CN113777672A - Variational quality control method based on three-dimensional variational assimilation - Google Patents

Variational quality control method based on three-dimensional variational assimilation Download PDF

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CN113777672A
CN113777672A CN202111132407.6A CN202111132407A CN113777672A CN 113777672 A CN113777672 A CN 113777672A CN 202111132407 A CN202111132407 A CN 202111132407A CN 113777672 A CN113777672 A CN 113777672A
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和杰
马旭林
成魏
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Abstract

The invention discloses a variational quality control method based on three-dimensional variational assimilation, belonging to the field of numerical weather forecast; a variational quality control method based on three-dimensional variational assimilation comprises the steps of constructing a probability density function of observation errors which obey Gaussian distribution and uniform distribution, and constructing a new observation target function, a gradient function and a weight function of the three-dimensional variational assimilation; the assimilation method for realizing the integration of variational quality control and three-dimensional variational assimilation is characterized in that variational quality control is synchronously carried out in the three-dimensional variational assimilation process, the quality of assimilation observation is effectively identified, the weight of observation with larger deviation is reduced, and larger weight of observation with smaller deviation and better quality is given, so that the quality of three-dimensional variational assimilation analysis cannot be damaged when bad data enters an assimilation system, and meanwhile, effective assimilation and absorption observation can be effectively carried out, and the quality of three-dimensional variational assimilation analysis is improved.

Description

Variational quality control method based on three-dimensional variational assimilation
Technical Field
The invention belongs to the field of numerical weather forecast, and particularly relates to a variational quality control method based on three-dimensional variational assimilation.
Background
The variational quality control method is based on a three-dimensional variational assimilation method, an assimilation method integrating variational quality control and three-dimensional variational assimilation is formed according to a Bayesian probability theory on the assumption that observation errors obey a non-Gaussian distribution model of Gaussian distribution and uniform distribution (uniform for short);
the probability density function of the observation error plays an important role in the three-dimensional variation and assimilation theory, and the distribution and the size of the probability density function have important influence on the accuracy of posterior analysis; and assuming that the two are subjected to Gaussian distribution and are independent of each other, the optimal linear unbiased estimation of the three-dimensional variational and assimilative posterior analysis can be obtained according to the Bayesian probability theory. In the field of data assimilation technology, the assumption of gaussian error distribution is widely applied, such as three-dimensional variational assimilation method, four-dimensional variational assimilation method and ensemble kalman filter assimilation method. According to bayesian probability theory, the error is not necessarily assumed to be gaussian distribution (Fowler and Leeuwen,2012,2013), for example, the particle filter assimilation technique considers the non-linear and non-gaussian characteristics of the weather process, which is more consistent with the real atmospheric motion law.
The effect of observations conforming to non-gaussian mis-observation difference distributions on three-dimensional variation and assimilation is uncertain, and it is generally a simple practice to reject these observations to make the innovation vectors obey gaussian distributions as much as possible to adapt to the assumptions of data assimilation gaussian distributions. Statistics of the innovation vectors based on assimilation observations show that the distribution of the innovation vectors of the current assimilation observations shows the characteristics of non-Gaussian distribution (Anderson and)
Figure BDA0003280902590000011
1999; he et al, 2021), compared with gaussian distribution, mainly shows the longer characteristics of two tail distributions, mainly because the threshold of the conventional quality control is empirical, and the incompletely accurate threshold setting causes the assimilation observation to include outlier, which is the main reason for the long tail distribution characteristics. Outliers are observations that are significantly different from surrounding observations. Conventional quality control generally considers outliers to be the result of gross errors. However, studies have shown that not all outliers are gross errors, which may be distributions that follow functions other than gaussian, but are correct or carry useful information observations (Hampel, 2001). Therefore, if the data assimilation method under the assumption of Gaussian distribution is used to assimilate the observed data with non-Gaussian error distribution, the minimized scoreThe analysis will be a sub-optimal a posteriori analysis only. Thus, it is necessary to consider the non-gaussian distribution characteristic of the observation error for the posterior analysis for improving data assimilation.
