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  • View in gallery

    Schematics explaining variables (a) for surface reference technique, (b) for analysis at an NP pixel near precipitation area, (c) for analysis at a P pixel with light precipitation, and (d) for analysis at a P pixel with heavy precipitation.

  • View in gallery

    Spatial distribution of Δσm0 (dB) for KuPR (a) at NPB1 pixels and (b) at NPA1 pixels, where blue means Δσm0 is negative. (c) The difference of (b) minus (a). (d) The zonal mean of Δσm0 at NPB1 (blue line) and that of NPA1 pixels (red line).

  • View in gallery

    Schematics explaining the sampling of NP pixels near the precipitation area. The areas within the large blue open circles are assumed to be filled with precipitation. The small circles represent pixels measured by (a) the PR and (b),(c) the DPR. The filled circles are P pixels and open circles are NP pixels. Arrows show the direction of satellite motion. The numbers in the open small circles show the distance in pixels from the nearest P pixel in (a) and (b) along-track and (c) cross-track directions.

  • View in gallery

    Spatial distribution of Δσm0 (dB) for KuPR (a) at NPW1 pixels and (b) NPE1 pixels, where blue means Δσm0 is negative. (c) The difference of (b) minus (a). (d) The zonal mean of Δσm0 at NPW1 pixels (blue line) and that of NPE1 pixels (red line).

  • View in gallery

    Spatial distribution of (a) Δσm0 (dB) and (b) Δσn0 (dB) for KaMS at NP pixels adjacent to a P pixel in cross-track direction, where blue denotes that (a) Δσm0 or (b) Δσn0 is negative. (c) The difference of (b) minus (a). (d) The zonal means of Δσm0 (solid line) and Δσn0 (dotted line).

  • View in gallery

    Angle bin dependence of the global averages of Δσm0 (solid lines; in dB) and Δσn0 (dotted lines; in dB) at the NP pixels adjacent to a P pixel in the cross-track direction. Blue and red denote KuPR and KaMS, respectively. The angle bin number refers to that of KuPR.

  • View in gallery

    Averages of Δσm0 (solid lines; in dB) and Δσn0 (dotted lines; in dB) at NP pixels located l pixels away (l = 1–8) from the nearest P pixel in the (a) along-track and (b) cross-track directions for the latitude zone between 50°S and 50°N. Blue lines are for KuPR with angle bin numbers 13–37. Red lines are for KaMS with angle bin numbers 1–25. Blue (red) bars represent Δσn0Δσm0 for KuPR (KaMS).

  • View in gallery

    Schematics explaining possible reasons for the fact that estimated Δσn0 of KaMS increases with distance from the precipitation area.

  • View in gallery

    Spatial distribution of Δσn0 (dB) at NPT1 pixels for (a) KuPR, (b) KaMS, and (c) KaHS. Blue means Δσn0 is negative. (d) The zonal means of Δσm0 (solid lines; in dB) and Δσn0 (dotted lines; in dB) at NPT1 pixels. Blue, red, and green lines represent KuPR, KaMS, and KaHS, respectively.

  • View in gallery

    Relationship between the global averages of Δσm0 (solid lines; in dB), Δσn0 (dotted lines; in dB), and Δσn0Δσm0 (bars) at NP pixels and the dry period duration. Blue, red, and green denote KuPR, KaMS, and KaHS, respectively.

  • View in gallery

    Global averages of Δσn0, Δσe0(HB), Δσe0(HYB), Δσe0(SLV), and Δσe0(SRT) for each precipitation rate category. The units are dB. (b),(d) Δσe0(FA), Δσe0(BA), and Δσe0(TR) are shown in addition and the ranges of Δσn0 and Δσe0 estimates are limited to between −2 and 2 dB. (a),(b) KuPR with angle bin numbers 13–37, and (c),(d) KaMS.

  • View in gallery

    Spatial distribution of Δσe0 estimates (dB) at precipitation rate category 4. (a) Δσe0(HB) of KuPR, (b) Δσe0(HB) of KaMS, (c) Δσe0(SRT) of KuPR, and (d) Δσe0(SRT) of KaMS. Blue means Δσe0 is negative.

  • View in gallery

    Δσe0(HB) (black dots), Δσe0(SRT) (purple dots), Δσe0[P] (black line), and Δσe0[X] (purple line) at grid (30°–35°N, 100°–95°W) and angle bin group 1. The units are dB. (a) KuPR and blue area represents δσe0, and (b) KaMS and red area represents δσe0.

  • View in gallery

    Spatial distribution of δσe0[9] (dB). (a) KuPR at angle bin group 1, (b) KaMS at angle bin group 1, (c) KuPR at angle bin group 3, and (d) KaMS at angle bin group 3. A gray grid indicates that the number of samples is less than 100 in all categories and no correction for Ap(SRT) is applied.

  • View in gallery

    Cumulative histograms of the δσe0[N] value (dB) for angle bin group 1. (a) KuPR and (b) KaMS. For KuPR (KaMS), histograms for N = 6–9 (5–9) are mostly overlapped.

  • View in gallery

    Cumulative histograms of the δσe0[9] value (dB) for different angle bin groups. (a) KuPR (angle bin groups 1–6) and (b) KaMS (angle bin groups 1–3).

  • View in gallery

    (bottom) 2D histograms of Rorg (horizontal axis) and Rmod (vertical axis). Red lines in bottom figures are the average Rmod for a 1 dB mm h−1 bin of Rorg. (top) Red lines are the fractional changes of R for a 1 dB mm h−1 bin of Rorg. (a) KuPR, (b) KaMS, and (c) KaHS.

  • View in gallery

    Angle bin dependence of the unconditional averages [mm (30 days)−1] of Rorg (black solid line), Rmod (blue solid line), and Rtest (red solid line) for (a) KuPR, (b) KaMS, and (c) KaHS. Blue and red dashed lines are the fractional changes (%) of Rmod and Rtest from Rorg, respectively.

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Correction of Path-Integrated Attenuation Estimates Considering the Soil Moisture Effect for the GPM Dual-Frequency Precipitation Radar

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  • 1 aGraduate School of Engineering, Nagasaki University, Nagasaki, Japan
  • | 2 bEarth System Science Interdisciplinary Center, University of Maryland, College Park, College Park, Maryland
  • | 3 cNASA Goddard Space Flight Center, Greenbelt, Maryland
Open access

Abstract

Spaceborne precipitation radars, including the Tropical Rainfall Measuring Mission’s Precipitation Radar (PR) and the Global Precipitation Measurement Mission’s Dual-Frequency Precipitation Radar (DPR), measure not only precipitation echoes but surface echoes as well, the latter of which are used to estimate the path-integrated attenuation (PIA) in the surface reference technique (SRT). In our previous study based on analyzing PR measurements, we found that attenuation-free surface backscattering cross sections (denoted by σe0) over land increased in the presence of precipitation. This behavior, called the soil moisture effect, causes an underestimate of the PIA by the SRT as the method does not explicitly consider this effect. In this study, measurements made by Ku-band Precipitation Radar (KuPR) and Ka-band Precipitation Radar (KaPR), which comprise the DPR, were analyzed to examine whether KuPR and KaPR exhibit similar dependencies on the soil moisture as does the PR. For both KuPR and KaPR, an increase in σe0 was observed for a large portion of the land area, except for forests and deserts. Results from the Hitschfeld–Bordan (HB) method suggest that σe0 increases with the surface precipitation rate for light precipitation events. Meanwhile, for heavy precipitation, owing to the degradation of the HB method, it is difficult to estimate σe0 quantitatively. Thus, a correction method for PIA that considers the soil moisture effect was developed and implemented into the DPR standard algorithm. With this correction, the surface precipitation rate estimates increased by approximately 18% for KuPR and 15% for the normal scan of KaPR over land.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Precipitation Retrieval Algorithms for GPM Special Collection.

