Learning System, Precipitable Water Estimation System, Method and Program for Precipitable Water Estimation Model

Abstract

Provided is a technology capable of observing water vapor in a local range without requiring calibration using liquid nitrogen.　A precipitable water estimation model learning system (4) comprises: a radio wave intensity acquisition part (40) for acquiring a radio wave intensity for a plurality of wave frequencies among radio waves received by a microwave radiometer (3); a precipitable water acquisition part (41) for acquiring precipitable water calculated on the basis of an atmospheric delay of a GNSS signal received by a GNSS receiver (2); and a learning part (43) for causing an estimation model (43a) to machine learn such that precipitable water is outputted on the basis of the radio wave intensity for the plurality of wave frequencies and the precipitable water at a plurality of times in a predetermined period, and using, as input, input data based on the radio wave intensity for the plurality of wave frequencies.

Description

Technical Field

[0001] The present disclosure relates to a learning system, a precipitable water estimation system, a method, and a program for a precipitable water estimation model.

Background Art

[0002] It is known that for the observation of precipitable water, that is, water vapor observation, a GNSS receiver, a microwave radiometer, etc. are used.

[0003] Water vapor observation by a GNSS receiver utilizes multi-frequency radio waves radiated from satellites. If radio waves radiated from four or more satellites at two or more different frequencies can be received, the delay amount of the radio waves can be captured. The delay amount of the radio waves corresponds to the amount of water vapor, and the amount of water vapor can be observed. Water vapor observation using GNSS (Global Navigation Satellite System) can be measured stably without calibration. However, since satellites are used that are variously arranged throughout the day by GNSS, an average value of water vapor over a wide area of the sky can be obtained, but water vapor in a local area cannot be observed. Note that Patent Document 1 describes water vapor observation by GNSS.

[0004] Water vapor observation by a microwave radiometer utilizes the fact that radio waves are radiated from water vapor in the atmosphere, and measures radio waves from water vapor and clouds. Due to the directivity of the antenna and horn of the receiver, water vapor in a local area of the sky can be measured compared to water vapor observation by GNSS. However, calibration using liquid nitrogen is required periodically to prevent drift of the device and measure the correct brightness temperature. Liquid nitrogen is difficult to transport and handle. Note that Patent Document 2 describes a microwave radiometer.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

[0006] The present disclosure provides a technique that eliminates the need for calibration using liquid nitrogen and enables the observation of the precipitation amount in a local area. [Means for Solving the Problems]

[0007] The learning system of the precipitation amount estimation model of the present disclosure includes a radio wave intensity acquisition unit that acquires the radio wave intensities of a plurality of frequencies among the radio waves received by a microwave radiometer, a precipitation amount acquisition unit that acquires the precipitation amount calculated based on the atmospheric delay of the GNSS signals received by a GNSS receiver, and a learning unit that machine-learns an estimation model so as to output the precipitation amount with the input data based on the radio wave intensities of the plurality of frequencies as an input based on the radio wave intensities of the plurality of frequencies and the precipitation amount at a plurality of time points within a predetermined period. [Brief Description of the Drawings]

[0008]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

[0009] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings.

[0010] FIG. 1 is a diagram showing the configurations of a precipitable water amount estimation model learning system 4 and a precipitable water amount estimation system 5 according to this embodiment.

[0011] As shown in FIG. 1, in this embodiment, the precipitable water amount estimation model learning system 4 and the precipitable water amount estimation system 5 are constructed on the same computer system, but can be operated independently. That is, only the learning system 4 may be implemented, or only the precipitable water amount estimation system 5 may be implemented.

[0012] <Learning system 4> The learning system 4 shown in FIG. 1 includes a radio wave intensity acquisition unit 40, a precipitable water amount acquisition unit 41, and a learning unit 43.

[0013] The radio wave intensity acquisition unit 40 shown in FIG. 1 acquires the radio wave intensities of a plurality of frequencies among the radio waves received by the microwave radiometer 3. In this embodiment, the radio wave intensities of N (N = 30) different frequencies among 18 GHz or more and 26.5 GHz are acquired. The radio wave intensity acquisition unit 40 acquires the radio wave intensities [p(f1), p(f2),..., p(f29), p(f30)] of 30 different frequencies (f1, f2,..., f29, f30). Here, it is denoted as the radio wave intensity p(f), and f represents the frequency. The radio wave intensities of a plurality of frequencies acquired by the radio wave intensity acquisition unit 40 are stored in the storage unit 42 as time series data D2 of the radio wave intensities.