The non-Gaussian observation error distribution model can better represent the long-tail probability density distribution characteristics of the observation errors. Therefore, the predecessor establishes a variation quality control method by assuming a new non-gaussian distribution model of the observation error and by Bayesian probability theory. The variation quality control and the three-dimensional variation assimilation are synchronously carried out, different weights can be given according to the observation quality in the iteration process to enable the variation quality control and the three-dimensional variation assimilation to be more effective in absorption and assimilation, namely, the essence is taken to remove dregs, so that the variation quality control is widely applied to the current three-dimensional variation assimilation system.
The variation quality control method is not finished before data assimilation like the traditional quality control method, but is based on a variation assimilation algorithm, and assumes that observation errors obey Gaussian distribution and uniform distribution according to the characteristic of long tail distribution of an actual innovation vector, and the Bayesian probability theory realizes the synchronous implementation of the variation data assimilation and the quality control. At present, a variation quality control method is adopted in a plurality of assimilation systems with numerical prediction modes. For example, a variation assimilation system of an integrated forecasting system of a middle-term weather forecasting center in Europe adopts a variation quality control method; the numerical forecasting system of the national environment forecasting center and the Canada meteorological center also establishes a variation quality control method; a variation quality control method is also developed and established by a global marine re-analysis system of the Mediterranean climate forecasting center; the Chinese numerical prediction assimilation system also initially establishes a variation quality control method (Haimin et al, 2013; Maxulin et al, 2017). However, no available variation quality control method is established in the three-dimensional variation assimilation system (WRFDA) of the current advanced mesoscale prediction mode (WRF). The variation quality control not only can effectively improve the utilization rate of assimilation observation, but also can realize the quality control of data assimilation observation, and is beneficial to improving the quality of three-dimensional variation assimilation analysis. Therefore, designing a variation quality control scheme of the three-dimensional variation assimilation system for establishing the mesoscale forecasting mode has important significance for further improving the accuracy of numerical weather forecasting.
The 'uniform' variation quality control method mainly relates to the selection of optimal parameters and the key technology of stable convergence of minimized iteration. At present, a uniform type variation quality control method is applied to a variation assimilation system of the European middle-term weather forecast center, but the variation assimilation system adopts a four-dimensional variation assimilation method, while a three-dimensional variation assimilation system in a WRF mode is a system developed and sourced by the United states, and the latter is not available with any variation quality control method, and different variation assimilation systems have obvious difference. Therefore, the parameter configuration and the minimized iteration stable convergence technology used by the existing method are not necessarily suitable for the three-dimensional variation assimilation system in the WRF mode. Therefore, the invention develops and establishes a uniform variable quality control method, establishes the optimal configuration of variable quality control parameters corresponding to various observation data, and simultaneously provides the relative optimal step number (15-20 steps) for ensuring the stable convergence of the minimized iteration, so that the uniform variable quality control method is started after the normal iteration reaches the step number, the stable convergence of the three-dimensional variable assimilation iteration can be met, and the higher-quality variable assimilation analysis solution can be obtained.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a variational quality control method based on three-dimensional variational assimilation, which effectively overcomes the defects of the traditional quality control, improves the utilization rate of observed data, and therefore improves the accuracy of three-dimensional variational assimilation analysis, and provides favorable quality control guarantee for further improving variational assimilation and mixed assimilation analysis fields and improving the accuracy of numerical weather forecast.
The purpose of the invention can be realized by the following technical scheme:
a variational quality control method based on three-dimensional variational assimilation comprises the following steps:
s1: constructing probability density functions of observation errors which obey Gaussian distribution and uniform distribution;
s2: and constructing a new observation target function, a new gradient function and a new weight function of three-dimensional variation and assimilation.
Further, in S1, the observation with higher quality and the observation with outlier are subdivided according to the probability of the outlier existing, and the errors of the observations are assumed to respectively follow gaussian distribution and uniform distribution.
