Using TRMM Latent Heat as a Source to Estimate Convection Induced Gravity Wave Momentum Flux in the Lower Stratosphere

Due to a lack of observations, it is a big challenge to quantify the momentum flux transported from the troposphere into the lower stratosphere by gravity waves generated by convection. This limits our understanding of the dynamics of general circulation in the stratosphere and the realism of simulations of the Quasi Biennial Oscillation. In the past decade, some general circulation models have linked the momentum flux to the latent heating from subgrid scale convective precipitation with some success. However, there is still a large uncertainty in the sources of subgrid scale convection in these models. This study applies the links between the momentum flux and convective latent heating directly to the convective precipitation derived from 16 years of TRMM precipitation radar observations in the tropics and subtropics. The total and directional momentum flux at 100 hPa are derived at individual convective pixels by using the TRMM Spectrum Latent Heating product and large‐scale wind profiles from the ERA‐Interim dataset. For the first time, we are able to estimate the geographical distribution of momentum flux at 100 hPa in tropics and subtropics from the observed convective sources. The diurnal, seasonal, and interannual variations of the derived momentum flux are presented and discussed. These results could provide a reference to validate the dynamic coupling between the tropical troposphere and the stratosphere in the general circulation models.

launch of the first spaceborne precipitation radar onboard the Tropical Rainfall Measuring Mission (TRMM, Kummerow et al., 1998) in late 1997, the global convection in tropics and subtropics has been examined with unprecedented detail. Specifically, they have been analyzed in their intensity (Zipser et al., 2006), vertical structure (Houze et al., 2015), latent heat release (Shige et al., 2004;Tao et al., 2006), and variations at different time scales (e.g. Nesbitt & Zipser, 2003;Liu et al., 2019). During 16+ years of operation from December 1997 to September 2014, the TRMM precipitation radar has collected a significant number of observations and derived characteristics of precipitation and convection within 36°S-36°N. The instantaneous measurements provide the best available estimates of sources of convective gravity waves.
In this study, we have designed a method to apply a physically-based convective gravity wave source parameterization scheme (Beres et al., 2004(Beres et al., , 2005 from the Whole Atmosphere Community Climate Model Version 6 (WACCM6, Gettelman et al., 2019) to the TRMM products. Using this method, we are able to estimate the MF within the limits of the gravity wave parameterization from TRMM convective gravity wave sources in tropics and subtropics (Alexander et al., 2021) and attempt to address the following questions: 1. What is the geographical distribution of convective gravity wave sources? How much MF is contributed by convection over different regions in the tropics and subtropics? 2. What are the different contributions of shallow or deep convection to the total MF in the lower stratosphere in tropics and subtropics? How are properties of convection related to their MF contributions? 3. How do directional components of MF in the lower stratosphere vary over different regions and different time scales, such as diurnally, seasonally, and interannually? 4. What are the uncertainties in the convective gravity wave sources from observations and parameterization schemes in GCMs?
In the following sections, the physical basis of the MF parameterization, data and methodology used in this study are introduced first in Section 2. Then, the global MF near the tropopause in tropics and subtropics are estimated by applying the WACCM6 parameterization scheme to 16-year TRMM convective sources. Spatial and temporal variations of the MF are presented in Section 3. The uncertainty in these analyses are discussed in Section 4, and the major findings are summarized in Section 5.

Data and Methodology
In WACCM6, the parameterization scheme of MF from convective gravity wave sources follows the line of study by Beres et al., (2004Beres et al., ( , 2005 and Richter et al., (2010). This scheme utilizes the subgrid scale Latent Heating rates (LH) in the model to estimate MF. However, the cloud LH is difficult to measure in reality. Therefore, assumptions of LH properties in convection and their large-scale environments have to be made in order to apply the parameterization scheme to the TRMM datasets.

