LH is not easily measured, as it is almost impossible to single out temperature changes by means of phase changes from the total observed temperature changes. However, heat and moisture budget studies have been conducted using sounding networks in field campaigns, where apparent heat sources (Q1) and apparent moisture sinks (Q2) from the budget study can be expressed as a function of LH (Yanai et al., 1973; Johnson, 1984; Demott, 1996). LH can then be calculated using a diagnostic heat budget method, which was first presented by Yanai et al. (1973) (Tao et al., 2006). Over a certain horizontal area, Q1 can be expressed through the equation below, which includes LH (Tao et al., 2006): 1Q1-QR=π‾-1ρ‾∂ρ‾w′θ∂z‾-∇•V′θ′‾+1cpLvc-e+Lff-m+Ls(d-s), where prime denotes deviations from horizontal averages, which are denoted by an upper bar. QR is the radiative heating rate; θ is the potential temperature; π is the non-dimensional pressure; ρ is the air density; cp is the specific heat at constant pressure; and R is the gas constant for dry air. Lv, Lf, and Ls represent the latent heats of condensation, freezing, and sublimation, while c, e, f, m, d, and s represent each microphysical process of condensation, evaporation, freezing, melting, deposition, and sublimation, respectively. The last six terms on the right-hand side of Eq. () represent the processes responsible for LH. Since Q1 can be obtained using vertical profiles of temperature, moisture, and wind data measured during field campaigns (Tao et al., 2006), the observed Q1 is used to indirectly validate GPM LH products that are retrieved together with Q1.

LH is fundamentally a temperature change resulting from the phase change of water in the atmosphere. Given the difficulties associated with measuring temperature change where condensation is occurring, further attributing those temperature changes to phase changes is not possible on a regular basis. Instead, many methods rely on the detection of hydrometeors, generally from microwave sensors, and then inferring LH from the hydrometeors. Precipitation observed from microwave sensors and latent heating are closely related, but since hydrometeors are created through condensation, LH derived from a microwave sensor is actually LH that is released at an earlier location before the observation time. Nonetheless, because LH products from ground- or space-based radars and radiometers can be routinely generated over broad scales, the advantages outweigh some of the time and space mismatches.

The DPR has two operational LH algorithms: CSH and SLH. In the GPM products, LH is provided along with additional variables: Q1–QR and Q2 in SLH and Q1–QR-LH, QR, and Q2 in CSH as well as the rain type (Tao et al., 2019). These algorithms were first developed for TRMM data but have been adapted to GPM data. Both algorithms use cloud-resolving model simulations to create LUTs relating hydrometeor profiles to modeled heating rates. Although there is no direct measurement for LH to validate the results, retrieved Q1 and Q2 are compared with sounding data from various field campaigns through the method mentioned in Sect. 2.1. The evolution of these products is well summarized in (Levizzani et al., 2020), but each algorithm is briefly explained here for completeness.

The CSH algorithm was first introduced by Tao et al. (1993). The initial algorithm by Tao et al. (1993) used surface rainfall rate and amount of stratiform rain as inputs to an LUT that was generated from a number of representative cloud model simulations. This LUT has since been improved by increasing the number of simulations, using finer resolutions in simulations, and adding new variables such as echo top heights and low-level vertical reflectivity gradients (Tao et al., 2019). For high-latitude regions observed by the GPM satellite, new LUTs have been created with simulations from the NASA Unified Weather Research and Forecasting model, which is known to be suitable for high-latitude weather systems (Levizzani et al., 2020). This new LUT uses surface rainfall rate, maximum reflectivity height, freezing level height, echo top height, decreasing flag (whether or not reflectivity values drop by more than 10 dBZ toward the surface), and maximum reflectivity intensity (Tao et al., 2019) to select the appropriate LH profile.