Corresponding author: Shinta Seto, seto@nagasaki-u.ac.jp

Abstract

Spaceborne precipitation radars, including the Tropical Rainfall Measuring Mission’s Precipitation Radar (PR) and the Global Precipitation Measurement Mission’s Dual-Frequency Precipitation Radar (DPR), measure not only precipitation echoes but surface echoes as well, the latter of which are used to estimate the path-integrated attenuation (PIA) in the surface reference technique (SRT). In our previous study based on analyzing PR measurements, we found that attenuation-free surface backscattering cross sections (denoted by σe0) over land increased in the presence of precipitation. This behavior, called the soil moisture effect, causes an underestimate of the PIA by the SRT as the method does not explicitly consider this effect. In this study, measurements made by Ku-band Precipitation Radar (KuPR) and Ka-band Precipitation Radar (KaPR), which comprise the DPR, were analyzed to examine whether KuPR and KaPR exhibit similar dependencies on the soil moisture as does the PR. For both KuPR and KaPR, an increase in σe0 was observed for a large portion of the land area, except for forests and deserts. Results from the Hitschfeld–Bordan (HB) method suggest that σe0 increases with the surface precipitation rate for light precipitation events. Meanwhile, for heavy precipitation, owing to the degradation of the HB method, it is difficult to estimate σe0 quantitatively. Thus, a correction method for PIA that considers the soil moisture effect was developed and implemented into the DPR standard algorithm. With this correction, the surface precipitation rate estimates increased by approximately 18% for KuPR and 15% for the normal scan of KaPR over land.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

This article is included in the Precipitation Retrieval Algorithms for GPM Special Collection.

Corresponding author: Shinta Seto, seto@nagasaki-u.ac.jp

1. Introduction

a. Background and study purpose

Spaceborne precipitation radars have been operating for more than 20 years (Nakamura 2021), beginning with the Precipitation Radar (PR; Kozu et al. 2001) on the Tropical Rainfall Measuring Mission (TRMM; Kummerow et al. 1998) satellite, which operated from 1997 to 2015, and continuing with the Dual-Frequency Precipitation Radar (DPR; Kojima et al. 2012; Iguchi 2020) on the Global Precipitation Measurement (GPM; Hou et al. 2014; Skofronick-Jackson et al. 2017) mission’s core satellite, which has been in operation since 2014. As spaceborne precipitation radars measure not only precipitation echo but also surface echo, the surface reference technique (SRT; Meneghini et al. 2000, 2004, 2012, 2015, 2021) can be applied to the precipitation retrieval. The SRT is a method for estimating path-integrated attenuation (PIA; its value in decibel is denoted by A) using the difference between the measured surface backscattering cross sections (values in decibels are denoted by σm0) inside and outside the precipitation area. Unless stated otherwise, all surface backscattering cross sections and path-integrated attenuations in this paper are expressed in decibels.

Seto and Iguchi (2007, hereafter SI07) analyzed the outputs of the PR standard algorithm version 6 (Iguchi et al. 2000; Meneghini et al. 2004) and showed that σm0 changes not only because of rain attenuation under rainfall but also because of rainfall-induced changes in the surface conditions. In particular, over land, the actual (attenuation-free) surface backscattering cross sections (denoted by σe0) increase in the presence of rainfall. This behavior is called the soil moisture effect. In general, the increase in the surface soil moisture causes an increase in the dielectric constant; as the dielectric constant is larger for water than that for soil particle, this leads to an increase in σe0. Several studies including Oki et al. (2000), Seto et al. (2003), Lee and Anagnostou (2004), and Stephen et al. (2010) revealed the relationship between σm0 by PR and surface soil moisture. Tagawa et al. (2004) showed the dependence of σm0 on surface soil moisture by an experiment using 35-GHz polarimetric scatterometer. Frappart et al. (2015) showed the relationship between σm0 using measurements from Ka-band altimeter (ALtiKa) on board the Satellite for Argos and ALtiKa (SARAL) and surface soil moisture. Fatras et al. (2016) conducted an experiment to show the relationship between σm0 at 34.5 GHz and surface soil moisture.

As the SRT does not explicitly consider changes in surface conditions, it may result in significantly biased PIA estimates. In the PR standard algorithm version 7 (Iguchi et al. 2009; TRMM Precipitation Radar Team 2011), following SI07, an adjustment term of 0.5 dB was added to the PIA estimated by the SRT to account for the soil moisture effect over land. In the DPR standard algorithm version 06 (Meneghini et al. 2021; Seto et al. 2021), no adjustment is given to the PIA estimated by the SRT. Therefore, in this study, the soil moisture effect was analyzed using outputs of the DPR standard algorithm version 06, and a correction method for the PIA estimated using the SRT was developed.

b. Overview of DPR

The DPR consists of a Ku-band Precipitation Radar (KuPR; 13.6 GHz) and a Ka-band Precipitation Radar (KaPR; 35.5 GHz). The microwave frequency of the KuPR is near that of the PR (13.8 GHz), and the scan pattern of the KuPR is the same as that of the PR; both radars scan in the cross-track direction and measure 49 pixels over each scan. An angle bin number i (1–49) is allocated to the pixels, where the incidence angle, measured at the surface, is given approximately by 0.75° × |25 − i|.

The KaPR has a normal mode and a high-sensitivity mode. It measures 25 pixels per scan in the normal mode. An angle bin number j (1–25) is allocated to the pixels, wherein the incidence angle is 0.75° × |13 − j|. The KaPR’s pixel with angle bin number j matches the KuPR’s pixel with an angle bin number j + 12. Dual-frequency measurements are available at these pixels. The KaPR measurements in the normal mode are called “KaPR for matched scan” (KaMS) hereafter in this study. In addition, the part of the swath where KaMS measurements are available is called the inner swath, while the rest of the swath is called the outer swath.

After the 25-pixel measurements by the KaMS, 24 pixels are measured using the KaPR in the high-sensitivity mode. These measurements are called “KaPR with high sensitivity” (KaHS). The KaHS measurements are inferior to the KaMS measurements in terms of the vertical resolution (500 m for KaHS and 250 m for KaMS). However, the KaHS is superior to the KaMS in terms of the minimum detection level (13.71 dBZ for KaHS and 19.18 dBZ for KaMS; Masaki et al. 2022). At the beginning of the mission, the KaHS beams were directed along the inner swath over a scan interleaved by two normal scans. An angle bin number h (1–24) is allocated to KaHS pixels, wherein the incidence angle is 0.75° × |h − 12.5|. The scan pattern of KaHS was changed in May 2018, but the data taken after the scan pattern change are not used in this study.

c. DPR standard algorithm

The level-2 DPR standard algorithm consists of the KuPR algorithm, the KaPR algorithm, and the dual-frequency algorithm. While the dual-frequency algorithm uses both KuPR and KaPR measurements, only KuPR (KaPR) measurements are available for the KuPR (KaPR) algorithm. Each algorithm is composed of six major modules: Preparation module, Vertical profile module, Classification module, SRT module, Drop size distribution module, and Solver module. As the details of the DPR standard algorithm and its modules are described in Iguchi et al. (2018) and other documents, the following explanation is limited to considerations relevant to this study.

1) Single-frequency algorithms

The single-frequency algorithms (KuPR and KaPR algorithms) are explained in this section. In the Preparation module, the presence or absence of precipitation is judged at each pixel. If precipitation is present, the pixel is called a precipitation pixel or P pixel. If there is no precipitation, the pixel is called a no-precipitation pixel or NP pixel. Further, σm0 is calculated from the surface echo, and the surface type (land, ocean, coast, or in-land water) is determined at each pixel.

In the Vertical profile module, the vertical profiles of cloud liquid water, water vapor, and oxygen are estimated, and the attenuation caused by these constituents (called nonprecipitation attenuation) is calculated. The path-integrated value is denoted by Anp. An environmental grid dataset (spatial resolution of 0.5° latitude × 0.5° longitude and temporal resolution of 6 h) was produced based on the Japan Meteorological Agency’s analysis and forecast data, and was used to estimate the profiles of cloud liquid water, water vapor, and oxygen at NP pixels. Meanwhile, at P pixels, the vertical profiles of water vapor and oxygen are estimated using the environmental grid dataset, and the vertical profile of cloud liquid water is estimated by referencing a database that was produced from the outputs of a global cloud resolving model. More details regarding the Vertical profile module are provided in Kubota et al. (2020a).