Estimation of Momentum Flux Using a Simple Lookup Table Approach
As described in Beres et al. (2005), the wave source spectrum can be calculated at the top of the heating region of convection as a two-dimensional MF spectrum in frequency and wavenumber. In practice, the calculation of momentum flux can be simplified by introducing a predefined lookup table in Equation 1.
where h is LH depth, v r is relative mean wind from the layer of LH to 700 hPa, v p is phase speed, Q is the maximum latent heating rate, and LT(ℎ, , ) is the predefined lookup table by integrating the wave spectra. Here the mean wind of heating layer is calculated by averaging the wind with positive LH. The steering wind at 700 hPa is assumed to describe the motion of convection. vr is projected wind vector from heating layer to the convection motion.
To build the lookup table LT(ℎ, , ) , a few key parameters are needed, including heating frequency distribution, horizontal scale, depth of the heating, and the mean wind vector in the heating region. In WACCM6, the horizontal scales of convective cells within the convective region is assumed to be 3 km in diameter. A red-noise frequency distribution for wave periods between 10 and 120 min is also assumed. The lookup table is created as Writing -review & editing: Joan Alexander, Jadwiga Richter, Julio Bacmeister discrete set of phase speeds ranging from ±100 ms −1 with 2.5 ms −1 intervals, mean relative LH layer wind with values ranging from ±40 ms −1 with 1 ms −1 intervals, and heating depth with values ranging from 1-20 km with 1 km intervals. An example of the lookup table F LT in Equation 1 is shown in Figure 1. Compared to the deep heating profiles (Figure 1d), shallower convective heating depth (Figures 1a-1c) would have larger wave MF at lower phase speed. As expected, mean relative wind would determine the directional variation in the momentum flux. This lookup table is implemented in the current WACCM6 to parameterize the MF by using model derived latent heating profiles after assuming a sub-grid areal fraction of convection.

TRMM Convective Latent Heat and ERA-Interim Large-Scale Wind Fields
TRMM was launched in 1997 with the first space born Precipitation Radar (PR) onboard (Kummerow et al., 1998). Before the end of mission in 2014, TRMM PR had collected the radar reflectivity at a resolution with 4.5 km in horizontal and 250 m in vertical describing vertical structure of precipitation in detail. With about 17 years of observation from non-sun synchronous orbit between 36°S-36°N, it provided a robust measurement of properties of convection and precipitation and their diurnal, seasonal and interannual variations in tropics and subtropics (e.g., Houze et al., 2015;Liu, 2011;Liu and Zipser, 2008). To provide the latent heating in observed convective cells, the version 7 pixel-level TRMM Spectral Latent Heating (SLH) dataset during 1998-2013 is used. In this product, the latent heating profile is derived by using the convective precipitation rates (Iguchi et al., 2000 and radar echo top height. Here precipitation rate is used to define the heating strength, and the echo top height is used to constrain the heating depth. Based on the precipitation types, different lookup tables are applied to the pixels with convective and stratiform precipitation separately. The convective and stratiform precipitation types are differentiated by examining the horizontal and vertical gradients of radar reflectivity as well as the presence of the reflectivity bright band (Awaka et al., 1998). The lookup tables relating precipitation rates and echo top heights to latent heating profiles are built based on the cloud resolving model simulations of a few field campaigns. Details of the SLH retrieval algorithm are described in Shige et al., (2004Shige et al., ( , 2009. As a hybrid approach of using simulated LH vertical structure constrained by observations, this product has been used to derive the global LH vertical structures statistically (Liu et al., 2015;Takayabu et al., 2010;Tao et al., 2016). However, at each individual pixel level, there could still be a large uncertainty in the instantaneous LH profile due to the assumptions made in the retrieval algorithm. We will revisit the uncertainties in the LH retrievals in Section 4.
In this study, the SLH latent heating profiles with 1 km vertical resolution at pixels with convective precipitation during 1998-2013 are used. At each pixel with convective precipitation, the maximum latent heating values (Q) are calculated from the LH profiles. To determine the V r in Equation 1, large-scale wind vector profiles are temporally interpolated from 6 hourly wind field in ERA-Interim reanalysis dataset (Dee et al., 2011) from the nearest 0.75° × 0.75° grid. Then the mean wind vectors in the layer with positive LH values, at 100 hPa, and 700 hPa are saved for each pixel. To apply the lookup table LT(ℎ, , ) in Equation 1 to the TRMM convective pixels, the difference in the assumption of convection size has to be addressed. TRMM PR have footprint size about 4.5 km, which is larger than the 3 km size assumed in the lookup table from WACCM. Therefore, the difference in area factor 2.2 has been used when applying the lookup table.
The geographical distribution of the population of more than 3 × 10 8 TRMM SLH profiles with convective precipitation over the course of 16 years is shown in Figure 2a. A large number of profile samples is adequate to generate robust statistics on 1° × 1° grids in tropics and subtropics. Note that there are more profile samples near 32°N/S latitudes due to the TRMM orbital inclination. This sample bias is removed from all the convection and gravity wave statistics in this study after normalizing by the total sampled pixels or by averaging. The geographical distributions of mean LH depth, and maximum LH in the profile on 1° × 1° grids are shown in Figures 2b and 2c. It is well known that convection over land tends to be stronger than over ocean (e.g., Zipser et al., 2006). There are numerous isolated shallow convective clouds over ocean (Liu & Zipser, 2009;Schumacher & Houze, 2003), whereas shallow convection can only be frequently found in specific regions over land, such as the Amazon and maritime continents. Most convection over tropical and subtropical land reach above the freezing level and have ice hydrometers. In general, this leads to a deeper convective heating layer and a stronger heating over land than over ocean, especially over the "hotspot" regions with the most intense convection, that is, central Africa, Southeast United States, Argentina etc. (Figures 2b and 2c).
The wind field plays a significant role in translating the convective latent heating to the gravity wave MF into the lower stratosphere. In the Inter-Tropical-Convergence-Zone (ITCZ), easterly wind is dominant in the lower troposphere, except over the north Indian Ocean (Figures 2b and 2d). At mid latitude, westerly wind is dominant. In addition to the regions with strong meridional trade winds, the 700 hPa wind determines the directional components of the total MF.