The SLH algorithm is based on the work of Shige et al. (2004, 2007). For tropical regions, the LUT is created from cloud-resolving model simulations for three different rain types: convective, shallow stratiform, and anvil (or deep stratiform) clouds. Inputs to the LUT are precipitation top height (PTH), precipitation rate at the surface (Ps), precipitation rate at the level that separates upper-level heating and lower-level heating (Pf), and precipitation at the melting level (Pm). Once non-convective rain is separated into either shallow stratiform or anvil types, a vertical profile for an anvil cloud is chosen based on Pm, and the magnitudes of upper-level heating and lower-level cooling are normalized by Pm and (Pm–Ps), respectively. For convective and shallow stratiform clouds, a vertical profile corresponding to the PTH is chosen, and then upper-level heating and lower-level heating are normalized by Pf and Ps, respectively. The DPR uses a new LUT created for mid and higher latitudes to account for expanded latitudinal coverage by GPM. Cloud in higher latitude regions is classified into six precipitation types: convective, shallow stratiform, three types of deep stratiform, and other. This creates six LUTs that provide LH as a function of precipitation type, PTH, precipitation bottom height, maximum precipitation, and Ps.

Figure 1 shows monthly gridded products from these two algorithms over CONUS for July of 2020 at three different heights as well as their vertically integrated heating rates. The overall horizontal patterns of the two products look similar, but there is a difference in the vertical distributions. At 2 or 5 km, CSH tends to show higher heating rates than SLH, while at 10 km, SLH shows higher heating rates than CSH. In addition, SLH tends to have larger cooling rates throughout. If integrated over the whole of the vertical layers, CSH tends to show higher heating rates in general. These discrepancies can be attributed to different configuration setups, such as the microphysical scheme used to run simulations for the LUT. The results demonstrate that the vertical profiles of LH are highly dependent on the simulations that generate the LUT as well as on different inputs to the LUTs.

Orbital data for these products are provided at the pixel scale (5 km), and although results may be interpreted as “instantaneous” LH, the temporal resolution from low-Earth orbit is too coarse to have much impact on regional forecast models that are initialized hourly if not more frequently.

In the operational HRRR model, LH profiles retrieved using radar reflectivity replace modeled LH profiles, which helps initiate convection at the appropriate locations. LH profiles in this case are constructed using a simple empirical formula that converts radar reflectivity to LH. In Eq. (2), reflectivity is converted to potential temperature tendency using a model pressure field. This equation is only applied when radar reflectivity exceeds 28 dBZ. The threshold of 28 dBZ was chosen based on the effectiveness of adding heating from reflectivity in HRRR (Bytheway et al., 2017). 2Tten=1000pRd/cpd(Lv+Lf)Qsn•cpdwhereQs=1.5×10z/17.8264083, where z is the grid radar and lightning proxy reflectivity; Tten is the temperature tendency; p is the background pressure (hPa); Rd is the specific gas constant for dry air; cpd is the specific heat of dry air at constant pressure; Lv is the latent heat of vaporization at 0 ∘C; Lf is the latent heat of fusion at 0 ∘C; and n is the number of forward-integration steps of digital filter initialization. Tten in Eq. (2) is produced in K s-1 to meet the needs during the short-term forecast. Although heating rate is not a general output of the forecast model, it is calculated at every time step by dividing the temperature change from the microphysical scheme by the time step, which is usually on the order of few tens of seconds. Therefore, this empirical formula is developed to produce LH consistent with the model framework so that added LH does not produce computational instabilities when ingested.

In order to make an LUT for LH profiles of convective clouds, convective grid points need to be defined in the model simulation. Convection can be defined in several different ways depending on the variables available, but the most direct and accurate way of defining it is to use vertical velocity (Zipser and Lutz, 1994; LeMone and Zipser, 1980; Xu and Randall, 2001; Houze, 1997; Steiner et al., 1995; Del Genio et al., 2012; Wu et al., 2009). Steiner et al. (1995) and Houze (1997) suggested that convective regions tend to have vertical velocity greater than 1 ms-1, and many previous studies that used vertical velocity to define convection used a threshold of 1 ms-1 (LeMone and Zipser, 1980; Xu and Randall, 2001; Wu et al., 2009). Similarly, this study uses a vertical velocity threshold to define the convective core, as it is one of the prognostic variables in the model simulations. However, in this study, a vertical velocity threshold is defined at the layer of maximum hydrometeor contents. This is intended to exclude potentially high values of negative vertical velocity that can occur at high levels in the cloud if evaporative cooling is present.