In the SRT module, the PIA is estimated at the P pixels. The estimate is denoted by A(SRT). NP pixels that have similar surface conditions to the target P pixel are used, and the sample mean and standard deviation of the σm0 values at the NP pixels are calculated. Over land, several reference methods are applied simultaneously, including the forward along-track reference method (FA), backward along-track reference method (BA), and temporal reference method (TR). In the FA (BA), the sample mean and standard deviation of the σm0 values from eight NP pixels measured before (after) the target P pixel, at the same angle bin number and surface type as the P pixel, constitute the rain-free reference data. If eight NP pixels are not found within a 50-pixel distance from the target P pixel, the reference method is not used. For the TR, the sample mean and standard deviation of the σm0 values at NP pixels are calculated in advance over a grid (0.5° latitude × 0.5° longitude) for each season (JJA, SON, DJF, and MAM) and incidence angle (each 0.75° bin). The values at the same grid, season, and incidence angle as the target P pixel are used. A(SRT) is given in Eq. (1):
A(SRT)=σm0[X]σm0[P],
where a variable with [X] denotes the value of the weighted average of the NP pixels referenced in SRT and a variable with [P] denotes the value at the target P pixel. The precise definition of the weighted average is given in the appendix. A detailed description of the SRT module is provided in Meneghini et al. (2021).
In the Solver module, A(SRT) is used as an input to retrieve physical variables, such as the precipitation rate. As A(SRT) is affected by nonprecipitation attenuation, it must be corrected before the retrieval procedure to provide the PIA caused by precipitation particles only (denoted by Ap). The terms appearing on the right-hand side of Eq. (1) are decomposed, as expressed in Eqs. (2) and (3):
σm0[P]=σe0[P]ApAnp[P]
and
σm0[X]=σe0[X]Anp[X].
By substituting Eqs. (2) and (3) into Eq. (1), Eq. (4) can be obtained:
A(SRT)=Ap+Anp[P]Anp[X]δσe0,
where
δσe0σe0[P]σe0[X]
From Eq. (4), Ap is given as follows:
Ap=A(SRT)+Anp[X]Anp[P]+δσe0.
However, in the version 06 algorithm, δσe0 is ignored, so that Ap is estimated by Eq. (7):
Ap(SRT)=A(SRT)+Anp[X]Anp[P],
where Ap is renamed as Ap(SRT) to describe the estimation method. The relationship among the variables related to SRT are summarized in Fig. 1a. For each method of SRT (FA, BA, and TR), similar equations are derived as shown in the appendix.
Fig. 1.
Fig. 1.

Schematics explaining variables (a) for surface reference technique, (b) for analysis at an NP pixel near precipitation area, (c) for analysis at a P pixel with light precipitation, and (d) for analysis at a P pixel with heavy precipitation.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

Ap(SRT) is usually different from the final estimate of Ap in the Solver module [denoted by Ap(SLV)]. As the reliability of the SRT increases, Ap(SLV) moves closer to Ap(SRT). More details regarding the Solver module are provided in Seto et al. (2021).

In the single-frequency algorithm, the six modules are executed twice. In the first execution, tentative estimates are obtained, and in the second execution, some of the tentative estimates are used to recalculate other variables. For example, cloud liquid water at a P pixel is given as a function of the surface precipitation rate estimates from the first execution. Note that the estimates provided by the second execution are the final estimates.

2) Dual-frequency algorithm

The dual-frequency algorithm has the same six modules as the single-frequency algorithms, but there are differences within each module. In this section, the differences related to this study are briefly explained.

In the SRT module, an estimate of the differential path attenuation, the difference in A between KuPR and KaPR (denoted by Aδ), is based on the difference in the σm0 values between KuPR and KaPR (denoted by σm,δ0). The method to derive Aδ from σm,δ0 is the same as that used to derive A from σm0 in the single-frequency algorithms and is called the dual-frequency surface reference technique (DSRT). In the Solver module, Aδ is used as an input to retrieve physical variables after it is corrected for nonprecipitation attenuation.

d. Data preparation

In this study, the outputs of the DPR standard algorithm (version 06A) from 2015 to 2020 were analyzed. Hereafter, unless otherwise specified, the period of analysis is 6 years for KuPR and KaMS, and 3 years (from 2015 to 2017) before the scan pattern change for KaHS. Note that KaHS after the scan pattern change was not processed in version 06A, and thus, it was not analyzed in this study.

In this study, the analysis preparation was as follows. The average σm0 at NP pixels over land is calculated over a monthly 1° latitude × 1° longitude grid for each angle bin. The average value is denoted by σm0¯, so that for an instantaneous value of σm0, the anomaly from the corresponding σm0¯ is denoted by Δσm0, as expressed in Eq. (8):
Δσm0=σm0σm0¯.
The surface backscattering cross section corrected for nonprecipitation attenuation is denoted by σn0, as expressed in Eq. (9):
σn0σm0+Anp.
A space–time average of σn0 at NP pixels over land is calculated in an identical manner to that for σm0 and is denoted by σn0¯. By taking the average of the both terms in Eq. (9), the following equations are obtained:
σn0¯=σm0¯+Anp¯,
where Anp¯ is the average Anp at NP pixels over land at each angle bin over the same space–time grid as described above. For an instantaneous value of σn0, the anomaly from the corresponding σn0¯ is denoted by Δσn0, as expressed in Eq. (11):
Δσn0=σn0σn0¯.
Relationship among the variables at an NP pixel is summarized in Fig. 1b.
At a P pixel, Eq. (12) is true:
σe0=σn0+Ap.
If Ap is estimated using method M, it is denoted by Ap(M), where M is a generic name to describe the method. For example, Ap(SRT) was estimated using Eq. (7). Thus, if σe0 is calculated with Ap(M), it is denoted by σe0(M) as follows:
σe0(M)=σn0+Ap(M).
For an instantaneous value of σe0(M), the anomaly from the corresponding σn0¯ is denoted by Δσe0(M), as expressed in Eq. (14):
Δσe0(M)=σe0(M)σn0¯.

The relationship among the variables at a P pixel is summarized in Figs. 1c and 1d. Δσe0 indicates the soil moisture effect; if a soil moisture effect exists, Δσe0 is positive. In the case of light precipitation (Fig. 1c), where Ap is not large, Δσm0 and Δσn0 may be positive. In the case of heavy precipitation (Fig. 1d), where Ap is large, Δσm0 and Δσn0 are negative.

e. Composition of this study

Based on the preparatory comments and definitions provided, the purpose of this study is to estimate the value of δσe0 to correct the Ap(SRT) to Ap (as illustrated in Fig. 1a). The remainder of this paper is organized as follows.

In section 2, Δσm0 and Δσn0 at NP pixels (as illustrated in Fig. 1b), either located near a P pixel or measured soon after a precipitation event, are analyzed. These NP pixels are expected to have a relatively higher surface soil moisture than other NP pixels and to exhibit a soil moisture effect. Note that the analysis of the NP pixels is free from the estimation error of Ap. In section 3, the estimates of Δσe0(M) at P pixels (as illustrated in Figs. 1c,d) are analyzed for different precipitation rate categories. In section 4, an estimation method for δσe0 is developed and implemented in the single-frequency algorithms. Further, the effect of the correction of Ap(SRT) on the precipitation rate estimates is examined. Finally, a summary is provided in section 5.

2. Analysis of the soil moisture effect at NP pixels

a. NP pixels adjacent to a P pixel

1) PR (review)

In SI07, using data from the PR, the behavior of Δσm0 at the NP pixels adjacent to a P pixel was analyzed. NP pixels measured one pixel before (after) a P pixel in the along-track direction are called NPB1 (NPA1) pixels. As these pixels are located near the precipitation area, it is more likely that they were inside the precipitation area for a short time before the measurement than NP pixels far away from precipitation area. If they were, in fact, inside the precipitation, the surface soil moisture would be higher, and a positive Δσm0 value would be observed. Thus, the fact that Δσm0 was positive in a large part of the land area, with the exception of tropical forests, such as Amazonia, and deserts, such as the Sahara Desert (Figs. 7a and 7b of SI07) indicates that this quantity is positively correlated with the anomaly of surface soil moisture. It was also found that Δσm0 is higher at NPB1 pixels than at NPA1 pixels at midlatitudes, but the opposite is true in the Sahel of Africa in the tropics (Fig. 7c of SI07). This could be because an NPB1 (NPA1) pixel is likely to be located west (east) of the precipitation area. Thus, in midlatitude areas, where the storm system usually moves from the west to the east, the probability that a pixel is inside the precipitation area for a short time before the measurement is higher at NPB1 pixels than at NPA1 pixels. Meanwhile, in the tropics, the storm system usually moves from east to west, making the reverse true.