[0014] As shown in FIG. 3, the peak of the intensity of the radio waves radiated from water vapor and cloud water in the sky is 22 GHz. In FIG. 3, the received intensity p(f) of the microwave radiometer 3 is shown, where f represents the frequency. For example, the radio waves at 22 GHz include the precipitable water amount, i.e., the water vapor component, and the cloud water component. In order to remove the amount of cloud water contained in the radio waves at 22 GHz, the cloud water component is calculated from the radio wave intensities at frequencies other than 22 GHz. Therefore, the radio wave intensities at a plurality of different frequencies are required. Note that, as an example, 22 GHz is shown, but since the water vapor component and the cloud water component are also included at frequencies other than 22 GHz, the combination of frequencies is not limited to the combination of 22 GHz and frequencies other than 22 GHz. In this embodiment, N = 30, but the number of N can be changed as appropriate. Also, the frequency range preferably includes 22 GHz or ±1 GHz before and after 22 GHz. In this embodiment, N = 30, but it is not limited to this. In order to improve the specific accuracy of the water vapor component and the cloud water component, N is preferably a natural number of 3 or more.

[0015] Note that, in this embodiment, a blackbody is periodically passed through the reception range of the antenna of the microwave radiometer 3 by an actuator, and the radio waves from the blackbody with a known intensity and the radio waves from the sky are received. The received intensity p(f) of the microwave radiometer 3 is the radio wave intensity ps(f) from the sky - the radio wave intensity pb(f) from the blackbody. Of course, the microwave radiometer 3 is not limited to this, and the mirror may be periodically moved to receive the radio waves from the blackbody.

[0016] The precipitable water amount acquisition unit 41 shown in FIG. 1 acquires the precipitable water amount calculated based on the atmospheric delay (strictly speaking, the tropospheric delay) of the GNSS signals received by the GNSS receiver 2. It is known that the precipitable water amount (PWV; Precipitable Water Vapor) by GNSS can be calculated based on GNSS signals, coordinate values such as altitude, temperature, and atmospheric pressure. The precipitable water amount acquisition unit 41 acquires the GNSS precipitable water amount using the GNSS signals and altitude information obtained from the GNSS receiver 2, and the temperature and atmospheric pressure obtained from the meteorological sensor 1. The GNSS precipitable water amount acquired by the precipitable water amount acquisition unit 41 is stored in the storage unit 42 as time-series data D1 of the GNSS precipitable water amount.

[0017] The learning unit 43 shown in FIG. 1 machine-learns the estimation model 43a based on the time-series data D1 of the precipitable water amount and the time-series data D2 of the radio wave intensity. Specifically, the learning unit 43 machine-learns the estimation model 43a so as to output the precipitable water amount with the input data based on the radio wave intensities of a plurality of frequencies at a plurality of time points within a predetermined period as the input. The teacher data set used by the learning unit 43 is data in which the precipitable water amount at a certain time point t is associated with the input data based on the radio wave intensities of a plurality of frequencies [p(f1), p(f2), …, p(f29), p(f30)] at the same time point t. The input data may be the radio wave intensities of a plurality of frequencies themselves or data obtained by reducing the dimensions of the radio wave intensities of a plurality of frequencies as long as it is data based on the radio wave intensities of a plurality of frequencies. As long as the estimation model 43a is a supervised machine learning model, various models such as linear regression, regression tree, random forest, support vector machine, neural network, and ensemble can be used. In this embodiment, although it will be described in detail later, it is polynomial regression using terms of the second degree or higher, and multiple regression having a plurality of types of variables is adopted, but it is not limited to this.

[0018] As shown in FIG. 1, the learning system 4 preferably includes a dimensionality reduction unit 44 that performs dimensionality reduction processing on radio wave intensities of a plurality of frequencies and calculates dimensionality-reduced input data indicating the radio wave intensities of the plurality of frequencies. By performing dimensionality reduction, it is possible to reduce the number of dimensions while reproducing the original features represented by the radio wave intensities of the plurality of frequencies, thereby reducing the calculation cost and avoiding the curse of dimensionality (overfitting). The dimensionality reduction method of the present embodiment is principal component analysis (PCA: Principal Component Analysis), but is not limited thereto. For example, other algorithms such as factor analysis, multi-factor analysis, Autoencoder, independent component analysis, and non-negative matrix factorization can be used.

