CN117093806A - Remote sensing-based full-space coverage offshore atmosphere CO 2 Column concentration calculation method - Google Patents
Remote sensing-based full-space coverage offshore atmosphere CO 2 Column concentration calculation method Download PDFInfo
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Abstract
The invention discloses a remote sensing-based full-space coverage offshore atmosphere CO 2 The invention relates to a method for calculating column concentration, in particular to CO 2 The field of column concentration calculation methods includes: step 1: land to sea atmosphere CO 2 Effect of column concentration the red band reflectance corrected for atmosphere can be used to construct a seawater eutrophication index, step 2: reconstructing missing data by a space-time interpolation method, and step 3: standardization processing, step 4: constructing a predicted random forest model by adopting a random forest method, and step 5: according to the downloaded data and the calculated seawater eutrophication index data, the step 2 space-time interpolation method and the step 3 standardization treatment are carried out, and the random forest model trained in the step 4 is utilized, so that all-weather and full-coverage marine atmosphere CO is predicted 2 The method provided by the invention can effectively calculate the CO of the offshore atmosphere 2 Column concentration.
Description
Technical Field
The present invention relates to CO 2 The field of column concentration calculation methods, in particular to a remote sensing-based full-space coverage offshore atmosphere CO 2 Column concentration calculation method.
Background
Atmospheric CO 2 The detection of column concentration can be divided into two methods, foundation and space-based. The foundation detection generally refers to the establishment of a site for observation, has higher precision, such as a global carbon column total amount observation network, is an observation network composed of foundation Fourier transform spectrometers, and can perform CO 2 ,CH 4 ,N 2 O，CO,H 2 The precise measurement of elements such as O and the like has the defects that the number of stations in the current observation network is small, the stations are sparsely distributed in the global scope, and the continuous atmospheric CO in a large area cannot be reflected 2 Is a distribution trend of (a). The space-based detection is generally based on satellites special for atmospheric air chamber gas detection, such as Japanese GOSAT and GOSAT2, american OCO-2 and OCO-3, china carbon satellites, and the like, and utilizes the shortwave infrared band carried by the satellites to carry CO to the atmosphere 2 The greatest advantage of the method is that the method has the detection capability of global coverage along with the earth-orbiting movement of satellites, but the channel characteristics determine that the observation revisit period is longer, and the daily full coverage detection of a large area cannot be realized.
To obtain a spatially fully covered atmosphere CO 2 The column concentration monitoring data and the space-based detection are low-cost and currently available methods, but the carbon satellite observation method has the problem of long revisit period. In order to overcome the problem, the common thinking is to build the satellite with the advantages of wide data range of the resolution ratio satellite such as the cloud satellite, MODIS and the like and capability of realizing the monitoring of earth coverage for multiple times per dayParameters obtained by inversion of sea-land-balloon layer and atmospheric CO obtained by carbon satellite 2 Correlation of column concentration, and further realizing atmospheric CO based on medium resolution satellite data 2 The column concentration was monitored over the whole range.
However, space-based detection still has 2 problems:
(1) The carbon circulation process involves multiple layers of biosphere, rock, water and atmosphere, although atmospheric CO 2 The concentration is relatively stable, but the influence of the underlying surface is obvious, and CO is between sea-gas and land-gas 2 Differences in partial pressure differences can lead to CO in the atmosphere 2 The concentration showed a temporal-spatial difference. Current pair CO 2 The concentration of the column is focused on the above-ground and less on the above-sea. There are many differences between sea and land, and above-land CO 2 The method for monitoring the concentration of the column is not suitable for the ocean space, so that the method is required to construct the atmospheric CO suitable for the ocean space 2 A new method for monitoring column concentration.
(2) The monitoring of the atmospheric and ocean parameters by the resolution satellite data in MODIS and the like is generally limited to clear sky areas, and cloud shielding in cloud areas can cause data loss, so that the daily spatial full coverage of atmospheric CO cannot be realized when the cloud exists in the monitoring area 2 And (5) monitoring column concentration.
For this purpose we provide remote sensing based full space coverage of the offshore atmosphere CO 2 The column concentration calculation method solves the above-mentioned problems.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a remote sensing-based full-space coverage offshore atmosphere CO 2 Column concentration calculation method solves the problem of spatial full coverage of atmospheric CO caused by data loss of atmospheric and ocean parameters and the like 2 There are missing problems with column concentration monitoring.
