the required time period through the database; A2. LiDAR Data Quality Control: Deadpoint Check, also known as Minimum Frequency Conversion Check, is a test for the observation value that remains unchanged for a long time due to instrument failure or other reasons during transmission or recording, resulting in inaccurate recording. The detection method is as follows: Z is the mean absolute difference of the intensity change of the echo signal, which is the change in the intensity of adjacent echo signal data. r is the correlation coefficient between adjacent radar echo signals, i.e., the degree of similarity of the echo waveforms; Where A and B represent two echo signals; Criterion: If continuous data appears, and the Z=0 between adjacent data points, and the corresponding r=1, then the adjacent data points are considered to be continuous dead values. A3. LiDAR Data Preprocessing: The fine particulate matter concentration profile obtained directly from lidar needs to be converted into a file in the common binary format of meteorological data required by the assimilation system. The following data formats have been established: PTID, CLONH, CLATH, CSIGLEV, TPHR, TYPO, COPOPM, where: PTID represents the data ID, which is an auto-incrementing integer; CLONH and CLATH represent the longitude and latitude information of the current radar location, respectively; CSIGLEV represents the vertical layer information corresponding to the lidar data; TPHR represents the offset from the current simulation time; TYPO represents the data type ID number of the assimilation parameter PM2.5, which is currently fixed at 11; COPOPM represents the PM2.5 concentration information of the current radar at the current spatial location. S2. Calculate the background error covariance matrix; the background error covariance matrix is the product of the background error matrix and the background correlation coefficient matrix, where the background error is the difference between two sets of forecast fields at the same time, and the background correlation coefficient is calculated using the Gaussian model method. S3. Calculate the objective function value; using the background field data simulated by the model and the measured data of the networked lidar, calculate the objective function value through a three-dimensional variational method; S4. Calculate the gradient value of the objective function; using the objective function value processed in the previous step, calculate the gradient value of the objective function. S5. Calculate the minimum value of the objective function; using the objective function value and the minimum value of the objective function calculated in the previous two steps as inputs to the stepwise iterative method, the minimum value of the objective function is calculated through the iterative conjugate gradient process; S6. Update the background field data; when the objective function of the previous step reaches the minimum value, the corresponding state variable is the optimal estimate, forming the final analysis field for networked lidar data assimilation.
2. The method for assimilation of networked lidar data based on three-dimensional variation as described in claim 1, characterized in that: The specific steps for calculating the background error covariance matrix include the following: B1. Calculate the background error matrix: Two sets of different initial forecast times are used to forecast the same future time. The difference between the two sets of forecast fields is used as an approximation of the forecast error. The background error covariance matrix of the chemical field variables in the statistical analysis mainly includes OC1, OC2, BC1, BC2, Sulfate, Sea salt1, and Dust1-2 in the GOCART model. B2. Calculate the background correlation coefficient matrix: Using the Gaussian model method, the background field correlation coefficient b(x, x0) between two points x and x0 is defined as a function of the distance dist(x-x0) between the two points. The specific calculation formula is as follows. B3. Calculate the background error covariance matrix: Multiply the results of B1 and B2 to obtain the background error covariance matrix.
3. The method for assimilation of networked lidar data based on three-dimensional variation as described in claim 1, characterized in that: The calculation of the objective function value specifically includes the following steps; C1. Define the objective function: Among them, X a The analysis vector, or analysis field, represents the result of the model simulation after assimilation with observed data; that is, the final output value of the assimilation system, X. b Forecast field or background field, representing the unassimilated simulated values from the model simulation, and O is a set of input values for the assimilation system. o The observed values represent the values observed by the instrument, and are also a set of input values for the assimilation system. In addition, B and O in the formula both represent error covariance matrices, where B is the background error covariance matrix and O is the observation error covariance matrix, which represents the observation error. H represents the observation operator, which represents the transformation method or function from the observed values to the model values. The superscript "T" indicates transpose, and the superscript "-1" indicates the inverse matrix. The first term on the right-hand side of the above formula is used to constrain the optimal parameters to make the model state as close as possible to the actual state. The second term is used to adjust the variables so that the model output is as close as possible to the continuous observations. The third term, Jc, represents a constant term. C2, Define the analysis increment. The objective function is rewritten as follows: Assuming H is a linear operator, the objective function can be rewritten as follows: Define the observation increment as The objective function is finally rewritten as: .
4. The method for assimilation of networked lidar data based on three-dimensional variation as described in claim 1, characterized in that: The calculation of the minimum value of the objective function specifically includes the following steps; D1. After determining the objective function for data assimilation, the next task is to minimize the objective function. Minimization means changing the independent variable to minimize the function value. At this point, solving for the minimization of the objective function under a series of external constraints is the solution for the cost function, or loss function or error function. The minimum value of the objective function is determined through a step-by-step iterative method, defining a new variable. Then the expression becomes: According to the chain rule in calculus, the gradients of the cost function J with respect to the background field x and the observation field y are respectively: The system of equations is minimized simultaneously through an iterative process of conjugate gradients. To find the optimal result, the iterative steps are as follows: Starting with the assumption: Iteration step n: The above iterations continue until the maximum number of iterations is reached or the two gradients meet the pre-defined minimization condition.