Results
After applying the MF lookup table to TRMM convective latent heating properties and ERA-Interim wind vectors, convective gravity wave MF at different phase speeds in four different directions at 100 hPa are derived at more than 3 × 10 8 convective pixels from 1998-2013.

Geographical Distribution of Convective Gravity Wave MF
The geographical distribution of mean MF at 100 hPa on 1° × 1° grids are summarized in Figure 3. First, the total amount of absolute MF is integrated from full phase speed spectra at four directions on each 1° × 1° grid. The conditional mean MF ( Figure 3b) is calculated by dividing the total number of convective samples at each grid. The unconditional mean MF ( Figure 3a) is calculated by dividing the total number of Ku radar pixel samples at each grid, including samples of non-precipitating pixels and those with non-convective precipitation. The distribution of the annual unconditional MF is close to the distribution of total annual convective precipitation in the literature (e.g., Houze et al., 2015;Schumacher & Houze, 2003), and similar to the map of total convective pixels in Figure 2a. There is a larger MF in the ITCZ and the South Pacific Convergence Zone (SPCZ) as well as over a few warm ocean currents, e.g. the Gulf Stream in the west edge of North Atlantic and the Kurishio current in the west edge of the North Pacific. The distribution of conditional MF in Figure 3b is close to the distribution of mean maximum latent heating rate in Figure 2c. Mean conditional MF is generally larger over land, where the maximum latent heating is also larger, than it is over ocean.