In order to achieve the aim, the invention adopts the remote sensing-based full-space coverage offshore atmosphere CO 2 A method of calculating column concentration comprising:
taking MODIS data as an example, the downloaded data comprise three types of MODIS data, one type is offshore parameters: sea surface temperature: SST, chlorophyll a concentration: chl-a,Photosynthetically active radiation: PAR; the second category is the atmospheric parameters: aerosol optical thickness: an AOT; three categories are band reflectivities: atmospheric corrected red band reflectivity, and XCO for OCO-2 satellites 2 Data, XCO 2 Data, namely atmospheric carbon dioxide column concentration;
step 1: land to sea atmosphere CO 2 The effect of column concentration can be used to construct a seawater eutrophication index using the atmospheric corrected red band reflectivity;
step 2: reconstructing missing data by a space-time interpolation method;
step 3: standardized treatments, sea surface temperature, chlorophyll a concentration, photosynthetically active radiation, aerosol optical thickness, sea water eutrophication index parameters, XCO of OCO-2 2 The data unify the spatial resolution to 0.05 DEG, wherein the sea surface temperature, chlorophyll a concentration, photosynthetically active radiation, aerosol optical thickness are interpolated using nearest neighbor method, sea water eutrophication index and XCO 2 The data is interpolated by a bilinear method and is unified into equal longitude and latitude projections;
step 4: constructing a predicted random forest model by adopting a random forest method, wherein sea surface temperature, chlorophyll a concentration, photosynthetic effective radiation, aerosol optical thickness and sea water eutrophication index are taken as independent variables, and XCO is taken as a reference value 2 Data as dependent variables:
step 5: according to downloaded sea surface temperature, chlorophyll a concentration, photosynthetic effective radiation, aerosol optical thickness data and calculated sea water eutrophication index data, through a space-time interpolation method of step 2, standardized treatment of step 3, and then utilizing a random forest model trained in step 4, all-weather and full-coverage sea atmosphere CO is predicted 2 Column concentration data.
As a further optimization of the scheme, missing data are reconstructed by a space-time interpolation method from chlorophyll a concentration, photosynthetic effective radiation, aerosol optical thickness and sea water eutrophication index.
As a further optimization of the above scheme, the seawater eutrophication index in step 1 is represented using SEI:
（1）
wherein SEI is the estimated seawater eutrophication index,is the red light band reflectivity after atmospheric correction.
As a further optimization of the above scheme, in the step 2, missing data is reconstructed by a space-time interpolation method, and the sea surface temperature is taken as an example for illustration:
first, sea surface temperature data which need to be reconstructed for a plurality of continuous days in a research area are set as a matrixMatrix->The row of (1) is all time sequence values of a certain spatial position point, the column is the value of all spatial points at a certain moment, and I is a missing point set to be reconstructed, wherein the missing value is expressed by NaN, and the workflow is as follows:
subtracting the effective average of its time dimension +.>The effective average value of the time dimension is the average value of the time dimension under the sea surface temperature data without the missing value, X is obtained, and 1% of the total effective data is randomly taken out from the X to be used as a cross verification set +.>For a pair ofAssigning data of the corresponding positions as NaNs, replacing all NaN points in X with 0, and defining P as a mode reserved number, wherein P=1;
pair matrixPerforming fancifulValue decomposition with
（2）
Using (3) to complement missing point data（3）；
Then calculate according to equation (4)Cross-validation set->Root mean square error R:
（4）；
to minimize the root mean square error R, let
（5）；
Reuse of the pair of (1)Performing singular value decomposition, and repeating the step 3 until the root mean square error R converges;
let the mode retention number p=1, 2, …,repeating the formulas (2) - (5), and recording the root mean square error at the corresponding P valueAt this time, there is always a P value enabling +.>Minimum, taking the P value as an optimal mode retention number k;
reconstructing the missing data by taking the optimal mode retention number k, and marking the obtained matrix as，/>And matrix->Is distinguished by->The missing values NaN have been reconstructed, < >>Add +.>Obtaining a final reconstruction matrix;
the sea surface temperature data of the area with missing data are reconstructed through the formulas (2) - (5), and all-weather and full-coverage sea surface temperature data are formed together with the existing clear sky data.