To establish the vertical velocity threshold in this study, several values are tested in order to match the convective fraction seen in the GOES-16 convection detection algorithm (described in Lee et al., 2021). The vertical velocity threshold whose convective fractions compared best to GOES-16 is chosen. The GOES-16 convection detection algorithm uses mesoscale sector data with one-minute intervals to detect convective regions from ABI imagery. Two separate detection methods are proposed: one for vertically growing clouds in their early stages, and one for mature convective clouds that move rather horizontally once they reach the tropopause and that often have overshooting tops. A detailed description of the methods can be found in Lee et al. (2021), but it is briefly explained here. The method for vertically growing clouds focuses on Tb decreases over 10 min for two water vapor channels. If the decrease is greater than the designated threshold (-0.5 K min-1 for channel 8 and -1.0 K min-1 for channel 10), it classifies the pixel as convective. For mature convective clouds, the method looks for grid points that have continuously high reflectance (reflectance greater than 0.8), low Tb (Tb less than 250 K), and lumpy cloud top (horizontal gradient values between 0.4 and 0.9) over 10 min. Lumpiness of the cloud top is calculated using the Sobel operator, which is commonly used for edge detection. These thresholds are chosen based on one month of data compared to “PrecipFlag” from the Multi-Radar Multi-Sensor System (MRMS), which classifies precipitation types by combining data from ground-based radar and rain gauge observations. Combining the two methods yielded false alarm rates of 14.4 % and a probability of detection of 45.3 % against the ground-based radar product, but 96.4 % of the false alarm cases were at least raining. Combining the two methods provides results comparable to the radar product, and these methods are rather simple and fast. These methods detect any type of convective region, and therefore, the analysis is conducted without distinguishing different types of convective clouds.

Table 1 shows convective fractions using the GOES-16 convection detecting algorithm and using different vertical velocity thresholds in the model outputs. Using higher thresholds can eliminate non-convective grid points, but at the same time, it will only include the strongest parts of the convective regions. Using a 1.5 m s-1 threshold shows a fractional area closest to the observed fraction; therefore, 1.5 m s-1 is used to define convection in the model output. This number is similar to values used in some previous modeling studies (1 m s-1 in LeMone and Zipser, 1980; Xu and Randall 2001; Wu et al., 2009) and in a satellite-based study (2–4 m s-1 in Luo et al., 2014).

Eleven convective cases are simulated using WRF to obtain enough samples to populate each cloud top temperature bin. The convective cases were chosen over CONUS within the NEXRAD network during May to August in 2017 and 2018. All simulations use the same configuration, shown in Table 2, and HRRR analysis data are used for initial and boundary conditions. All the convective cases are run from the start of any convective activity in the scene for at least several hours, depending on the longevity of convection in each case, and model outputs are collected every 10 min so that the LUT includes LH profiles at all stages and types of convection. However, the LUT is not divided into different types of convection, as it is hard to distinguish convective types from observations. One thing to note is that the magnitude of LH can vary depending on the model configuration, such as spatial resolution, time step, and microphysical scheme. This study uses the same model configuration as the HRRR model for all simulations, which avoids discrepancies in magnitude between the modeled LH and the derived LH that will be inserted into the forecast models. Tbs at 11.2 µm are calculated using the Community Radiative Transfer Model (CRTM). In each scene, convective grid points are defined by the threshold established in the previous section (1.5 m s-1), and LH profiles from the convective grid points with the same Tb from channel 14 are averaged to produce mean profiles for each Tb bin of the LUT. LH profiles included in the LUT are provided in K s-1, as for NEXRAD.

LH profiles of convective clouds from 11 WRF simulations are sorted into 16 bins based on the cloud top temperature at 11.2 µm. The 16 bins range from below 200 K to above 270 K, with a bin size of 5 K. Figure 2 shows the mean vertical profiles of LH in each bin. All profiles exhibit slightly negative LH near the ground due to evaporation, but positive LH is shown at most layers. It is also clear in the figure that, as the Tbs decreases, the profile stretches up in the vertical. Interestingly though, the maximum heating rate is not perfectly proportional to Tb. Considering the maximum LH that is allowed in the HRRR model, which is 0.01 K s-1, these values seem quite reasonable. Table 3 shows the mean surface precipitation rate for each bin. The precipitation rate is inversely proportional to Tb in Table 3. This is expected, as deeper and higher clouds tend to precipitate more. This provides more evidence that mean LH profiles for each bin can reasonably be obtained from GOES-16.