2) KuPR

The same analysis that was used in SI07 was applied to the KuPR data to check whether KuPR shows soil moisture effects similar to those found for the PR. For the NPB1 and NPA1 pixels of KuPR, Δσm0 was averaged over 1° latitude × 1° longitude cells. In this analysis, if an NP pixel is between two P pixels in the along-track direction, it is taken neither as an NPB1 pixel nor as an NPA1 pixel. The spatial distribution of Δσm0 at the NPB1 (NPA1) pixels is shown in Fig. 2a (Fig. 2b), where negative values of Δσm0 are shown in blue. In large portions of the land area, with the exception of forest, desert, and high mountains, the Δσm0 is positive for both NPB1 and NPA1 pixels. It is worth noting, however, that vegetation and snow cover can degrade the relationship between the surface soil moisture and the surface backscattering cross sections. Between 35°S and 35°N, the results are similar to those of the PR. Figure 2c shows the differences between Figs. 2a and 2b, in which the blue (red) color indicates that Δσm0 is higher at the NPB1 (NPA1) pixels. Note that blue areas mainly occur at midlatitudes and red areas occur in the Sahel of Africa. However, this difference is not as distinct as in the case of the PR. Some cells along the coastline or over remote islands show large absolute values of the difference in Δσm0 if the number of samples is not large. Figure 2d shows the zonal mean of the Δσm0 for the NPB1 and NPA1 pixels. With the exception of the region near 60°S, where the number of pixels is small, the zonal mean of Δσm0 is positive. Moreover, the NPB1 pixels have higher Δσm0 values than the NPA1 pixels at midlatitudes, but they have nearly the same Δσm0 in the tropics.

Fig. 2.
Fig. 2.

Spatial distribution of Δσm0 (dB) for KuPR (a) at NPB1 pixels and (b) at NPA1 pixels, where blue means Δσm0 is negative. (c) The difference of (b) minus (a). (d) The zonal mean of Δσm0 at NPB1 (blue line) and that of NPA1 pixels (red line).

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

As the orbit inclination angle of the TRMM satellite is 35°, the orbit track passes the precipitation area in a nearly west to east direction (Fig. 3a). In this case, an NPB1 (NPA1) pixel is likely to be located west (east) of the precipitation area. However, as the orbit inclination angle of the GPM core satellite is 65°, an orbit track passes the precipitation area from the southwest to northeast direction (in ascending orbit) or from the northwest to southeast direction (in descending orbit) rather than from a more west to east direction (Fig. 3b). In an ascending orbit, an NPB1 (NPA1) pixel is likely to be located south (north) of the precipitation area. Meanwhile, the opposite is true in a descending orbit. The difference in the satellite orbit inclination angle is the main reason that Fig. 2c is different from Fig. 7c of SI07. These general rules apply up to 50°. At higher latitude, an orbit track passes the precipitation area in a west to east direction rather than in a north to south or south to north direction.

Fig. 3.
Fig. 3.

Schematics explaining the sampling of NP pixels near the precipitation area. The areas within the large blue open circles are assumed to be filled with precipitation. The small circles represent pixels measured by (a) the PR and (b),(c) the DPR. The filled circles are P pixels and open circles are NP pixels. Arrows show the direction of satellite motion. The numbers in the open small circles show the distance in pixels from the nearest P pixel in (a) and (b) along-track and (c) cross-track directions.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

Considering this difference, the NP pixels adjacent to a P pixel in the cross-track direction were obtained for KuPR (Fig. 3c). These pixels may be located either west or east of the precipitation area. In particular, NP pixels located one pixel to the left (right) of a P pixel in an ascending (descending) orbit are likely to be located west of the precipitation area. These pixels are called NPW1 pixels. Conversely, NP pixels located one pixel to the right (left) of a P pixel in an ascending (descending) orbit are likely to be located east of the precipitation area. These pixels are called NPE1 pixels. If an NP pixel is between two P pixels in the cross-track direction, the pixel is taken neither as an NPW1 pixel nor as an NPE1 pixel. At the scan edge, some NPW1 and NPE1 pixels can be missed if a precipitation area exists close to the scan but does not overlay the scan. This may affect the quality of analysis. The average Δσm0 at the NPW1 (NPE1) pixels for 1° latitude × 1° longitude was calculated, and the spatial distribution is shown in Fig. 4a (Fig. 4b). Similar to Figs. 2a and 2b, positive Δσm0 values were observed over land, with the exception of forest, desert, and high mountains. Figure 4c shows the differences between Figs. 4a and 4b. The blue (red) color shows that the Δσm0 is higher for the NPW1 (NPE1) pixels. At midlatitude, the Δσm0 at the NPW1 pixels are higher. However, in the Sahel of Africa, the Δσm0 values at the NPE1 pixels are higher. The difference in the Sahel of Africa can be observed clearly as shown in Fig. 7c of SI07. Moreover, Fig. 4d shows the zonal mean of Δσm0 for the NPW1 and NPE1 pixels. The NPW1 pixels show a higher Δσm0 than the NPE1 pixels at midlatitudes, whereas the NPE1 pixels show a higher Δσm0 than the NPW1 pixels around 10°N. Based on these findings, it is confirmed that KuPR shows a soil moisture effect similar to that of PR.

Fig. 4.
Fig. 4.

Spatial distribution of Δσm0 (dB) for KuPR (a) at NPW1 pixels and (b) NPE1 pixels, where blue means Δσm0 is negative. (c) The difference of (b) minus (a). (d) The zonal mean of Δσm0 at NPW1 pixels (blue line) and that of NPE1 pixels (red line).

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

3) KaMS

In this subsection, we examine whether the KaPR has a similar sensitivity to soil moisture as the KuPR. Using the same analysis as that used for KuPR, NP pixels adjacent to a P pixel in the cross-track direction were obtained, and the Δσm0 values of KaMS were analyzed. As KuPR has a better minimum detection level (15.46 dBZ) than that of KaMS (19.18 dBZ) and KuPR is always available at matched pixels, the precipitation judgment from the KuPR data was used to define NP and P pixels for the analysis of the KaMS measurements.

The average Δσm0 at the NP pixels adjacent to a P pixel in the cross-track direction was calculated over 1° latitude × 1° longitude cells. To reduce the number of figures, the NPW1 and NPE1 pixels were not separated while the difference in Δσm0 between NPW1 and NPE1 is similar to those for KuPR. The spatial distribution is shown in Fig. 5a. The area with positive Δσm0 values is limited compared with the KuPR results shown in Figs. 4a and 4b. Figure 5b shows the Δσn0 values instead of the Δσm0 values. Here, the area with positive Δσn0 values is slightly larger than that in Fig. 5a. Meanwhile, Fig. 5c shows Δσn0 minus Δσm0, revealing a difference as small as zero in the tropics, and a difference of 0–0.5 dB at midlatitudes. Figure 5d shows the zonal mean values of Δσm0 and Δσn0. In general, Δσm0 was negative in most of the latitude zones. Further, Δσn0 was larger than Δσm0 at midlatitudes, but negative in the tropics and around 60°N.

Fig. 5.
Fig. 5.

Spatial distribution of (a) Δσm0 (dB) and (b) Δσn0 (dB) for KaMS at NP pixels adjacent to a P pixel in cross-track direction, where blue denotes that (a) Δσm0 or (b) Δσn0 is negative. (c) The difference of (b) minus (a). (d) The zonal means of Δσm0 (solid line) and Δσn0 (dotted line).

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

Subtracting Eq. (8) from Eq. (11) and using Eqs. (9) and (10), Eq. (15) is obtained:
Δσn0Δσm0=AnpAnp¯.
The fact that Δσn0 is larger than Δσm0 indicates that Anp is larger at the NP pixels adjacent to a P pixel than at normal NP pixels. Thus, it is reasonable to assume that Anp is higher near the precipitation area.

Regarding KaMS, as nonprecipitation attenuation is larger than that for KuPR, correction for nonprecipitation attenuation is necessary. However, Δσn0 is negative in some regions, which cannot be explained by the soil moisture effect. A possible reason for this is that the nonprecipitation attenuation is not well corrected in Δσn0.