Further, the observation target function, the gradient function and the weight function are constructed by the following steps:
assuming that observation errors are not related to each other and the prior probability obeying Gaussian distribution and outlier is zero, an observation target function of the three-dimensional variational assimilation method can be deduced according to the Bayesian probability theory
Figure BDA0003280902590000041
And gradient function thereof
Figure BDA0003280902590000042
Respectively as follows:
Figure BDA0003280902590000043
Figure BDA0003280902590000044
wherein, yoRepresenting an observed value; hx is the observation equivalent of the observation operator acting on the analysis variable x; h is an observation operator. If the prior probability of the observed data outlier is assumed to be A, the probability of the observation without the outlier is 1-A; the gaussian and uniform distribution model for a single observation can be written as:
pQC＝(1-A)N+AF. (3)
n and F are gaussian and uniform distributions, respectively, with density functions:
Figure BDA0003280902590000045
Figure BDA0003280902590000046
wherein d represents the maximum multiple allowed for identifying the standard deviation of the outliers; if yo-Hx|≥dσoIf so, the observation data is eliminated in the process of climate extreme value inspection or background field inspection, so that the condition that F is 0 cannot occur; the probability density function with uniform distribution can better fit the characteristic that two tails of actual observation error distribution are longer;
because the uniform probability distribution of outliers does not depend on the overall observation, the Bayesian theory can derive the objective function of the quality-controlled observation based on the Gaussian distribution in combination with the uniformly distributed model, i.e., equation (3)
Figure BDA0003280902590000051
Gradient function
Figure BDA0003280902590000052
And a weight function (W)QC) Respectively as follows:
Figure BDA0003280902590000053
Figure BDA0003280902590000054
Figure BDA0003280902590000055
wherein,
Figure BDA0003280902590000056
is a constant; p is the posterior probability of the outlier; wQCEssentially a function of the three-dimensional variational and assimilation intermediate iteration innovation vectors.
Further, the variation quality control is realized by the following steps:
the first step is as follows: registering essential parameters (varqc, nstep _ novalqc, flat _ soundva, flat _ soundvd, flat _ sounddta, flat _ sounddtd, flat _ soundqa and flat _ soundqd) for a WRFDA registry file (registry), and configuring parameters of a variation quality control scheme when three-dimensional variation assimilation is prepared; varqc controls whether to start variational quality control, default value False; the nstep _ novarqc starts variation quality control after several steps of variation and assimilation iteration, and the default value is 15 steps; flat _ soundva represents that the prior probability of the wind field outlier is A; flat _ soundvd represents the width d of the wind field uniform distribution; other similarities, respectively, indicate the relevant parameters of temperature and specific humidity;
the second step is that: transmitting the sounding observation variation quality control parameters in the first step to a WRFDA sounding observation assimilation Fortran source code (da _ sound.inc) so as to apply the WRFDA sounding observation assimilation Fortran source code to a three-dimensional variation assimilation algorithm;
the third step: modifying Fortran source codes (da _ jo _ sound _ uvtq.inc.) of an observation objective function of WRFDA three-dimensional variation assimilation probe observation according to the formula (6); WRFDA three-dimensional variation and assimilation are respectively used for assimilating the temperature, humidity and wind observed by sounding; therefore, the variation quality control algorithm of the observation objective function needs to be updated for each variable;
the fourth step: modifying an observation objective function gradient term (Fortran source code da _ calculated _ gradient _ sound.inc.) of the WRFDA three-dimensional variation assimilation probe observation according to the formula (7); WRFDA three-dimensional variation and assimilation are respectively used for assimilating the temperature, humidity and wind observed by sounding; therefore, the variation quality control algorithm for observing the gradient term of the objective function needs to be updated for each variable;
the invention has the beneficial effects that: although the traditional quality control scheme is well established and good in application, it has inherent deficiencies. First, conventional quality control is pre-processing before assimilation, which means that in an iterative analysis process, even if some observations are determined again by conventional quality control as erroneous (correct) observations, they are not rejected (accepted) in the assimilation analysis process, which is obviously unreasonable. Secondly, the threshold setting of the traditional quality control method is empirical, if the threshold setting is too large (small), the observation data which may be wrong (correct) can be missed (rejected), the assimilation and absorption of the observation which may be wrong can make the analysis solution suboptimal or even wrong, the rejection of the observation which may be correct can waste rare observation, and the traditional quality control method cannot control the uncertainty. However, the application of the variation quality control can effectively solve the defects of the traditional quality control, improve the utilization rate of the observation data, improve the accuracy of three-dimensional variation and assimilation analysis, and provide favorable quality control guarantee for further improving variation and assimilation analysis fields and improving the accuracy of numerical weather forecast.