[0019] In the present embodiment, the dimensionality reduction unit 44 uses principal component analysis and selects the first principal component, the second principal component, and the third principal component as input data. Of course, it is not limited thereto and can be variously changed. For example, the input data may be only the first principal component of the principal component analysis, or the first and second principal components. That is, a predetermined number (any natural number of 1 or more) of principal components after the first rank are selected as input data. The predetermined number can be appropriately set according to the required accuracy. The first principal component is always included because the degree of reproduction of the original features of the first principal component is the highest.

[0020] The normalization processing unit 45 shown in FIG. 1 performs normalization processing on the radio wave intensities [p(f1), p(f2), …, p(f29), p(f30)] of multiple frequencies at multiple time points before the dimensionality reduction processing by principal component analysis. The normalization processing unit 45 performs normalization processing on the time-series data D2 of the radio wave intensities stored in the storage unit 42, and stores the normalized time-series data D3 of the radio wave intensities in the storage unit 42. The normalization processing is a process for performing centering to make the average value 0 and scaling to make the standard deviation 1. The normalization processing calculates the average value and the standard deviation for each of the radio wave intensities at multiple time points, and divides the value obtained by subtracting the average value from the original data by the standard deviation to convert each original radio wave intensity into a normalized radio wave intensity. The calculated average value and standard deviation are stored in the storage unit 42 as normalization parameters for use in the normalization processing of the precipitable water amount estimation system 5 described later (see FIG. 1).

[0021] Note that the learning system 4 of the present embodiment includes a dimensionality reduction unit 44 and a normalization processing unit 45, but these are optional.

[0022] <Specific examples of the learning unit 43 and the estimation model 43a> The learning unit 43 shown in FIG. 1 constructs an estimation model 43a for calculating the precipitable water amount (PWV) using the first principal component PC1, the second principal component PC2, and the third principal component PC3 as input data. The estimation model 43a is a conversion formula using multiple regression and is expressed by the following formula (1). By fitting using the least squares method, the following unknown coefficients S1 to S 10 are calculated to construct the estimation model 43a.

Equation

[0023] <Precipitable water amount estimation system 5> The precipitable water amount estimation system 5 shown in FIG. 1 includes a radio wave intensity acquisition unit 40 and an estimation unit 50. The estimation unit 50 uses the estimation model 43a constructed by the learning unit 43, inputs input data based on the radio wave intensities of a plurality of frequencies acquired by the radio wave intensity acquisition unit 40, and outputs the corresponding precipitable water amount. Although the radio wave intensities [p(f1), p(f2), …, p(f29), p(f30)] of a plurality of frequencies at the estimation time may be input to the estimation unit 50, it is preferable to provide a normalization processing unit 51 and a dimensionality reduction unit 52 for improving accuracy.

[0024] The normalization processing unit 51 shown in FIG. 1 performs normalization processing on the radio wave intensities of a plurality of frequencies using predetermined parameters before the dimensionality reduction processing by the dimensionality reduction unit 52. The normalization parameters are the parameters (average value, standard deviation) calculated by the normalization processing unit 45 of the learning system 4. The normalization processing unit 51 does not calculate the parameters (average value, standard deviation), but other processing is the same as that of the normalization processing unit 45 of the learning system 4.

[0025] The dimensionality reduction unit 52 shown in FIG. 1 performs dimensionality reduction processing on the radio wave intensities of a plurality of frequencies and calculates input data with reduced dimensionality indicating the radio wave intensities of a plurality of frequencies. The dimensionality reduction unit 52 uses the same parameters as those calculated by the dimensionality reduction unit 44 of the learning system 4.

[0026] <Learning Method of Precipitable Water Amount Estimation Model> The learning method of the precipitable water amount estimation model will be described with reference to FIG. 2. As shown in FIG. 2, in step ST100, the radio wave intensity acquisition unit 40 acquires the radio wave intensities of a plurality of frequencies among the radio waves received by the microwave radiometer. In step ST101, the precipitable water amount acquisition unit 41 acquires the precipitable water amount calculated based on the atmospheric delay of the GNSS signal received by the GNSS receiver. Steps ST100 and ST101 may be in any order.