Directional Convective Gravity Wave MF
The geographical distribution of components of unconditional MF at 100 hPa in four cardinal directions are shown in Figure 4. In the tropics, the eastward MF has the largest magnitude. This is corresponding to the prevalent heating layer easterly wind environment of the tropics (Figure 2b). Figure 1 showed that for deeper convective cells, momentum fluxes tend to be enhanced in the direction opposite to the flow. In the subtropics, westward MF is stronger (Figure 4b), corresponding to the dominant westerly wind environment at these latitudes. The meridional MFs at 100 hPa have relatively lower magnitudes compared to the east and westward MFs, which is associated with more frequent occurrences of zonally directed 700 hPa winds. In the tropics, a larger total 6 of 18 meridional MF is found over the Maritime continents and Panama area. This is due to the combination of frequent relatively intense convection ( Figure 2c) as well as the meridional flow steered by land and ocean interaction over these regions (Figure 2b). In the subtropics, larger meridional MF are found over the regions with warm ocean currents, for example, southward over the Gulf Stream and Kuroshio current (Figure 4d), and are populated with low level jets, e.g. over the plains east of the Rockies and Andes mountains. Both the main meridional flow and convection are stronger over these areas than over other places in spring and summer.
The geographical distribution of mean directional MF per convective cell (conditional MF) is shown in Figure 5. In the tropics, the intense convection in central Africa and Sahel is the most efficient at generating eastward MF at 100 hPa due to the large latent heating rate (Figures 2c, 3b and 5a, 5b). In the subtropics, intense convection occurs over warm currents and down slopes of major mountains where larger conditional westward MFs are found, including the southeastern US, Argentina, and the south slope of the Himalayas. Although the SPCZ has a large total MF (Figures 3a and 4), a larger mean westward and northward conditional MF is found south of the main SPCZ region (Figures 3b and 5). This is consistent with a relatively stronger convective heating ( Figure 2c) and shallower heating depth (Figure 2b) over this region than over the main SPCZ region.
The geographical distributions of the total zonal (eastward-westward) and meridional (northward-southward) MF are shown in Figure 6. The zonal MF transport into the stratosphere is important in forcing the QBO in the tropics. It is clear that eastward MF dominates over the tropics in the 16-year mean (Figure 6a), with the exception of a small area of larger westward MF over the north Indian Ocean. The tropical eastward MF is on average about 20% larger than the westward MF. Model studies suggest that about half of the total forcing of the eastward QBO phase is by planetary scale Kelvin waves, with the other half of the forcing by gravity waves, while the forcing of the westward QBO phase is dominated by gravity waves. So the east-west asymmetry in the MF in Figure 6a appears to have the wrong sign. As pointed out in Alexander et al., (2021), other gravity wave components are probably needed to compensate for the eastward dominance in the current calculation, such as the stationary wave MF.
Regarding the meridional MF, subtropical MF mostly points toward the equator. In the tropics, northward MF is more prevalent, especially over the Sahel and India, which is driven by the summer monsoon circulations (Hahn & Manabe, 1975;Parker et al., 2005).
We further examine tropical convection of various depths and their contributions to the total MF in Figure 7.
In the tropics (20°S-20°N), more convective cells (79.3%) occur over ocean than over land mainly due to the 71% ocean coverage of the globe. Over tropical ocean, shallow convection with echo top height below 4.5 km, a height around 0°C, is more frequent than the convection with ice that is indicated by the echo top height above the freezing level (Figure 7a). Over land, more convective cells include ice processes. In general, convection that develops deeper and lifts hydrometeors above the freezing level are more intense and have relatively larger latent heating rate and higher surface precipitation rate than shallow convection. Though less frequent than shallow convection, convection with echo top height above freezing level around 6-8 km contribute to a larger proportion of the total MF in the lower stratosphere (Figure 7b). There are numerous samples of shallow convection over ocean. They have a significant contribution to the westward MF, which could be very important for understanding how waves drive QBO. Though there are more deep convective pixels with radar echo top reaching above 12 km over land than over ocean, they do not contribute a dominant portion of the net east and west MF. This is somewhat surprising since the deep convection over land is associated with stronger gravity waves that are detectable in the mid-upper stratosphere from satellites (e.g., Ern et al., 2018;Hoffmann et al., 2013;Hoffmann & Alexander, 2009). Here the MF shown in Figure 7 are analyzed at 100 hPa. This may be due in part to satellite observational filters and limited local time coverage, but also shallower clouds may be associated with slower phase speed waves that more often dissipate below the satellite observation levels.

Diurnal Variation
It is well known that convection has a distinct diurnal variation over land and a weak variation over ocean (Gray & Jacobson, 1977;Hall & Vonder Haar, 1999;Liu & Zipser, 2009;Nesbitt & Zipser, 2003). Consequently, diurnal variation of the convective gravity wave MF is anticipated. However, the diurnal variations of the eastward and 10.1029/2021JD035785 9 of 18 westward MF could be quite different from the convective latent heating. This is because wind vectors change diurnally over some specific regions, especially near mountains (e.g. Banta et al., 2004) and coasts (e.g. Miller et al., 2003). As shown in Figure 8, an obvious peak of high MF in the early afternoon around 1,500 LT is found over tropical land, which corresponds to the numerous isolated and early stages of organized convection over land. Note that this peak is prior to the late afternoon peaks around 1,700 LT in cold clouds, when organized convective systems mature (Liu & Zipser, 2008). In the tropics as a whole, the diurnal variation of the total eastward and westward MF is relatively weak due to the dominance of the oceanic convection, which varies only slightly at different times of the day. Though only covering 29% of the area in the tropics, land has a total amount MF that is comparable to MF of the ocean in 1,400-1,700 LT. Therefore, the late afternoon peak at 1,400-1,500 LT appears in the diurnal variation of total MF in tropics in Figure 8a.

