1. Introduction
Warm-rain processes are common over the open oceans and have important effects on large-scale circulations and on Earth’s radiative energy balance (Kubar et al. 2009; Nuijens et al. 2017; Jing and Suzuki 2018; Nelson and L’Ecuyer 2018). However, many warm-rain-dominated regions of the globe feature large discrepancies between satellite rainfall retrievals (Berg et al. 2010; Andersson et al. 2011; Behrangi et al. 2016; Behrangi and Song 2020). This paper is the second of a two-part study designed to better understand what the most important sources of uncertainty are for the retrieval of warm rain and drizzle, and how the inclusion of different satellite measurements affects retrieval uncertainty. This work is particularly relevant as NASA plans its next major precipitation measurement mission, tentatively given the name Atmosphere Observing System (AOS; Stavros et al. 2021). This mission comes out of NASA’s last decadal survey and the desire to design a mission to link the study of aerosols, clouds, convection, and precipitation (National Academies of Sciences, Engineering, and Medicine 2018).
In the first part of this study (Schulte et al. 2022, hereinafter Part I), we focused primarily on uncertain drop size distribution assumptions by using surface disdrometer data from the Ocean Rainfall and Ice-Phase Precipitation Measurement Network (OceanRAIN; Klepp et al. 2018) and the Atmospheric Radiation Measurement (ARM) Eastern North Atlantic (ENA) atmospheric observatory (Giangrande et al. 2019). We developed an optimal estimation (OE) retrieval algorithm and applied it to synthetic observations generated for three different satellite architectures: One similar to the Global Precipitation Measurement (GPM) Core Observatory (Skofronick-Jackson et al. 2017), one similar to CloudSat (Stephens et al. 2002), and one similar to the type of architecture envisioned for AOS. We quantified retrieval uncertainties stemming from instrument noise and detection limits, uncertainties coming from ancillary assumptions about the atmospheric profile, such as the assumed temperature and water vapor profiles, and uncertainties based on the inability of assumed drop size distribution (DSD) models to accurately represent the DSD variability seen in disdrometer observations. We found that the uncertainties due to DSD assumptions were quite significant, with biases in retrieved rain rate (RR) approaching 100% for some simple DSD models.
Disdrometer measurements are valuable because of their ability to accurately measure DSD shapes at a particular point. However, other retrieval uncertainties result from the vertical structure of the raining column, which is not measurable from a disdrometer alone, or from inhomogeneity within the satellite field of view, which likewise is hard to determine from a point measurement. These other uncertainties are the focus of this paper, and for that reason we rely upon simulations from a state-of-the-art cloud-resolving model, the Colorado State University (CSU) Regional Atmospheric Modeling System (RAMS; Cotton et al. 2003; Saleeby and van den Heever 2013). We use synthetic satellite observations generated from these simulations to study three additional sources of retrieval uncertainty: nonuniform beamfilling (NUBF), vertical variability in the rain and cloud profiles, and the inability to obtain radar measurements close to the surface due to surface clutter.
The fact that NUBF can affect the accuracy of precipitation retrievals has been recognized for decades. Graves (1993) documented that passive microwave (PMW) instruments will generally underestimate rain rates due to NUBF. This follows from the fact that the relationship between liquid water path and PMW brightness temperatures TB tends to be concave down; that is, increasing the liquid water path from zero by a certain amount x will change the TB by more than if x is increased to 2x. On the other hand, the relationship between rain rate and radar reflectivity Z is concave up (in the Rayleigh regime). Consequently, as demonstrated by Nakamura (1991), a rain retrieval algorithm that converts measured radar reflectivity (neglecting attenuation) to rain rate will overestimate the rain rate due to NUBF. Meanwhile an attenuation-only based method such as the surface reference technique (SRT; Meneghini et al. 2000) will always underestimate the rain rate, for similar reasons as in the PMW case. The underestimation increases as the attenuation increases, due to either heavier rain or a deeper raining column. Combining these effects, Durden et al. (1998) found that NUBF overall negatively biased rain-rate estimates from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar. This bias came mostly from convection and other high-rain-rate cases in which attenuation was significant. Many methods for correcting NUBF effects in satellite precipitation retrievals have been proposed or adopted (Zhang et al. 2004; Takahashi et al. 2006; Hilburn and Wentz 2008; Short et al. 2015; Grecu et al. 2016), but validating and improving NUBF correction algorithms remains a challenge (Iguchi et al. 2009; Leinonen et al. 2015). In this paper, we focus specifically on how NUBF affects the retrieval of light, warm rain, and explore how the NUBF effects from active and passive measurements behave in combination for the three satellite architectures from Part I.