[0027] In the next step ST102, the normalization processing unit 45 performs normalization processing on the radio wave intensities of a plurality of frequencies at a plurality of time points. In the next step ST103, the dimensionality reduction unit 44 performs dimensionality reduction processing on the radio wave intensities of a plurality of frequencies by principal component analysis, and calculates input data after dimensionality reduction indicating the radio wave intensities of the plurality of frequencies. In the next step ST104, the learning unit 43 machine-learns an estimation model so as to output the precipitation amount using, as input, the input data based on the radio wave intensities of a plurality of frequencies and using the radio wave intensities of the plurality of frequencies at a plurality of time points within a predetermined period and the precipitation amount as input.

[0028] <Precipitation amount estimation method> The precipitation amount estimation method will be described with reference to FIG. 3. As shown in FIG. 3, in step ST201, the radio wave intensity acquisition unit 40 acquires the radio wave intensities of a plurality of frequencies among the radio waves received by the microwave radiometer. In the next step ST202, the normalization processing unit 51 performs normalization processing on the radio wave intensities of a plurality of frequencies. In the next step ST203, the dimensionality reduction unit 52 performs dimensionality reduction processing on the radio wave intensities of a plurality of frequencies by principal component analysis, and calculates input data after dimensionality reduction indicating the radio wave intensities of the plurality of frequencies. In the next step ST204, the estimation unit 50 outputs the precipitation amount corresponding to the input data based on the radio wave intensities of the plurality of frequencies acquired, using the estimation model 43a machine-learned to output the precipitation amount using, as input, the input data based on the radio wave intensities of the plurality of frequencies.

[0029] FIG. 5 is a diagram showing a comparison between the precipitation amount estimated by the estimation model constructed by the learning system 4 and the precipitation amount estimated by the precipitation amount estimation system 5 for a certain period, and the precipitation amount based on the Sonde data for the same period. The Sonde data is data publicly released by the Japan Meteorological Agency, and is actual meteorological observation values measured by flying a real weather balloon equipped with a sensor into the sky. As shown in FIG. 5, the RMSE (Root Mean Square Error) is 1.8 mm, indicating that a certain degree of accuracy has been obtained.

[0030] In addition, since this method acquires the radio wave intensities of multiple frequencies, even if noise is included in the radio wave intensities of some frequencies by adopting a general-purpose amplifier with a high noise temperature, the influence of the noise can be suppressed because multiple frequencies are used. Therefore, for example, it is considered to be more resistant to noise than the case of estimating the precipitation amount by a predetermined arithmetic expression using two specific frequencies. Conversely, even if there is some noise, since it can be covered by multiple frequencies, high performance is not necessarily required for the equipment to be used, and it becomes possible to reduce the cost of the system.

[0031] As described above, the learning system 4 of the precipitation amount estimation model according to the present embodiment includes a radio wave intensity acquisition unit 40 that acquires the radio wave intensities of multiple frequencies among the radio waves received by the microwave radiometer 3, a precipitation amount acquisition unit 41 that acquires the precipitation amount calculated based on the atmospheric delay of the GNSS signal received by the GNSS receiver 2, and a learning unit 43 that machine-learns an estimation model 43a so as to output the precipitation amount with the input data based on the radio wave intensities of multiple frequencies as input, based on the radio wave intensities of multiple frequencies and the precipitation amount at multiple time points within a predetermined period.

[0032] The learning method of the precipitation amount estimation model according to the present embodiment includes acquiring the radio wave intensities of multiple frequencies among the radio waves received by the microwave radiometer 3, acquiring the precipitation amount calculated based on the atmospheric delay of the GNSS signal received by the GNSS receiver 2, and machine-learning an estimation model 43a so as to output the precipitation amount with the input data based on the radio wave intensities of multiple frequencies as input, based on the radio wave intensities of multiple frequencies and the precipitation amount at multiple time points within a predetermined period.

[0033] The precipitation amount estimation system according to the present embodiment includes a radio wave intensity acquisition unit 40 that acquires the radio wave intensities of multiple frequencies among the radio waves received by the microwave radiometer 3, and an estimation unit 50 that outputs the precipitation amount corresponding to the input data based on the radio wave intensities of the acquired multiple frequencies, using an estimation model 43a that is machine-learned to output the precipitation amount with the input data based on the radio wave intensities of multiple frequencies as input.