For further optimization of the above scheme, in equation (2):，/>，/>the spatial characteristic mode, the singular value matrix and the time characteristic mode which correspond to SVD after decomposition are respectively +.>Representing the matrix transpose.
As a further optimization of the above scheme, in formula (3):，/>and->Column t, < > -of spatial and temporal feature modes respectively>For the corresponding singular value +.>For missing point data, P is the mode retention.
As a further optimization of the above scheme, in formula (4): n is a cross validation setR is +.>Cross-validation set->Root mean square error->For the reconstruction value of the missing point data, +.>Is the original value of the missing point data.
As a further optimization of the above scheme, in formula (5):is a correction value matrix of missing points.
As a further optimization of the above scheme, the random forest model formula in the step 4 is:
（6）。
as a further optimization of the above scheme, in the step 4, according to the requirement of the random forest model, the number of leaves is set to be 5, the number of trees is set to be 70, 90% of the randomly selected data set is used as a training set, the remaining 10% is used as a test set for evaluating the accuracy of the prediction model, and the randomly selected data set refers to 5 independent variables and1 dependent variable of a plurality of times after the processing of the steps 1,2 and 3.
The invention relates to a remote sensing-based full-space coverage offshore atmosphere CO 2 The column concentration calculating method has the following beneficial effects:
the method provided by the invention can effectively calculate the CO in the offshore atmosphere 2 Column concentration.
Fully considers various elements of sea-land-gas related to carbon circulation for offshore atmosphere CO 2 The seawater eutrophication index provided by the invention can effectively reflect the influence of offshore suspended sediment and organic matters on ocean CO 2 The influence of partial pressure can better explain the CO in the offshore atmosphere 2 Is affected by the land of the coastal zone.
The invention firstly reconstructs the missing data by using a space-time interpolation method, and is all-weather and fully covered marine atmosphere CO 2 Column concentration calculations provide the necessary basis.
Specific embodiments of the invention have been disclosed in detail below with reference to the following description and drawings, indicating the manner in which the principles of the invention may be employed, it being understood that the embodiments of the invention are not limited in scope but are capable of numerous variations, modifications and equivalents within the spirit and scope of the appended claims.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Detailed Description
The present invention will be further described in detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the detailed description and specific examples, while indicating the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
It should be noted that, when an element is referred to as being "disposed on," or having an intermediate element, it can be directly on the other element or intervening elements may be present, and when an element is referred to as being "connected to," or having an intermediate element, it may be directly connected to the other element or intervening elements may be present, and the term "fixedly connected" is used herein in a wide variety of manners and is not intended to be limiting, and the terms "vertical", "horizontal", "left", "right", and the like are used herein for illustrative purposes only and are not meant to be exclusive embodiments.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs, and the terms used herein in this description are for the purpose of describing particular embodiments only and are not intended to limit the invention to any and all combinations of one or more of the associated listed items;
referring to fig. 1 of the specification, the present invention provides a technical solution: remote sensing-based full-space coverage offshore atmosphere CO 2 The invention relates to a column concentration calculation method, which is used for atmospheric CO under the large background of carbon circulation 2 Column concentration is spatially and spatially varying, thus sea and land-based CO 2 Column concentrations all need to be monitored to be able to detect global CO 2 The total concentration is accurately known, and the methods in the prior art are all aimed at the atmospheric CO on land 2 The method provided by the invention can effectively calculate the CO in the offshore atmosphere 2 Column concentration:
taking MODIS data as an example, the data used in the invention comprise three types of data of MODIS, one type is marine parameters: sea Surface Temperature (SST), chlorophyll a concentration (Chl-a), photosynthetically Active Radiation (PAR); the second category is the atmospheric parameters: aerosol Optical Thickness (AOT); three categories are band reflectivities: the reflectance of the red light wave Band (Band 1, 620-670 nm) corrected by the atmosphere; XCO of OCO-2 satellite 2 Data, XCO 2 The data is the atmospheric carbon dioxide column concentration. The above data may be downloaded from a website.