The LUT in Fig. 2 is used throughout the later sections, but it can be further divided with additional inputs. A decrease in the brightness temperature is one of the options, but it is not considered in this study for several reasons. Since clouds move over time, cloud advection adds uncertainty to the change in brightness temperature if calculated per pixel. To measure a robust brightness temperature decrease, the decrease can be calculated per cloud and not per pixel. However, LH profiles would have to be assigned for each cloud, and the assigned profile would be inconsistent with the observed cloud top temperature for each pixel. Therefore, using brightness temperature decreases as additional inputs to the LUT is not included in this study, and it remains a topic of inquiry for future studies. Instead, each cloud top temperature bin can be further divided according to composite radar reflectivity, and the additional LUT is presented in Appendix A. Composite reflectivity, if available, can be used to adjust the maximum intensity of LH profiles, as the SLH algorithm adjusts the amplitude by multiplying Ps and Pf. Although it is challenging to get the full vertical profile of radar reflectivity from GOES-16 data, there are algorithms developed to estimate composite reflectivity from GOES-16, such as GOES Radar Estimation via Machine Learning to Inform NWP (GREMLIN; Hilburn et al., 2021). Therefore, this additional LUT could be used along with such an estimator to assign LH profiles in more detail, but it is not used further in this study.

LH from three different instruments – GOES-16 ABI, NEXRAD, and GPM DPR – are examined in this section. Methods using GOES-16 and DPR products are similar in the sense that they use cloud top height or PTH to look for mean profiles in the LUT created with model simulations, although DPR has additional parameters such as surface rain rate, which is used to vary the magnitude of the heating rate. In contrast, NEXRAD uses an empirical formula to convert radar reflectivity to LH regardless of PTH. They are all instantaneous heating but are provided in different units. LH from GOES-16 and NEXRAD are in K s-1 to easily match with modeled heating rate, while DPR products are in K h-1. Therefore, LH in K h-1 from DPR products are converted to K s-1 for comparison.

A scene from 18 June 2019 is shown in Fig. 3 to compare the precipitation types (convective or stratiform) of the three products, as this is one of the major factors in estimating LH profiles. The regions with reflectivity greater than 28dBZ in Fig. 3a are regions where LH is estimated from NEXRAD reflectivity to be used in HRRR but not necessarily convective regions. Pink regions on top of the visible image at channel 2 (0.65 µm) in Fig. 3b are convective regions detected by GOES-16, and they represent the smallest convective areas relative to the other two methods. The number of convective grid points from each product after interpolating into the 3km-resolution WRF grid is presented in Table 4 for a quantitative comparison. Even though areal coverage differs by the methods, the locations of the convective cores matches well between the products.

Clouds in the colored boxes in Fig. 3 are all convective clouds but in different evolutional stages. Clouds in red, green, and blue boxes have high, low, and mid-level cloud top temperature, respectively. Since the three products have different spatial resolutions, LH profiles from NEXRAD, GOES-16, and CSH for these clouds are interpolated into the same WRF grid with a 3 km resolution for a direct comparison in Figs. 4, 5, and 6. CSH provides LH for both convective and stratiform regions; thus, the different colors of the lines in Figs. 4c, 5c, and 6c represent different cloud types. Lines with a light blue color are LH profiles of convective grid points, while the blue line is the mean of these profiles. Similarly, LH profiles of each stratiform gird point are in light green, while the mean of these profiles is in dark green. The mean of all LH profiles is colored in red. Convective LH profiles from CSH show heating throughout the vertical layers, as expected, except near the surface due to evaporation at lower levels. LH profiles in stratiform regions show cooling at low levels below a melting level and heating at levels above. LH profiles from GOES-16 (GOES LH) corresponding to the three convective clouds are shown in Figs. 4b, 5b, and 6b. When GOES LH and CSH are compared, the mean profile of convective LH from CSH (Figs. 4c, 5c, and 6c) is similar to GOES LH in blue (Figs. 4b, 5b, and 6b), both in terms of the magnitude and the vertical shape.