[0034] The precipitable water amount estimation method of the present embodiment includes obtaining the radio wave intensities of a plurality of frequencies among the radio waves received by the microwave radiometer 3, and using an estimation model 43a that is machine-learned to output the precipitable water amount with the input data based on the radio wave intensities of the plurality of frequencies as input, and outputting the precipitable water amount corresponding to the input data based on the radio wave intensities of the obtained plurality of frequencies.

[0035] According to the above learning method, estimation method, and system, since machine learning is performed using input data based on the radio wave intensities of a plurality of frequencies, the correlation between the radio wave intensity and the precipitable water amount that could not be elucidated with a single frequency because both the water vapor amount and cloud water are included in the radio wave intensity can be clarified by machine learning, and the water vapor amount (precipitable water amount) can be estimated. Nevertheless, since the radio wave intensities at a plurality of time points and the precipitable water amount based on GNSS are used during a predetermined period, local water vapor data without an accurate absolute value based on the microwave radiometer can be converted into reliable local water vapor data with a matching absolute value. High-reliability data can be obtained without calibrating the microwave radiometer with liquid nitrogen.

[0036] Preferably, as in the present embodiment, a dimensionality reduction unit 44, 52 is provided that performs dimensionality reduction processing on the radio wave intensities of a plurality of frequencies and calculates input data with reduced dimensions indicating the radio wave intensities of the plurality of frequencies. By dimensionality reduction in this way, among the plurality of frequencies, sensitive frequencies processed in a portion with good receiver performance are selected, so that estimation is possible even using a general-purpose and inexpensive amplifier. That is, if dimensionality reduction is not performed, frequency bands with poor sensitivity processed in a portion with poor receiver performance are directly used for estimation, and data in frequency bands with poor sensitivity will have an adverse effect on the estimation accuracy. Dimensionality reduction makes it possible to save the trouble of manually removing frequencies with poor sensitivity from among the plurality of frequencies, and moreover, it is possible to avoid deterioration of the estimation accuracy.

[0037] As in this embodiment, it is preferable that the dimensionality reduction units 44 and 52 perform dimensionality reduction by principal component analysis and select a predetermined number of principal components from the first rank onwards as input data. Thus, it is preferable to use principal component analysis for dimensionality reduction.

[0038] As in the learning system 4 of this embodiment, it is preferable to include a normalization processing unit 45 that performs normalization processing on the radio wave intensities of a plurality of frequencies at a plurality of time points before the dimensionality reduction processing by the dimensionality reduction unit 44. As in the precipitable water amount estimation system 5 of this embodiment, it is preferable to include a normalization processing unit 51 that performs normalization processing on the radio wave intensities of a plurality of frequencies using predetermined normalization parameters before the dimensionality reduction processing by the dimensionality reduction unit 52. Thereby, appropriate dimensionality reduction becomes possible, and it becomes possible to improve the estimation accuracy.

[0039] As in this embodiment, the radio wave intensity acquisition unit 40 acquires the radio wave intensities of N different frequencies, where N is a natural number of 3 or more, and the dimensionality reduction units 44 and 52 preferably perform dimensionality reduction on the radio wave intensities of N frequencies into input data having a number smaller than N. Thus, by dimensionality reduction, it is possible to reduce the number of dimensions while reproducing the original features represented by the radio wave intensities of N frequencies, and it becomes possible to reduce the calculation cost and avoid the curse of dimensionality (overfitting).

[0040] The program of this embodiment is a program that causes a computer (one or more processors) to execute the above method. Also, a computer-readable temporary recording medium according to this embodiment stores the above program.

[0041] As described above, the embodiments of the present disclosure have been described with reference to the drawings, but the specific configuration should be considered not to be limited to these embodiments. The scope of the present disclosure is shown not only by the description of the above embodiments but also by the claims, and further includes all modifications within the meaning and scope equivalent to the claims.

[0042] It is possible to adopt the structures employed in the above-described embodiments in any other embodiments.

[0043] The specific configurations of each part are not limited to the above-described embodiments only, and various modifications are possible without departing from the spirit of the present disclosure.