4) Angle bin dependence

Figure 6 shows the angle bin dependence of Δσm0 and Δσn0 at the NP pixels adjacent to a P pixel in the cross-track direction. For KuPR, the Δσm0 and Δσn0 in inner swath are slightly larger than those in outer swath. For KaMS, Δσm0 and Δσn0 are larger at nadir and are smaller at the edge of the inner swath. At the edge of the normal scan, some NPW1 and NPE1 pixels may be missed, but the effects of this on Δσm0 and Δσn0 are not clearly seen.

Fig. 6.
Fig. 6.

Angle bin dependence of the global averages of Δσm0 (solid lines; in dB) and Δσn0 (dotted lines; in dB) at the NP pixels adjacent to a P pixel in the cross-track direction. Blue and red denote KuPR and KaMS, respectively. The angle bin number refers to that of KuPR.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

b. NP pixels near a P pixel

In this subsection, the analysis was extended to NP pixels located within eight pixels from a P pixel. At NP pixels located l (1–8) pixels away from the nearest P pixel in the along-track direction, the averages of Δσm0 and Δσn0 between 50°S and 50°N were calculated for each l. If the distance from an NP pixel to the nearest P pixel is the same for the two directions, the NP pixel is excluded from the analysis. The situation as illustrated in Fig. 3 is valid in this latitude zone. In Fig. 7a, the solid (dotted) lines represent Δσm0(Δσn0) and the bar shows Δσn0Δσm0, where the blue (red) color is used for KuPR (KaMS). The KuPR analysis is limited to angle bin numbers 13–37 in order to ensure that the KuPR and KaMS results are obtained under the same conditions. Figure 7b is the same as Fig. 7a, except the distance from the nearest P pixel is measured in the cross-track direction.

Fig. 7.
Fig. 7.

Averages of Δσm0 (solid lines; in dB) and Δσn0 (dotted lines; in dB) at NP pixels located l pixels away (l = 1–8) from the nearest P pixel in the (a) along-track and (b) cross-track directions for the latitude zone between 50°S and 50°N. Blue lines are for KuPR with angle bin numbers 13–37. Red lines are for KaMS with angle bin numbers 1–25. Blue (red) bars represent Δσn0Δσm0 for KuPR (KaMS).

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

For KuPR, as Δσn0Δσm0 is as small as approximately 0.01 dB, it can be confirmed that nonprecipitation attenuation does not hinder the analysis of the soil moisture effect. In the along-track direction, the Δσm0 decreases as the distance increases from 0.25 dB (l = 1) to 0.14 dB (l = 8). Meanwhile, in the cross-track direction, Δσm0 is not strongly dependent on the distance and it maintains a value of approximately 0.25 dB up to l = 8. In the case of PR, as shown in Fig. 6 of SI07, Δσm0 is not strongly dependent on the distance in the along-track direction. These results suggest that the soil moisture effect weakens more significantly with increasing distance in the north-to-south direction than in the west-to-east direction.

Regarding KaMS, Δσn0Δσm0 is nearly 0.1 dB, which is larger than that for KuPR. In the along-track direction, the Δσm0 and Δσn0 at l = 1 are −0.08 and 0.00 dB, respectively, and both increase slowly with increasing distance. Meanwhile, at l = 8, Δσm0 and Δσn0 are 0.02 and 0.07 dB, respectively. In the cross-track direction, Δσm0 and Δσn0 at l = 1 are −0.07 and 0.02 dB, respectively, and increase rapidly with distance, reaching values of 0.10 and 0.16 dB at l = 8, respectively. The increase in Δσm0 and Δσn0 with distance cannot be explained by the soil moisture effect.

We assume that the real Δσn0 of KaMS decreases with distance as that of KuPR in the along-track direction. The real Anp is also assumed to decrease with distance, while the estimated Anp does not decrease significantly with distance. Figure 8 illustrates the situation. At l = 1, Anp and Δσn0 are larger than those at l = 8, respectively. If the estimated Anp at l = 1 is underestimated and is the same as that at l = 8, then the calculated Δσn0 at l = 1 is smaller than that at l = 8. This is an interpretation of the results in Fig. 7. As Anp is estimated by the environmental grid dataset with a spatial resolution of 0.5° latitude × 0.5° longitude, it may be difficult to estimate the change in Anp over the eight fields of view (approximately 40 km). Nevertheless, as the real Anp or Δσn0 are not obtained, we cannot establish a soil moisture effect in the KaPR data.

Fig. 8.
Fig. 8.

Schematics explaining possible reasons for the fact that estimated Δσn0 of KaMS increases with distance from the precipitation area.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

c. NP pixels measured shortly after a precipitation event

The Global Satellite Mapping of Precipitation (GSMaP) Microwave–IR Combined Product (GSMaP_MVK version 7; Kubota et al. 2020b) was used to identify NP pixels measured shortly after a precipitation event. GSMaP_MVK has a spatial resolution of 0.1° latitude × 0.1° longitude and a temporal resolution of 1 h. As the target area of GSMaP_MVK is from 60°S to 60°N, the analysis was performed in this latitude zone. When GSMaP_MVK estimates precipitation rates higher than 0.1 mm h−1, the 1-h period is regarded as a wet period. Times at which the rate is lower than the threshold are regarded as dry periods. Based on this, the dry period duration after a precipitation event was calculated. If an NP pixel is measured when the dry period duration is 1 h, the pixel is called an NPT1 pixel.

Δσn0 values at the NPT1 pixels were averaged over 1° latitude × 1° longitude cells. Figure 9a shows the Δσn0 of KuPR at the NPT1 pixels. Δσn0 is positive in many of the grids over land, except for those over forests and deserts. Figure 9b shows the Δσn0 values of the KaMS measurements at the NPT1 pixels, revealing that they are positive in many of the grids over land, but the values are smaller than those of KuPR. Figure 9c shows the Δσn0 of KaHS at the NPT1 pixels. The results are similar to those of the KaMS. Furthermore, Fig. 9d shows the zonal mean values of Δσm0 and Δσn0 for KuPR, KaMS, and KaHS. KuPR’s Δσm0 at the NPT1 pixels is higher than those at the NPB1, NPA1, NPW1, and NPE1 pixels shown in Figs. 2d and 4d particularly around 10°N. Thus, the probability that the NPT1 pixels were inside the precipitation area just before the measurement should be higher than that of the other pixels. Further, the soil moisture effect is more distinct at the NPT1 pixels. KaMS’s Δσm0 values at the NPT1 pixels are higher than those at the NPW1 and NPE1 pixels, as shown in Fig. 5d, suggesting that nonprecipitation attenuation at the NPT1 pixels is smaller than that at the NPW1 and NPE1 pixels. KaMS’s Δσn0 values at the NPT1 pixels are smaller than those of KuPR by 0.1–0.3 dB. The Δσm0 and Δσn0 values of KaHS are similar to those of KaMS.

Fig. 9.
Fig. 9.

Spatial distribution of Δσn0 (dB) at NPT1 pixels for (a) KuPR, (b) KaMS, and (c) KaHS. Blue means Δσn0 is negative. (d) The zonal means of Δσm0 (solid lines; in dB) and Δσn0 (dotted lines; in dB) at NPT1 pixels. Blue, red, and green lines represent KuPR, KaMS, and KaHS, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

In addition, the analysis was extended to NP pixels measured when the dry period duration (denoted by t) was 1–24 h. The global averages of the Δσm0 and Δσn0 were calculated for t from 1 to 24 h (Fig. 10). For KuPR, the Δσm0 and Δσn0 values were similar, and decreased with increasing t. Meanwhile, for KuPR, the Δσn0 was 0.30 dB at t = 1 h and 0.08 dB at t = 24 h. For KaMS, Δσn0 decreased with increasing t, from 0.19 dB at t = 1 h to 0.02 dB at t = 24 h. Thus, Δσm0 was smaller than Δσn0 by approximately 0.1 dB at t = 1 h, while Δσm0 and Δσn0 become closer with increasing t and are almost the same at t = 18 h. This indicates that Anp is larger than the nominal value at t = 1 h, but decreases toward the background value with increasing t. As the temporal resolution of the environmental grid dataset was 6 h, changes in the Anp within 24 h should be reliable. As the KaMS’s Δσn0 is nearly zero at t = 24 h, the soil moisture effect of KaMS appears to last for approximately 24 h after a precipitation event. Further, KaHS’s Δσm0 and Δσn0 values are nearly the same as those of KaMS.