In contrast, LH from NEXRAD (NEXRAD LH) shows a different vertical profile than GOES LH and CSH, which both use the LUT consisting of model simulations. GOES LH and CSH peak around the middle of the atmosphere, while the NEXRAD LH in the convective core tends to peak at low levels where radar reflectivity is high (Figs. 4a, 5a, and 6a). At low levels where model simulations have cooling, NEXRAD LH does not show cooling due to Eq. (2), which is designed to only produce positive values. This heating at lower levels induces convergence in the lower atmosphere and divergence in the upper atmosphere, and thus, convection can be effectively initiated from the added heating.

Although their vertical shapes are different, the magnitude of the NEXRAD LH is similar to the other products. Overall values of the mean convective LH profiles from NEXRAD in blue are slightly smaller than the mean convective profile of GOES LH and CSH (blue line) but are closer to the total mean profile of CSH (red line), which indicates that the 28dBZ threshold might include some stratiform regions as well. The smaller mean of the NEXRAD LH is mainly attributed to anvil regions where reflectivity is greater than 28 dBZ, which only exist at a few vertical layers, with reflectivity being equal to 0 dBZ elsewhere.

Even though the mean NEXRAD LH is smaller, the total LH for the region can be similar when it is summed up over the region due to the broader area determined by the threshold of 28 dBZ in Fig. 3a relative to that of GOES-16 (Fig. 3b). Therefore, the total LH of each cloud is again compared between the three products (Table 5). Here, “total LH” is defined as the vertically and horizontally integrated LH over each convective cloud. This comparison is intended to account for differences in the area and for convective definitions that make direct comparison between vertical levels difficult. In addition, comparing combined values will be meaningful, as those are the values that will be used to initiate each convective cloud. Table 5 shows that the total LH from CSH tends to be higher than that from the other two products, while the total LH is shown to be similar between NEXRAD and GOES-16, although GOES LH is slightly larger. Despite the smaller mean of NEXRAD LH that was shown in Figs. 4, 5, and 6, it shows a good agreement with GOES LH in total heating.

The case study from Sect. 4.1 is presented to show how the vertical structure of GOES LH compares to other radar products. In this section, three months of data from May, June, and July of 2020 are used to compare total LH for convective clouds between GOES-16 and NEXRAD. Total LH used in this section is, again, vertically and horizontally integrated over each convective cloud. Both GOES-16 brightness temperature and NEXRAD reflectivity are resampled to the 3 km HRRR grid for a direct comparison and are compared under several conditions that the HRRR model uses to avoid disruption in the existing model physics. During the convective initiation step in the HRRR model, LH is calculated from NEXRAD radar reflectivity following Eq. (2) if the layer is cloudy, is under the GOES cloud top (using level 2 cloud top pressure data), is above the planetary boundary layer, and has a temperature less than 277.15 K. Additionally, LH is calculated for temperatures greater than 277.15 K only if the corresponding reflectivity exceeds 28 dBZ.

GOES LH is calculated with the same criteria described above, except for the additional 28 dBZ categorization. Adjacent convective grid points by the detection algorithm are clustered to define a convective cloud. In order to minimize errors coming from different definitions of convection in GOES and NEXRAD, total LH is compared only in clouds where both NEXRAD and GOES detect convection. Since the area defined as convective cloud tends to be wider in NEXRAD than in GOES-16 and since one convective cloud from NEXRAD tends to include multiple convective cloud systems defined by GOES, the comparison is done by combining all convective clouds from GOES-16 that overlap with each convective cloud by NEXRAD. Regions with low radar quality, as indicated by the radar quality flag, are excluded in the analysis.

Among the 4045 convective clouds collected during the three months of the analysis, only 2660 convective clouds are within reasonable range of each other in both GOES-16 and NEXRAD. Here, we define “reasonable range” as follows: the number of convective grid points from GOES-16 does not exceed 5 times that of NEXRAD, and vice versa. A total of 2660 clouds are selected, and the total LH for these clouds from both GOES-16 and NEXRAD is fitted to a linear regression model. Figure 7 shows a scatter plot of NEXRAD LH and GOES LH for each convective cloud using log–log space. A decent correlation coefficient of 0.83 is obtained between NEXRAD LH and GOES LH in Fig. 7. In most cases, large discrepancies in total LH seem to be caused by a corresponding discrepancy in the number of convective grid points, which is inevitable, but overall, the total LH values seem to agree well if the number of convective grid points is similar.