Explanation of Reference Numerals

[0044] 4 Learning system 40 Radio wave intensity acquisition unit 41 Precipitable water acquisition unit 43 Learning unit 44 Dimension reduction unit 45 Standardization processing unit 5 Precipitable water estimation system 50 Estimation unit 51 Standardization processing unit 52 Dimension reduction unit

Claims

1. Among the radio waves received by the microwave radiometer, a radio wave intensity acquisition unit that acquires the radio wave intensities of a plurality of frequencies, A precipitable water amount acquisition unit that acquires a precipitable water amount calculated based on the atmospheric delay of the GNSS signal received by the GNSS receiver, A learning unit that machine-learns an estimation model so as to output the precipitable water amount with the input data based on the radio wave intensities of the plurality of frequencies as an input, based on the radio wave intensities of the plurality of frequencies and the precipitable water amount at a plurality of time points within a predetermined period, A learning system for a precipitable water amount estimation model, comprising:

2. The system according to claim 1, A learning system for a precipitable water amount estimation model, comprising a dimensionality reduction unit that performs a dimensionality reduction process on the radio wave intensities of the plurality of frequencies and calculates the input data with the dimensionality reduction that indicates the radio wave intensities of the plurality of frequencies.

3. The system according to claim 2, The learning system for a precipitable water amount estimation model, wherein the dimensionality reduction unit performs the dimensionality reduction by principal component analysis and selects a predetermined number of principal components from the first rank onwards as the input data.

4. The system according to claim 2 or 3, A learning system for a precipitable water amount estimation model, comprising a normalization processing unit that performs a normalization process on the radio wave intensities of the plurality of frequencies at the plurality of time points before the dimensionality reduction process by the dimensionality reduction unit.

5. The system according to any one of claims 2 to 4, The radio wave intensity acquisition unit acquires the radio wave intensities of N different frequencies, where N is a natural number of 3 or more, The learning system for a precipitable water amount estimation model, wherein the dimensionality reduction unit reduces the dimensionality of the radio wave intensities of the N frequencies to the input data of a number smaller than N.

6. Among the radio waves received by the microwave radiometer, a radio wave intensity acquisition unit that acquires the radio wave intensities of a plurality of frequencies, An estimation unit that outputs the precipitable water amount corresponding to the input data based on the radio wave intensities of the plurality of frequencies acquired, using an estimation model machine-learned to output the precipitable water amount with the input data based on the radio wave intensities of the plurality of frequencies as an input, A precipitable water amount estimation system, comprising:

7. The system according to claim 6, A precipitable water amount estimation system, comprising a dimensionality reduction unit that performs a dimensionality reduction process on the radio wave intensities of the plurality of frequencies and calculates the input data with the dimensionality reduction that indicates the radio wave intensities of the plurality of frequencies.

8. The system according to claim 7, The dimensionality reduction unit performs the dimensionality reduction by principal component analysis and selects a predetermined number of principal components after the first rank for the input data, a precipitable water amount estimation system.

9. The system according to claim 7 or 8, Before the dimensionality reduction process by the dimensionality reduction unit, a normalization processing unit that performs a normalization process on the radio wave intensities of the plurality of frequencies using a predetermined normalization parameter is provided, a precipitable water amount estimation system.

10. The system according to any one of claims 7 to 9, The radio wave intensity acquisition unit acquires radio wave intensities of N different frequencies, where N is a natural number of 3 or more, The dimensionality reduction unit reduces the dimensionality of the radio wave intensities of the N frequencies to input data having a number smaller than N, a precipitable water amount estimation system.

11. Obtaining radio wave intensities of a plurality of frequencies among the radio waves received by the microwave radiometer; Obtaining a precipitable water amount calculated based on the atmospheric delay of the GNSS signal received by the GNSS receiver; Based on the radio wave intensities of the plurality of frequencies and the precipitable water amount at a plurality of time points within a predetermined period, training a prediction model so as to output the precipitable water amount with the input data based on the radio wave intensities of the plurality of frequencies as an input; A method for training a precipitable water amount prediction model, including.

12. Obtaining radio wave intensities of a plurality of frequencies among the radio waves received by the microwave radiometer; Outputting the precipitable water amount corresponding to the input data based on the radio wave intensities of the plurality of frequencies obtained, using a prediction model trained to output the precipitable water amount with the input data based on the radio wave intensities of the plurality of frequencies as an input; A precipitable water amount estimation method, including.

13. A program for causing one or more processors to execute the method according to claim 11 or 12.

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