Fig. 10.
Fig. 10.

Relationship between the global averages of Δσm0 (solid lines; in dB), Δσn0 (dotted lines; in dB), and Δσn0Δσm0 (bars) at NP pixels and the dry period duration. Blue, red, and green denote KuPR, KaMS, and KaHS, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

3. Analysis of soil moisture effect at P pixels

In this section, the Δσe0(M) estimates at the P pixels are analyzed. Δσe0(SRT), Δσe0(FA), Δσe0(BA), and Δσe0(TR) were analyzed to determine if the SRT is affected by soil moisture. Ap(SRT) was estimated using Eq. (7) and Ap(FA), Ap(BA), and Ap(TR) were estimated using Eq. (A4).

Anp[X] and Anp[Xi] in Eqs. (7) and (A4) are difficult to obtain as they are not stored in the standard product. Thus, they are approximately given as follows.

  • Anp[X1] (for FA) is replaced by Anp at the NP pixel measured 1 pixel before the precipitation area that includes the target P pixel.

  • Anp[X2] (for BA) is replaced by Anp at the NP pixel measured 1 pixel after the precipitation area that includes the target P pixel.

  • Anp[X3] (for TR) is replaced by the Anp¯ from the same grid, month, and angle bin in which the target P pixel is contained.

  • Anp[X] is replaced by the simple average of Anp[X1] and Anp[X2].

Another estimate of Δσe0 using a method independent of the SRT is required to evaluate the Δσe0(SRT), Δσe0(FA), Δσe0(BA), and Δσe0(TR). Ap can be estimated using the Hitschfeld–Bordan (HB; Hitschfeld and Bordan 1954) method as follows:
Ap=10βlog10(1ζ),
where
ζ=0.2(ln⁡ 10)β0rsα(r)Zmβ(r)dr,
where Zm is the measured radar reflectivity factor, r is the distance from the radar, and rs is the value of r at the surface. In addition, α and β are the coefficients of the kZe relation as follows:
k(r)=α(r)Zeβ(r),
where k is the specific attenuation and Ze is the attenuation-corrected radar reflectivity factor. This calculation was performed in the SRT module (Meneghini et al. 2021). The value of Eq. (16) is denoted by Ap(HB). Using HB as M in Eqs. (13) and (14), Δσe0(HB) is obtained.

A hybrid estimate of Ap by the HB and SRT methods is given in the SRT module, which is denoted by Ap(HYB). Moreover, in the Solver module, Ap(SLV) is given as the final estimate of Ap, as explained before. Using HYB and SLV as M in Eqs. (13) and (14), Δσe0(HYB) and Δσe0(SLV) are obtained. As Ap(HYB) and Ap(SLV) are not independent of Ap(SRT), Δσe0(HYB) and Δσe0(SLV) will be shown just as reference.

The soil moisture effect may depend on the precipitation rate as the surface soil moisture increases with increasing precipitation rate. To investigate the dependence of Δσe0 on the precipitation rate, P pixels were categorized by the surface precipitation rate estimates (variable name is precipRateESurface; denoted by R) of the KuPR algorithm. R is categorized as listed in Table 1. For each category, the global averages of Δσn0, Δσe0(HB), Δσe0(HYB), Δσe0(SLV), Δσe0(SRT), Δσe0(FA), Δσe0(BA), and Δσe0(TR) were calculated. Figure 11a shows the Δσn0, Δσe0(HB), Δσe0(HYB), Δσe0(SLV) and Δσe0(SRT) of the KuPR with angle bin numbers of 13–37. In Fig. 11b, Δσe0(FA), Δσe0(BA), and Δσe0(TR) are added and Δσn0 and Δσe0 estimates are plotted between −2 and 2 dB. Figures 11c and 11d are the same as Figs. 11a and 11b, but for KaMS, where R is estimated by KuPR as the precipitation rate estimates by KaMS are generally not as reliable as those by KuPR.

Fig. 11.
Fig. 11.

Global averages of Δσn0, Δσe0(HB), Δσe0(HYB), Δσe0(SLV), and Δσe0(SRT) for each precipitation rate category. The units are dB. (b),(d) Δσe0(FA), Δσe0(BA), and Δσe0(TR) are shown in addition and the ranges of Δσn0 and Δσe0 estimates are limited to between −2 and 2 dB. (a),(b) KuPR with angle bin numbers 13–37, and (c),(d) KaMS.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

Table 1

Range of R for precipitation rate categories.

Table 1

As shown in Figs. 11a and 11b, the Δσn0 is positive for categories 1–4 (R < 4 mm h−1), and negative for categories 5–9. As the real Δσe0 is larger than Δσn0, it is positive for categories 1–4. Further, Δσe0(HB) is positive and increases with R for categories 1–4, while it decreases with R for higher categories, eventually becoming negative for categories 7–9. As the HB method is not reliable for heavy precipitation (Meneghini et al. 2021), Δσe0(HB) are probably underestimated for the higher categories.

Δσe0(FA) and Δσe0(BA) were positive in every category. As FA and BA reference NP pixels near the precipitation area, the NP pixels show, to some extent, the soil moisture effect. However, Δσe0(TR) is not expected to show the soil moisture effect, and it is slightly negative. The Δσe0(SRT) is positive, as are Δσe0(FA) and Δσe0(BA), but it is less than 1 dB, except for category 9, and smaller than Δσe0(HB) for categories 1–6. Moreover, Δσe0(SRT) is smaller than Δσn0 for categories 1–4. These results confirm that the SRT of KuPR underestimates the soil moisture effect and must be corrected.

Δσe0(HYB) and Δσe0(SLV) take values between Δσe0(HB) and Δσe0(SRT). Δσe0(HYB) is close to Δσe0(HB), and it increases for categories 1–4, but decreases for higher categories. Δσe0(SLV) is close to Δσe0(SRT) for heavy precipitation and maintains a positive value for all categories.

Regarding KaMS, as shown in Fig. 11c, Δσn0 is nearly zero for category 1 and negative for higher categories because of heavy precipitation attenuation. Moreover, Δσe0(HB) is positive for categories 1–4, nearly zero for category 5, and negative for categories 6–9. The negative value of Δσe0(HB) is the result of the underestimation of the HB method. Meanwhile, as shown in Fig. 11d, Δσe0(FA) and Δσe0(BA) are nearly zero for all categories, as the σn0 values at NP pixels near the precipitation area are underestimated possibly because of an insufficient correction for nonprecipitation attenuation (as discussed in section 2b). In addition, Δσe0(TR) and Δσe0(SRT) were also approximately zero. These results confirm that the SRT of KaMS does not account for the soil moisture effect and must be corrected. Δσe0(HYB) and Δσe0(SLV) are similar to each other, and they are close to Δσe0(HB) for categories 1–4, but decrease for higher categories.

The spatial distributions of Δσe0(HB) and Δσe0(SRT) in category 4 are shown in Fig. 12. KuPR’s Δσe0(HB) is positive over almost all land areas, from slightly positive values in forests to values as high as 5 dB in some parts of the Sahel of Africa and Australia. KaMS’s Δσe0(HB) shows a spatial distribution similar to that of KuPR, but with smaller values. KuPR’s Δσe0(SRT) is positive in some regions, but it is much smaller than Δσe0(HB). KaMS’s Δσe0(SRT) is smaller than KuPR’s Δσe0(SRT).

Fig. 12.
Fig. 12.

Spatial distribution of Δσe0 estimates (dB) at precipitation rate category 4. (a) Δσe0(HB) of KuPR, (b) Δσe0(HB) of KaMS, (c) Δσe0(SRT) of KuPR, and (d) Δσe0(SRT) of KaMS. Blue means Δσe0 is negative.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

4. Correction of PIA estimates and effects on precipitation rate estimates

The value of δσe0 needs to be estimated to correct for Ap(SRT). Therefore, in this section, an estimation method is developed and implemented for the single-frequency algorithms of DPR. The modified algorithm was tested using a 1-month set of data, and the effects of the correction on the precipitation rate estimates were examined.