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In order to more clearly illustrate the embodiments or technical solutions in the prior art of the present invention, the drawings used in the description of the embodiments or prior art will be briefly described below, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without creative efforts.
FIG. 1 is a flow chart of quality control of sounding observations according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A variational quality control method based on three-dimensional variational assimilation comprises the following steps:
firstly, subdividing observation with higher quality and outlier observation according to the probability of the existence of the outlier, and assuming that errors of the observation and the outlier observation respectively obey Gaussian distribution and uniform distribution to form a probability density function of which the observation error obeys the Gaussian distribution and the uniform distribution, wherein the probability density function is longer than the tail part of the Gaussian distribution and better accords with the distribution characteristic of the actual observation error;
secondly, deducing a variation quality control observation objective function by a Bayes probability theory according to the probability density function to obtain a new three-dimensional variation assimilation observation objective function, wherein a gradient function item of the new three-dimensional variation assimilation observation objective function comprises a weight change, and different weights are given to observation according to the observation deviation in the minimization iteration process, so that the quality control and the three-dimensional variation assimilation are synchronously carried out;
the objective function of the three-dimensional variational assimilation method consists of an ambient field objective function and an observation objective function, the observation objective function of the three-dimensional variational assimilation method can be deduced according to the Bayesian probability theory under the assumption that observation errors are not related and the prior probability obeying Gaussian distribution and outliers is zero
Figure BDA0003280902590000071
And gradient function thereof
Figure BDA0003280902590000072
Respectively as follows:
Figure BDA0003280902590000073
Figure BDA0003280902590000074
wherein, yoRepresenting an observed value; hx is the observation equivalent of the observation operator acting on the analysis variable x; h is an observation operator. If the prior probability of observation outliers is assumed to be A, then the probability of no outliers observation is 1-A. The gaussian and uniform distribution model for a single observation is:
pQC＝(1-A)N+AF. (3)
n and F are gaussian and uniform distributions, respectively, with density functions:
Figure BDA0003280902590000081
Figure BDA0003280902590000082
where d represents the maximum multiple allowed to identify the standard deviation of the outliers. If yo-Hx|≥dσoThe observation data is rejected during the climate extreme value inspection or the background field inspection, so that the condition that F is 0 cannot occur. The probability density function with uniform distribution can better fit the characteristic that two tails of actual observation error distribution are longer.
Because the uniform probability distribution of outliers does not depend on the overall observation, a new observation objective function for variable-quality control can be derived from Bayesian theory based on a Gaussian distribution combined with a model of uniform distribution, equation (3)
Figure BDA0003280902590000083
Gradient function
Figure BDA0003280902590000084
And a weight function (W)QC) Respectively as follows:
Figure BDA0003280902590000085
Figure BDA0003280902590000086
Figure BDA0003280902590000087
wherein,
Figure BDA0003280902590000088
is a constant; p is the posterior probability of the outlier; wQCEssentially a function of the three-dimensional variational and assimilation intermediate iteration innovation vectors. The formulas (6) to (8) establish a variation quality control method based on three-dimensional variation assimilation, which is called Flat-VarQC for short.