Step 1: the distribution of phytoplankton on the surface layer of the seawater is also time-space different under the influence of the distribution difference of nutrient substances contained in the seawater, and the phytoplankton can absorb and release CO through photosynthesis and respiration 2 Influence on seaCO in water 2 Partial pressure, and thus through sea-gas CO 2 Exchange influences atmospheric CO 2 Column concentration, in offshore areas, due to human activity and the large amount of sediment and nutrients carried by the incoming river, often bursts of red tide due to eutrophication, at this time for the surface CO of the sea water 2 The partial pressure has a great influence on the offshore atmosphere CO 2 The effect of column concentration can be expressed using the atmospheric corrected red band reflectivity to construct the sea water eutrophication index (SEI):
（1）
wherein SEI is the estimated seawater eutrophication index;is the red light band reflectivity after atmospheric correction.
The invention fully considers various elements of sea-land-gas related to carbon circulation for offshore atmosphere CO 2 The seawater eutrophication index provided by the invention can effectively reflect the influence of offshore suspended sediment and organic matters on ocean CO 2 The influence of partial pressure can better explain the CO in the offshore atmosphere 2 Is affected by the land of the coastal zone.
Step 2: the Sea Surface Temperature (SST), chlorophyll a concentration (Chl-a), photosynthetic effective radiation (PAR), aerosol Optical Thickness (AOT) and calculated sea water eutrophication index (SEI) can be obtained only under clear sky condition by space-time interpolation method, when sea surface is covered by cloud, the sea area and the related parameters of atmosphere above the sea area are deleted, the deleted data are reconstructed by space-time interpolation method, and the whole atmosphere CO is covered for the next step 2 Column concentration monitoring lays a foundation.
The following strategy applies to all 5 parameters, and the sea surface temperature is taken as an example for illustration, and other parameters are the same as the above:
first, sea surface temperature data (assuming m spatial positions, n days) to be reconstructed for a plurality of consecutive days in a study area is set as a matrixMatrix->The row of (1) is all time sequence values of a certain spatial position point, the column is the value of all spatial points at a certain moment, and I is a missing point set to be reconstructed, wherein the missing value is expressed by NaN, and the workflow is as follows:
1：subtracting the effective (non-NaN) average value of its time dimension +.>The effective average value of the time dimension is the average value of the time dimension under the sea surface temperature data without the deletion value, and the +.>From->1% of the total amount of data available for random access as cross-validation set->For->The data of the corresponding position is assigned NaN, and +.>The point of all NaN in (1) is replaced with 0, and P is defined as the mode retention number, where p=1.
2: pair matrixSingular value decomposition is performed with
（2）
Wherein,，/>，/>the spatial characteristic mode, the singular value matrix and the time characteristic mode which correspond to SVD after decomposition are respectively +.>Representing the matrix transpose.
3: using (3) to complement missing point data
3）
Wherein,，/>and->Column t, < > -of spatial and temporal feature modes respectively>For the corresponding singular value of the value,for missing point data, P is the mode retention number, and then +.>Cross-validation set->Root mean square error R:
4）
wherein N is a cross testSyndrome setR is +.>Cross-validation set->Root mean square error of>For the reconstruction value of the missing point data, +.>Is the original value of the missing point data.
4: to minimize the root mean square error R, let
（5）
Wherein,for correction value matrix of missing points, equation (1) is reused for +.>And (3) performing singular value decomposition, and repeating the step (3) until the root mean square error R converges.
5: let the mode retention number p=1, 2, …,repeating the formulas (2) - (5), and recording the root mean square error +.>. At this time there is always a P value enabling +.>And (3) taking the P value as the optimal mode retention number k.
6: reconstructing the missing data by taking the optimal mode retention number k to obtainThe matrix is marked as，/>And matrix->Is distinguished by->The deletion value (NaN) has been reconstructed,/->Add +.>And obtaining a final reconstruction matrix.
The sea surface temperature data of the area with missing data are reconstructed through the formulas (2) - (5), and all-weather and full-coverage sea surface temperature data are formed together with the existing clear sky data.