Though we have analyzed many candidates for Δσe0, Δσe0(HB) will be used for the correction. In section 2, the behavior of Δσm0 and Δσn0 at NP pixels clearly shows evidence of a soil moisture effect. Nevertheless, correction for this effect would yield estimates that are smaller than those given by Δσe0(HB). This suggests that the soil moisture effect is only one part of the error in the SRT and that the fluctuations in the surface cross section limit the accuracy of the method, particularly over land at Ku band. The estimates Δσe0(HYB) and Δσe0(SLV), shown as references in section 3, should not be used to correct the SRT, however, as they themselves depend on the SRT.

a. Database

δσe0=σe0[P]σe0[X] can be rewritten as δσe0=Δσe0[P]Δσe0[X] by subtracting σn0¯ from both terms. Δσe0(HB) and Δσe0(SRT) can be used for estimates of Δσe0[P] and Δσe0[X], respectively, but it must be kept in mind that Δσe0(HB) is underestimated in heavy precipitation. Using a 5° latitude × 5° longitude grid, the Δσe0(HB) and Δσe0(SRT) are averaged over each precipitation rate category (Table 1), and angle bin group (Table 2).

Table 2

Definitions of angle bin groups.

Table 2

Figure 13 shows the Δσe0(HB) and Δσe0(SRT) values for each precipitation rate category at grid (100°–95°W, 30°–35°N) and angle bin group 1 as an example. Δσe0(HB) and Δσe0(SRT) are represented by black and purple circles, respectively. Open circles are used if the number of samples is less than 100. As shown in Fig. 13a, for KuPR, Δσe0(HB) reaches a maximum in category 5, and decreases for categories greater than 6. Below category 5, Δσe0[P] is set equal to Δσe0(HB) in each category, whereas at categories 6 and higher, Δσe0(HB) should be discarded, and Δσe0[P] is set equal to Δσe0(HB) at category 5 to ensure that Δσe0[P] is given as the black line. In reality, Δσe0[P] may increase for categories 6 and higher, but there is no way to estimate it quantitatively. On the other hand, Δσe0[X] is set equal to the average of Δσe0(SRT) for categories 1–9 as Δσe0(SRT) is not strongly dependent on precipitation rate categories. Δσe0[X] is represented by the purple line, and δσe0 is denoted by the blue area. Figure 13b shows the results for KaMS, in which δσe0 is determined in the same manner as for KuPR and is represented by the red area.

Fig. 13.
Fig. 13.

Δσe0(HB) (black dots), Δσe0(SRT) (purple dots), Δσe0[P] (black line), and Δσe0[X] (purple line) at grid (30°–35°N, 100°–95°W) and angle bin group 1. The units are dB. (a) KuPR and blue area represents δσe0, and (b) KaMS and red area represents δσe0.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

In general, the following procedures are applied for each grid and angle bin group to determine δσe0:

  • The maximum value of Δσe0(HB) is searched among categories 1–9 (except for categories with a sample number of less than 100). If the category number with the maximum Δσe0(HB) is Nmax, Δσe0[P] is equal to Δσe0(HB) for categories 1 to Nmax and Δσe0[P] is equal to the maximum value of Δσe0(HB) for categories Nmax + 1 to 9.

  • Δσe0[X] is equal to the average of Δσe0(SRT) for categories 1–9.

  • δσe0 is given by Δσe0[P]Δσe0[X]. If the value is negative, it is replaced by 0.

  • If the number of samples is fewer than 100 in all categories, δσe0 cannot be determined for all categories and no correction for Ap(SRT) is applied.

The value of δσe0 in category N is denoted by δσe0[N]. The δσe0[N] values for each category, grid, and angle bin have been compiled into a database.

Figure 14 shows the spatial variation of δσe0[9] for angle bin group 1 (Figs. 14a,b) and angle bin group 3 (Figs. 14c,d), wherein Figs. 14a,c and 14b,d show the KuPR and KaMS results, respectively. A gray grid indicates that the number of samples is fewer than 100 in all categories and no correction for Ap(SRT) is applied. Only limited land pixels at small and remote islands are excluded from the correction. Note that δσe0[9] is higher in the Sahel of Africa, Australia, and the central part of the United States. KuPR and KaMS results are similar, but KuPR shows larger area of high δσe0[9]. δσe0[9] is smaller at angle bin group 3 than at angle bin group 1.

Fig. 14.
Fig. 14.

Spatial distribution of δσe0[9] (dB). (a) KuPR at angle bin group 1, (b) KaMS at angle bin group 1, (c) KuPR at angle bin group 3, and (d) KaMS at angle bin group 3. A gray grid indicates that the number of samples is less than 100 in all categories and no correction for Ap(SRT) is applied.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

Figure 15 is a cumulative histogram of the δσe0[N] value for angle bin group 1. Figure 15a shows the KuPR results. For some cells, δσe0[N] is zero. The lines of δσe0[N] for categories 6–9 are the same, suggesting that Δσe0(HB) reaches a maximum in category 6 or lower. δσe0[9] is higher than 2 dB in nearly half of land grids. Figure 15b shows the KaMS results, revealing that the δσe0[9] values are similar to those of KuPR.

Fig. 15.
Fig. 15.

Cumulative histograms of the δσe0[N] value (dB) for angle bin group 1. (a) KuPR and (b) KaMS. For KuPR (KaMS), histograms for N = 6–9 (5–9) are mostly overlapped.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

Figure 16 is a cumulative histogram of the δσe0[9] value for each angle bin group. Figures 16a and 16b show the KuPR (angle bin groups 1–6) and KaMS (angle bin groups 1–3) results, respectively. The cumulative histogram for angle bin group 1 shows higher values than those for the other angle bin groups.

Fig. 16.
Fig. 16.

Cumulative histograms of the δσe0[9] value (dB) for different angle bin groups. (a) KuPR (angle bin groups 1–6) and (b) KaMS (angle bin groups 1–3).

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

b. Algorithm modification

The single-frequency algorithms were modified to correct for Ap(SRT) by referencing the compiled database. In the first execution, the correction is not applied, and the tentative estimate of the surface precipitation rate is denoted by R1 (mm h−1). In the second execution, δσe0 is given by referencing the database and R1. As the precipitation category N is for 2N−3 < R1 < 2N−2, δσe0 is set equal to δσe0[N] when R1 = 2N−2.5. For other R1 values, δσe0 is log-linearly interpolated with R1, as follows:
δσe0={δσe0[1](R121.5)δσe0[N+1]{log2(R1)(N2.5)}+δσe0[N]{(N1.5)log2(R1)}(2N2.5<R12N1.5;N=18)δσe0[9](26.5<R1).

The database of δσe0[N] was prepared for both KuPR and KaMS. For KaHS, the KaMS database was used because the effects of soil moisture on KaHS and KaMS are similar as described in section 2.

c. Effects on precipitation rate estimates

The modified single-frequency algorithms were applied to the DPR measurements from 467 orbits (orbit numbers 012826–013292) in June 2016. Then, the modified and original algorithms (version 06A) were compared for their surface precipitation rate estimates. Table 3 summarizes the unconditional average of R (mm in 30 days) for all land pixels. For KuPR (angle bin numbers 1–49), R is 59.97 mm in the original algorithm and 70.79 mm in the modified algorithm, which constitutes an increase of 18.0%. For the inner swath, the increase was 18.3% for KuPR, 15.1% for KaMS, and 13.5% for KaHS. According to Figs. 1416, δσe0 did not vary much between KuPR and KaMS. As the SRT is more reliable with KaMS than with KuPR, the change in Ap(SLV) should be larger for KaMS. On the other hand, the sensitivity of R to the change of Ap(SLV) is higher for KuPR than for KaMS. Owing to these effects, the increases in R are not very different between KuPR and KaMS.

Table 3

Unconditional average [mm (30 days)−1] of R for over land. Percentages in the parentheses are the fractional changes of R from the original algorithm.