A variational quality control implementation method based on three-dimensional variational assimilation comprises the following steps:
the implementation steps of the variation quality control of different observation data types have similarity, and the implementation of the uniform variation quality control algorithm of the invention has the following steps based on the assimilation system software (WRFDA, version 3.8.1) of the mesoscale prediction mode by taking the variation of the sounding observation data as an example:
the first step is as follows: the WRFDA registry file (registry. var) is registered with essential parameters (varqc, nstep _ novalqc, flat _ soundva, flat _ soundvd, flat _ sounddta, flat _ sounddtd, flat _ soundqa and flat _ soundqd) for sounding observation variation quality control, and when three-dimensional variation assimilation is prepared, parameters of a variation quality control scheme are configured. varqc controls whether to start variational quality control, default value False; the nstep _ novarqc starts variation quality control after several steps of variation and assimilation iteration, and the default value is 15 steps; flat _ soundva represents that the prior probability of the wind field outlier is A; flat _ soundvd represents the width d of the wind field uniform distribution; other similarities, respectively, indicate the relevant parameters of temperature and specific humidity;
the second step is that: transmitting the sounding observation variation quality control parameters in the first step to a WRFDA sounding observation assimilation Fortran source code (da _ sound.inc) so as to apply the WRFDA sounding observation assimilation Fortran source code to a three-dimensional variation assimilation algorithm;
the third step: modifying Fortran source codes (da _ jo _ sound _ uvtq.inc.) of an observation objective function of WRFDA three-dimensional variation assimilation probe observation according to a formula (6); WRFDA three-dimensional variation and assimilation respectively assimilate the temperature, humidity and wind observed by sounding. Therefore, the variation quality control algorithm of the observation objective function needs to be updated for each variable;
the fourth step: and modifying an observation objective function gradient term (Fortran source code da _ calculated _ gradient _ sound.inc.) of the WRFDA three-dimensional variation assimilation probe observation according to the formula (7). WRFDA three-dimensional variation and assimilation are respectively used for assimilating the temperature, humidity and wind observed by sounding; therefore, the variation quality control algorithm for observing the gradient term of the objective function needs to be updated for each variable;
the fifth step: if the variation quality control algorithm of other observation types is realized, only the first step to the fourth step need to be repeated;
and a sixth step: and finishing normal compilation of the WRFDA software, wherein the successful editing means that the variational quality control algorithm is successfully updated.
According to the WRFDA software of variation quality control, the following specific application example of three-dimensional variation and assimilation with a variation quality control algorithm is executed (taking variation quality control of sounding observation as an example):
the first step is as follows: according to the software input requirement, providing sounding original observation data to a WRFDA observation preprocessing module, processing and generating a sounding observation data format which can be input, and changing the format into ob. Field pre-processing is observed as in fig. 1;
the second step is that: according to software input requirements, providing background field raw data to a WRFDA background field preprocessing module, and processing to generate an input background field data format, which is named wrfinput _ d 01. As in fig. 1 background field preprocessing;
the third step: linking or copying a WRFDA-owned static fixed background error covariance matrix file be.dat.cv3, and is renamed to be.dat; as fig. 1 background error statistics;
the fourth step: configure the parameters of Flat-VarQC, such as namelist. Please refer to Anderson and
Figure BDA0003280902590000102
(1999)；
the fifth step: executing a three-dimensional variational assimilation compiler da _ wrfvar.exe in WRFDA, wherein the program integrates the Flat-VarQC algorithm of the invention;
and a sixth step: and finishing the execution program to generate a three-dimensional variational assimilation analysis field added with a Flat-VarQC algorithm.
In addition, the parameter configuration of the other observation type Flat-VarQC algorithm is shown in the following table:
Figure BDA0003280902590000101
in the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.

Claims (4)

1. A variational quality control method based on three-dimensional variational assimilation is characterized by comprising the following steps:
s1: constructing probability density functions of observation errors which obey Gaussian distribution and uniform distribution;
s2: and constructing a new observation target function, a new gradient function and a new weight function of three-dimensional variation and assimilation.
2. The method of claim 1, wherein in said S1, according to the probability of outliers existing, the higher quality observation and the outliers observation are subdivided, and their errors are assumed to obey gaussian distribution and uniform distribution, respectively.