The Sea Surface Temperature (SST), chlorophyll a concentration (Chl-a), photosynthetically Active Radiation (PAR), aerosol Optical Thickness (AOT) and sea water eutrophication index (SEI) of the invention can be obtained only under the condition of clear sky, if only depending on the clear sky data, all-weather and full-coverage sea atmosphere CO can not be established 2 Column concentration monitoring algorithm. Therefore, the invention firstly reconstructs the missing data into all-weather and full-coverage offshore atmosphere CO by using a space-time interpolation method 2 Column concentration calculations provide the necessary basis.
Step 3: normalization processing, XCO of the above 5 parameters and OCO-2 2 Data uniform spatial resolution to 0.05 °, wherein Sea Surface Temperature (SST), chlorophyll a concentration (Chl-a), photosynthetically Active Radiation (PAR), aerosol Optical Thickness (AOT) are interpolated using nearest neighbor (nearest) sea water eutrophication index (SEI) and XCO 2 The data are interpolated by a bilinear method (linear) and are unified into equal longitude and latitude projections.
Step 4: constructing a predicted random forest model by adopting a random forest method, wherein Sea Surface Temperature (SST), chlorophyll a concentration (Chl-a), photosynthetic effective radiation (PAR), aerosol Optical Thickness (AOT) and sea water eutrophication index (SEI) are taken as independent variables, and XCO is taken as a reference point 2 As a dependent variable:
6）
the conceptual model shown in equation (6) is a dependent variable on the left, an independent variable in parentheses on the right, and RF is only an explanatory Random Forest (RF) method.
The number of leaves was set to 5 and the number of trees was set to 70 according to the requirements of the random forest model. 90% of the data set (referring to 5 independent variables and1 dependent variable at a plurality of times after the processing of steps 1,2, 3) was randomly selected as the training set, and the remaining 10% was used as the test set for evaluating the accuracy of the predictive model.
Step 5: in practical use, according to downloaded Sea Surface Temperature (SST), chlorophyll a concentration (Chl-a), photosynthetic effective radiation (PAR), aerosol Optical Thickness (AOT) data and calculated sea water eutrophication index (SEI) data, all-weather and full-coverage sea atmosphere CO can be predicted by performing space-time interpolation method of step 2, standardization processing of step 3 and using the random forest model trained in step 4 2 Column concentration data.
It should be understood that the invention is not limited to the preferred embodiments, but is intended to cover modifications, equivalents, or alternatives falling within the spirit and principles of the invention.
Claims (10)
1. Remote sensing-based full-space coverage offshore atmosphere CO 2 A method for calculating column concentration, comprising:
taking MODIS data as an example, the downloaded data comprise three types of MODIS data, one type is offshore parameters: sea surface temperature: SST, chlorophyll a concentration: chl-a, photosynthetically active radiation: PAR; class IIIs an atmospheric parameter: aerosol optical thickness: an AOT; three categories are band reflectivities: atmospheric corrected red band reflectivity, and XCO for OCO-2 satellites 2 Data, XCO 2 Data, namely atmospheric carbon dioxide column concentration;
step 1: land to sea atmosphere CO 2 The effect of column concentration can be used to construct a seawater eutrophication index using the atmospheric corrected red band reflectivity;
step 2: reconstructing missing data by a space-time interpolation method;
step 3: standardized treatments, sea surface temperature, chlorophyll a concentration, photosynthetically active radiation, aerosol optical thickness, sea water eutrophication index parameters, XCO of OCO-2 2 The data unify the spatial resolution to 0.05 DEG, wherein the sea surface temperature, chlorophyll a concentration, photosynthetically active radiation, aerosol optical thickness are interpolated using nearest neighbor method, sea water eutrophication index and XCO 2 The data is interpolated by a bilinear method and is unified into equal longitude and latitude projections;
step 4: constructing a predicted random forest model by adopting a random forest method, wherein sea surface temperature, chlorophyll a concentration, photosynthetic effective radiation, aerosol optical thickness and sea water eutrophication index are taken as independent variables, and XCO is taken as a reference value 2 Data as dependent variables:
step 5: according to downloaded sea surface temperature, chlorophyll a concentration, photosynthetic effective radiation, aerosol optical thickness data and calculated sea water eutrophication index data, through a space-time interpolation method of step 2, standardized treatment of step 3, and then utilizing a random forest model trained in step 4, all-weather and full-coverage sea atmosphere CO is predicted 2 Column concentration data.