Table 3

The bottom figures in Fig. 17 show the scatterplots between R in the original algorithm (Rorg) and R in the modified algorithm (Rmod). The red line is the average Rmod for a 1 dB mm h−1 bin of Rorg. Meanwhile, the fractional change [(RmodRorg)/Rorg] for a 1 dB mm h−1 bin of Rorg are shown in the upper figures of Fig. 17. In Fig. 17a, for KuPR, a change in R is observed when Rorg is greater than 1 mm h−1. The fractional change reached as high as 40% when Rorg was approximately 10 mm h−1. In Fig. 17b for KaMS and Fig. 17c for KaHS, changes in R are observable even if Rorg is less than 1 mm h−1 because the SRT of KaPR is more reliable than that of KuPR. Overall, the fractional change in R was less than 20%. Moreover, the fractional change decreases when Rorg is approximately 100 mm h−1. This is probably consequence of the fact that the SRT estimate is not available as the surface echo disappears because of strong attenuation. In the standard algorithm, the SRT is judged to be questionable and is not used if Ap(SRT) is more than 10 times as large as Ap(HB). In cases where the original Ap(SRT) is smaller than 10 times of Ap(HB) and the corrected Ap(SRT) is larger than 10 times of Ap(HB), Rmod is estimated without the SRT and can be smaller than Rorg.

Fig. 17.
Fig. 17.

(bottom) 2D histograms of Rorg (horizontal axis) and Rmod (vertical axis). Red lines in bottom figures are the average Rmod for a 1 dB mm h−1 bin of Rorg. (top) Red lines are the fractional changes of R for a 1 dB mm h−1 bin of Rorg. (a) KuPR, (b) KaMS, and (c) KaHS.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

For reference, the same correction method with PR version 7 algorithm was applied, in which δσe0 was set to be 0.5 dB for all pixels over land. R in this test is denoted by Rtest and is higher than that in the original product by 5.6% for KuPR, 4.4% for KaMS, and 4.2% for KaHS, as listed in Table 3. Therefore, if the correction method developed in this study is applied to the standard algorithms of DPR or PR, the average precipitation rate estimates should increase.

Figure 18 shows the angle bin dependence of the unconditional average of Rorg, Rmod, and Rtest. The fractional changes [(RmodRorg)/Rorg] and [(RtestRorg)/Rorg] are also shown in Fig. 18. For KuPR, Rmod and Rtest as well as Rorg has strong angle bin dependence. At larger incidence angles, light precipitation is likely to be missed. At angle bins 20 and 30, R is higher than the values at the neighboring angle bins due to side-lobe clutter effects. At near angle bin 25, R is higher partly because SRT is unstable over land at nadir (Hirose et al. 2021). The fractional changes are not strongly dependent on the incidence angle except for Rmod within angle bin group 1 (angle bins 21–29); they are larger at angle bins 21 and 29 and become smaller in approaching angle bin 25. It may be mitigated if δσe0[N] is determined at each single angle bin. For KaMS and KaHS in Figs. 18b and 18c, respectively, R exhibits the angle bin dependence but the fractional changes are not strongly dependent on the angle bin numbers.

Fig. 18.
Fig. 18.

Angle bin dependence of the unconditional averages [mm (30 days)−1] of Rorg (black solid line), Rmod (blue solid line), and Rtest (red solid line) for (a) KuPR, (b) KaMS, and (c) KaHS. Blue and red dashed lines are the fractional changes (%) of Rmod and Rtest from Rorg, respectively.

Citation: Journal of Atmospheric and Oceanic Technology 39, 6; 10.1175/JTECH-D-21-0111.1

5. Summary and conclusions

In this study, the soil moisture effect was analyzed for the DPR, and a correction method for Ap(SRT) that considers the soil moisture effect was developed. As discussed in section 2, for the KuPR, following the same analysis as in SI07, the soil moisture effect, or positive Δσm0, was found for a large portion of land areas, with the exception of forests and deserts. For KaMS, in contrast to KuPR, the soil moisture effect was not clearly confirmed. As mentioned in section 3, Δσe0(HB) increases with the precipitation rate for light precipitation, but decreases under heavy precipitation. The former result suggests a dependence of Δσe0 on the precipitation rate, whereas the latter is a result of the underestimation of the HB method. Moreover, Δσe0(SRT) was slightly positive for KuPR and nearly zero for KaMS. As Δσe0(HB) is larger than Δσe0(SRT) for light precipitation, it was confirmed that Ap(SRT) must be corrected for the soil moisture effect. In section 4, the database of δσe0 was produced from Δσe0(HB) and Δσe0(SRT). Using the database, R increased by 18.3% for KuPR (inner swath), 15.1% for KaMS, and 13.5% for KaHS, as compared with the original algorithm (version 06A). The correction method is implemented in the DPR standard algorithm version 07. For version 07, the database of δσe0 is prepared also for the full swath of KaPR after the scan pattern change in the same way with KuPR and the inner swath of KaPR. The value of δσe0 in the outer swath of KaPR is similar to that in the inner swath of KaPR.

Some issues remain to be solved. The correction method for the dual-frequency algorithm needs to be studied. In the DSRT, the soil moisture effect was expected to be small in Aδ, as it is canceled by taking the difference between KuPR and KaPR. Therefore, a more accurate analysis is necessary to correct Aδ. Another issue concerns the HB method. For Ap(HB), a fixed kZe relation is assumed and nonuniform beam filling effects are not considered. For heavy precipitation, as the HB method is unreliable, Δσe0(HB) is discarded and the dependence of Δσe0 on precipitation rate is neglected for heavy precipitation. This may result in an underestimation of the heavy precipitation rates. A combined algorithm with DPR and GPM Microwave Imager (GMI) to estimate δσe0 will be considered in future work. As the soil moisture can be estimated by microwave radiometers (e.g., Turk et al. 2014), data from the GMI may help improve estimates of surface soil moisture and δσe0.

Acknowledgments.

This work was a result of Precipitation Measurement Mission of NASA and JAXA. It is financially supported by JAXA under Second Research Announcement on the Earth Observations. Seto would like to thank Prof. Taikan Oki at The University of Tokyo for encouraging him in the study on soil moisture retrieval using TRMM data, which became a basis of this study.

Data availability statement.

GPM DPR standard products (version 06A) used in this study are openly available through from NASA Goddard Earth Sciences Data and Information Services Center at https://doi.org/10.5067/GPM/DPR/Ku/2A/06 and https://doi.org/10.5067/GPM/DPR/Ka/2A/06. GSMaP_MVK product (version 7) used in this study is openly available through JAXA Global Rainfall Watch (https://sharaku.eorc.jaxa.jp/GSMaP/index.htm).

APPENDIX

Derivation of Ap in SRT

For notational convenience, the reference methods are renamed SRTi where SRT1 is “FA,” SRT2 is “BA,” and SRT3 is “TR.” The PIA estimate in SRTi is given in Eq. (A1):
A(SRTi)=σm0[Xi]σm0[P],
where a variable with [Xi] denotes that the value is the average for the NP pixels used in SRTi. σm0[Xi] is decomposed, as expressed in Eq. (A2):
σm0[Xi]=σe0[Xi]Anp[Xi].
By substituting Eqs. (A2) and (2) into Eq. (A1), Eq. (A3) can be obtained:
A(SRTi)=Ap+Anp[P]Anp[Xi]{σe0[P]σe0[Xi]}.
As in the Solver module, the terms of σe0[P]σe0[Xi] are assumed to be zero and Ap is estimated as in Eq. (A4):
Ap(SRTi)=A(SRTi)+Anp[Xi]Anp[P].
The three A(SRTi) estimates are combined into a single estimate, A(SRT), as shown in Eq. (A5):
A(SRT)=i=13w(SRTi)A(SRTi),
where w(SRTi) is the weight factor for SRTi, and Eq. (A6) always holds:
i=13w(SRTi)=1.
By substituting Eq. (A1) for i = 1–3 into Eq. (A5) and using Eq. (A6), Eq. (A7) is obtained:
A(SRT)={i=13w(SRTi)σm0[Xi]}σm0[P].
By defining σm0[X] as in Eq. (A8), Eq. (A7) becomes Eq. (1):
σm0[X]i=13w(SRTi)σm0[Xi].
By substituting Eq. (A3) for i = 1–3 into Eq. (A5), Eq. (A9) is obtained:
A(SRT)=Ap+Anp[P]{i=13w(SRTi)Anp[Xi]}σe0[P]+{i=13w(SRTi)σe0[Xi]}.
By defining Anp[X] and σe0[X] as in the following equations, Eq. (A9) becomes Eq. (6):
Anp[X]i=13w(SRTi)Anp[Xi]
and
σe0[X]i=13w(SRTi)σe0[Xi].

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