Seasonal Variation
In order to compare to the previous study of Richter et al., (2010) and examine differences by using the observed convective sources and reanalysis wind fields, the mean unconditional MFs from 16-year TRMM convective pixels are calculated as a function of month and latitude. This is shown in Figure 9. The pattern of MF seasonal-latitudinal variation is close to the result from WACCM3.5 (i.e., Figure 2 of Richter et al., 2010) with a few significant differences. First, the magnitude of the MF is about ∼50% weaker than the result of WACCM3.5. Compared to Richter et al., (2010), results from TRMM show earlier seasonal peaks in all directions, for example, TRMM eastward MF peaks in June vs. WACCM in July. Similar patterns are observed from TRMM vs. WAC-CM, respectively: westward in May-June vs. June-July, northward in August-September vs. September-October, southward in August vs. September. Results using TRMM do not show a clear strip of MF south of equator as WACCM does, which is likely from the known issue of an exaggerated secondary ITCZ in general circulation models (Lin, 2007). It is important to understand the regional contributions of eastward and westward MFs and their seasonal variations in the tropics. The mean unconditional MF as a function of month and longitude between 20°S-20°N is shown in Figure 10.

Interannual Variation
The QBO has been recognized as having links to the ENSO cycles (Gray et al., 1992). To interpret interannual variation in MF, the variation of zonal circulation in tropical troposphere could be crucial. Interannual variation of zonal winds and convection may directly modulate the MF (Alexander et al., 2017). During the 16+ year TRMM era, there are several ENSO cycles that are closely tied to the strength of Walker circulation (Power & Smith, 2007), including strong ENSO cycles in 1998-2011. This provides enough samples to examine the general differences in convection and precipitation between two ENSO phases (e.g., Liu et al., 2019). Using the multi-variational ENSO index (Wolter & Timlin, 2011), we selected three Januarys with the highest positive and the lowest negative index values and repeated the process for February through December as shown in Figure 11. Then, the mean eastward and westward MF and their differences as a function of month and longitude are calculated from 36 months of data in two different ENSO phases. Compared to the westward MF, the eastward MF is stronger over maritime continents in the La Nina phase when a stronger Walker circulation is driven by the warmer west Pacific and relatively cold east Pacific. In consistence with literature, convection is more active over South America under La Nina. During the El Nino phase, westward MF is more comparable to the eastward MF, especially during January-April.

Uncertainties and Comparison to WACCM6
Using TRMM observations, we are able to estimate MF at 100 hPa in tropics and subtropics and examine the variation of MF at different time scales. However, there are many assumptions in the calculations that should be mitigated to understand the uncertainties in these results.

Uncertainties in the Implementation of Beres' Method
In this study, we used a lookup table created for the WACCM to estimate the MF. There are several assumptions built in this lookup table. First, the size of the convective cell is assumed to be 3 km. This is somewhat comparable to the TRMM PR footprint (∼4.5 km), and it is taken into account by an area adjustment factor. However, the size of the updraft cores varies significantly from sub kilometer in single cells to 7-10 km in super cells ( Giangrande et al., 2013;Heymsfield et al., 2010). It is questionable that a universal size of convection can represent the variation of convection and their intensity.
Westward MF is found relatively weaker than eastward MF in the current estimation from TRMM. Based on Figure 7b, the shallow convection over tropical ocean would contribute to a substantial westward MF. This may point to the key role of shallow convection. Note that TRMM PR can only detect radar reflectivity above 18 dBZ. It misses all of the cumulus clouds without precipitation size hydrometeors (Lebsock & L'Ecuyer, 2011). Because most of these cumulus clouds are shallow, they may have large MF contributions. This raises a question whether observations sensitive to small cloud droplets, such as from CloudSat, should be used to include weak cloud systems in the MF calculation. This makes it more difficult to understand the directional MF transport into the stratosphere necessary to interpret the QBO.