2. Remote sensing-based full space coverage marine atmospheric CO as defined in claim 1 2 The column concentration calculation method is characterized in that: the chlorophyll a concentration, photosynthetic effective radiation, aerosol optical thickness and sea water eutrophication index are all reconstructed into missing data by a space-time interpolation method.
3. Root of Chinese characterRemote sensing-based full space coverage marine atmospheric CO as defined in claim 1 2 The column concentration calculation method is characterized in that: the seawater eutrophication index in step 1 is represented using SEI:（1）
wherein SEI is the estimated seawater eutrophication index,is the red light band reflectivity after atmospheric correction.
4. A remote sensing based full space coverage marine atmospheric CO as defined in claim 3 2 The column concentration calculation method is characterized in that: in the step 2, missing data is reconstructed by a space-time interpolation method, and the sea surface temperature is taken as an example for explanation:
first, sea surface temperature data which need to be reconstructed for a plurality of continuous days in a research area are set as a matrixMatrix->The row of (1) is all time sequence values of a certain spatial position point, the column is the value of all spatial points at a certain moment, and I is a missing point set to be reconstructed, wherein the missing value is expressed by NaN, and the workflow is as follows:
subtracting the effective average of its time dimension +.>The effective average value of the time dimension is the average value of the time dimension under the sea surface temperature data without the missing value, X is obtained, and 1% of the total effective data is randomly taken out from the X to be used as a cross verification set +.>For->Assigning data of the corresponding positions as NaNs, replacing all NaN points in X with 0, and defining P as a mode reserved number, wherein P=1;
singular value decomposition of matrix X is performed, with
（2）；
Using (3) to complement missing point data
（3）；
Then calculate according to equation (4)Cross-validation set->Root mean square error R:
（4）；
to minimize the root mean square error R, let
（5）；
Reuse of the pair of (1)Performing singular value decomposition, and repeating the step 3 until the root mean square error R converges;
let the mode retention number p=1, 2, …,repeating the formulas (2) - (5), and recording the root mean square error +.>At this time, there is always a P value enabling +.>Minimum, taking the P value as an optimal mode retention number k; reconstructing the missing data by taking the optimal mode retention number k, and marking the obtained matrix as +.>And matrix->Is distinguished by->The missing values NaN have been reconstructed, < >>Add +.>Obtaining a final reconstruction matrix;
the sea surface temperature data of the area with missing data are reconstructed through the formulas (2) - (5), and all-weather and full-coverage sea surface temperature data are formed together with the existing clear sky data.
5. The remote sensing-based full space coverage marine atmospheric CO of claim 4 2 The column concentration calculation method is characterized in that: in formula (2): u, S, V are the corresponding spatial characteristic mode, singular value matrix and time characteristic mode after SVD decomposition, T represents matrix transposition.
6. The remote sensing-based full space coverage sea of claim 4Upper atmosphere CO 2 The column concentration calculation method is characterized in that: in formula (3):，/>and->Column t, < > -of spatial and temporal feature modes respectively>For the corresponding singular value +.>For missing point data, P is the mode retention.
7. The remote sensing-based full space coverage marine atmospheric CO of claim 4 2 The column concentration calculation method is characterized in that: in formula (4): n is a cross validation setR is +.>Cross-validation set->Root mean square error of>For the reconstruction value of the missing point data, +.>Is the original value of the missing point data.
8. Tele-based according to claim 4Full space coverage of the sea atmosphere CO 2 The column concentration calculation method is characterized in that: in formula (5):is a correction value matrix of missing points.
9. Remote sensing-based full space coverage marine atmospheric CO as defined in claim 1 2 The column concentration calculation method is characterized in that: the random forest model formula in the step 4 is as follows:
（6）。
10. remote sensing-based full space coverage marine atmospheric CO as defined in claim 1 2 The column concentration calculation method is characterized in that: in the step 4, according to the requirement of the random forest model, the number of leaves is set to be 5, the number of trees is 70, 90% of the randomly selected data set is used as a training set, the remaining 10% is used as a test set for evaluating the accuracy of the prediction model, and the randomly selected data set refers to 5 independent variables and1 dependent variable of a plurality of times after the processing in the steps 1,2 and 3.
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