3. The method for controlling the quality of the three-dimensional variational assimilation-based variational variables according to claim 1, wherein the observation objective function, the gradient function and the weight function are constructed by the following steps:
assuming that observation errors are not related to each other and the prior probability obeying Gaussian distribution and outlier is zero, an observation target function of the three-dimensional variational assimilation method can be deduced according to the Bayesian probability theory
Figure FDA0003280902580000011
And gradient function thereof
Figure FDA0003280902580000012
Respectively as follows:
Figure FDA0003280902580000013
Figure FDA0003280902580000014
wherein, yoRepresenting an observed value; hx is the observation equivalent of the observation operator acting on the analysis variable x; h is an observation operator. If the prior probability of observation outliers is assumed to be A, then the probability of no outliers observation is 1-A. The gaussian and uniform distribution model for a single observation can be written as:
pQC＝(1-A)N+AF. (3)
n and F are gaussian and uniform distributions, respectively, with density functions:
Figure FDA0003280902580000015
Figure FDA0003280902580000021
wherein d represents the maximum multiple allowed for identifying the standard deviation of the outliers; if yo-Hx|≥dσoIf so, the observation data is eliminated in the process of climate extreme value inspection or background field inspection, so that the condition that F is 0 cannot occur; the probability density function with uniform distribution can better fit the characteristic that two tails of actual observation error distribution are longer;
since the uniform probability distribution of outliers does not depend on the overall observation, then the basis is highThe Bayesian theory can derive the objective function of variable quality control by combining the Gaussian distribution with the uniformly distributed model, namely formula (3)
Figure FDA0003280902580000022
Gradient function
Figure FDA0003280902580000023
And a weight function (W)QC) Respectively as follows:
Figure FDA0003280902580000024
Figure FDA0003280902580000025
Figure FDA0003280902580000026
wherein,
Figure FDA0003280902580000027
is a constant; p is the posterior probability of the outlier; wQCEssentially a function of the three-dimensional variational and assimilation intermediate iteration innovation vectors.
4. The method for controlling the quality of the variational system based on the three-dimensional variational assimilation according to claim 3, wherein the variational quality control is realized by the following steps:
the first step is as follows: registering essential parameters (varqc, nstep _ novalqc, flat _ soundva, flat _ soundvd, flat _ sounddta, flat _ sounddtd, flat _ soundqa and flat _ soundqd) for a WRFDA registry file (registry), and configuring parameters of a variation quality control scheme when three-dimensional variation assimilation is prepared; varqc controls whether to start variational quality control, default value False;
the nstep _ novarqc starts variation quality control after several steps of variation and assimilation iteration, and the default value is 15 steps;
flat _ soundva represents that the prior probability of the wind field outlier is A; flat _ soundvd represents the width d of the wind field uniform distribution; other similarities, respectively, indicate the relevant parameters of temperature and specific humidity;
the second step is that: transmitting the sounding observation variation quality control parameters in the first step to a WRFDA sounding observation assimilation Fortran source code (da _ sound.inc) so as to apply the WRFDA sounding observation assimilation Fortran source code to a three-dimensional variation assimilation algorithm;
the third step: modifying Fortran source codes (da _ jo _ sound _ uvtq.inc.) of an observation objective function of WRFDA three-dimensional variation assimilation probe observation according to the formula (6); WRFDA three-dimensional variation and assimilation are respectively used for assimilating the temperature, humidity and wind observed by sounding; therefore, the variation quality control algorithm of the observation objective function needs to be updated for each variable;
the fourth step: modifying an observation objective function gradient term (Fortran source code da _ calculated _ gradient _ sound.inc.) of the WRFDA three-dimensional variation assimilation probe observation according to the formula (7); WRFDA three-dimensional variation and assimilation are respectively used for assimilating the temperature, humidity and wind observed by sounding; therefore, the variation quality control algorithm for observing the gradient term of the objective function needs to be updated for each variable;
the fifth step: if the variation quality control algorithm of other observation types is realized, only the first step to the fourth step need to be repeated;
and a sixth step: and finishing normal compilation of the WRFDA software, wherein the successful editing means that the variational quality control algorithm is successfully updated.
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CN118260509A (en) * 2024-05-31 2024-06-28 南京信息工程大学 Double-local hybrid variation assimilation method based on six-order tangential implicit low-pass filtering
CN118260509B (en) * 2024-05-31 2024-09-06 南京信息工程大学 Double-local hybrid variation assimilation method based on six-order tangential implicit low-pass filtering

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