Uncertainties in the Convective Latent Heating Data
Only the TRMM PR pixels with convective type precipitation are used in this study. The algorithm to separate convective and stratiform precipitation types (Awaka et al., 1998;Awaka et al., 2009) relies on the detection of the 13 of 18 bright band from the horizontal and vertical gradients of radar reflectivity values. It is not always accurate over some specific regions (Funk and Schumacher 2013). However, the misclassification of convective precipitation should not be significant in this study at a global scale.
Because latent heat releases when hydrometeors form and grow, the radar observed hydrometeors with larger precipitation sizes must have a time lag from the heat release. Because of this time lag, the location of radar echo can be mismatched from when and where the latent heating occurs. The retrievals at each satellite pixel may not necessarily represent the true instantaneous latent heating rate. Especially, the heating rate in intense convection can be underestimated at pixels because most of the hydrometeors lifted by intense updrafts would fall at a different location. There is an inequality between the surface convective precipitation and latent heat release through the strong updraft cores at pixel level. This may lead to an underestimated MF from deep convection. Note that deep convection contributes more to the eastward MF (Figure 7b). If the contribution of MF from deep convection is enhanced, the eastward MF would be even stronger.

Uncertainties in the Wind Field
Wind field directly determines the direction of MF transport into the stratosphere. In this study, we interpolated 0.75°, 6 hourly ERA-Interim U and V components at pressure levels to the time and location of TRMM convective pixels to describe the wind field at 100 hPa, steering wind at 700 hPa, and mean wind through the heating depth. It is well known that wind shear at low levels plays an important role in the intense convection (Weisman & Klemp, 1982;Weisman & Rotunno, 2000). The moist transport by low-level jets of different depths is one key feature for intense convection over different hotspot regions around the world (Liu et al., 2020

Comparison to WACCM6
Keeping all above uncertainties in mind, the objective of this study is to build an observation-driven dataset to diagnose, validate, and understand the weaknesses of the parameterization of convective gravity wave momentum flux in GCMs. A comparison of the mean annual total MFs at 100 hPa in 2010 generated by WACCM6 and TRMM is shown in Figure 12. There are several obvious regional differences between WACCM6 and TRMM. Near Panama and Indonesia, WACCM6 have generated much larger MF than TRMM (Figure 12a). WACCM6 underestimates the MF over the central Amazon and central Africa, but overestimates the MF over the Brazilian high plains compared to what TRMM estimates. Sharing the same problem of exaggerated double ITCZ by GCMs (Lin, 2007;Zhang et al., 2019), WACCM6 generates a secondary ITCZ near the equator and a weaker ITCZ over the central and west Pacific (Figure 12a) than what TRMM suggests ( Figure 12b). It is important to note that WACCM6 does not produce much MF in the subtropics due to tapering convective gravity waves to zeros by 30° latitude. Therefore, on average, WACCM6 has smaller MF transport in the tropics than what TRMM estimates (Table 1). Though there are many different ways to diagnose the differences between the WACCM6 and TRMM, the detailed comparisons between WACCM6 and TRMM calculations warrants a separate study.

Summary
After applying WACCM6 convective gravity wave MF parameterization to the TRMM observed 16-year convection sources, gravity wave momentum flux in the lower stratosphere is estimated globally over the tropics and the subtropics. The major findings include: 1. 16 years of TRMM observations describe the variations of convection in the tropics and the subtropics well. The latent heat retrievals from TRMM observations can be used to estimate the momentum transport into the lower stratosphere by gravity waves associated with convection. This could provide a tool to validate the parameterization of momentum transport by convection at different time scales. 2. Based on the current WACCM convective gravity wave parameterization, the magnitude of MF from convection is related to the depth and magnitude of latent heating rate, the wind vectors in the heating layer, and the horizontal motion of convection. Mean conditional MF is generally larger over land than over ocean, mainly due to the larger latent heating rates. 3. There are still large differences in the convective gravity wave momentum flux between TRMM and WAC-CM6. In addition to the different latent heat rates along with the precipitation amount between the two, the differences in wind circulation around convection could be another factor. 4. Uncertainty of TRMM MF calculation may be from the assumptions in the model parameterization and the simplification of Equation 1, from inaccurate wind field due to coarse temporal and spatial resolution of reanalysis data, regional circulation errors associated with mismatch between reanalyzed precipitation and TRMM precipitation, and from TRMM LH retrievals. Further study is needed to quantify these uncertainties.

Data Availability Statement
Many thanks to the Precipitation Processing System (PPS) team at NASA Goddard Space Flight Center for data processing assistance. All TRMM SLH data can be downloaded at https://pps.gsfc.nasa.gov/; ERA-Interim reanalysis product is available from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era-interim.