Additional retrieval complications not dealt with in Part I include the many simplifying assumptions made about the vertical structure of the cloud and rainwater. Identifying the cloud-top height, or especially the cloud-base height, from a satellite radar or radiometer can be challenging. Within the cloud, assumptions must be made about the way the cloud water is distributed vertically and the size distribution of the cloud drops, unless these things are explicitly solved for. Perhaps most significantly, Part I assumed a uniform rain DSD. In reality, rainwater tends to increase toward cloud base, as falling drops collect smaller drops, and then decrease due to evaporation below cloud base, with smaller drops preferentially evaporating first (e.g., Comstock et al. 2004; Rapp et al. 2013; Kalmus and Lebsock 2017; Ojo et al. 2021). However, retrieving multiple moments of the DSD at each vertical level in a raining column may not be feasible due to information content limitations. For this reason, many satellite radar retrieval algorithms assume some kind of relationship between DSD parameters so as to reduce the number of free variables that must be retrieved. For example, the CloudSat 2C-RAIN-PROFILE algorithm (Lebsock and L’Ecuyer 2011) assumes an inverse exponential DSD, but the intercept and slope parameters are constrained to follow a strict relationship as defined in Abel and Boutle (2012, hereinafter AB12). This relationship can equivalently be expressed in the form of a relationship between rain rate and mass-weighted mean diameter (an R–Dm relationship) or between rainwater content and Dm (RWC–Dm relationship). Many alternative DSD relationships meant to reduce the dimensionality of the DSD retrieval problem have been proposed in the literature (e.g., Protat et al. 2019; Liao et al. 2020; Seto et al. 2021).
Surface clutter is an issue that affects all spaceborne radars. The ocean surface is typically two to five orders of magnitude more reflective than hydrometeors (Marchand et al. 2008). This large signal means that reflection from outside of the nominal radar resolution volume can bleed into the radar range bins above the surface, masking precipitation (Durden et al. 2001; Marchand et al. 2008; Kubota et al. 2016). For the CloudSat Cloud Profiling Radar (CPR), precipitation below about 750 m in height is missed (Tanelli et al. 2008). Surface clutter is even more of a factor for GPM, with the lowest reliable range bin around 1000 m at nadir and rising to 1500 m near the edge of swath (Kidd et al. 2021). Surface clutter could cause a spaceborne radar to miss shallow precipitation altogether. Even if the top of the raining column is high enough to be detected, assumptions must be made about collision–coalescence processes (e.g., Porcacchia et al. 2019) and/or evaporation (Kalmus and Lebsock 2017) if one wants to estimate the surface rain rate.
After first describing the RAMS simulations and the OE retrieval that we used (section 2), we will investigate each of these sources of uncertainty individually. Horizontal NUBF is covered in section 3. Vertical inhomogeneity issues, including algorithm assumptions about the vertical structure as well as vertical NUBF effects, are addressed in section 4. Section 5 looks at the effects of surface clutter, and in section 6 we combine all these sources of uncertainty and quantify how they would affect retrieval uncertainties for a theoretical AOS satellite. In section 7 we offer conclusions and discuss implications for current and future satellite precipitation algorithms.
2. Data and methods
a. RAMS simulations
RAMS, version 6.0 (Cotton et al. 2003), is a versatile model designed for simulating meteorological phenomena at the mesoscale and microscale. For our experiments, it was run on a 20 km × 20 km × 4 km model domain with a horizontal resolution of 100 m and a vertical resolution of 50 m. The simulation was initialized from a composite average atmospheric sounding from the Atlantic Trade Wind Experiment (ATEX) (Augstein et al. 1973, 1974; Brümmer et al. 1974) with a sea surface temperature of 298 K (Stevens et al. 2001). ATEX simulations have been used in the past to study warm phase cloud processes (e.g., Stevens et al. 2001; Xue et al. 2008; Saleeby et al. 2015). Small near-surface potential temperature perturbations were applied to break the initial horizontal homogeneity. The simulation used doubly periodic horizontal boundary conditions, a turbulent diffusion scheme (Smagorinsky 1963), the Land Ecosystem–Atmosphere Feedback (LEAF) surface flux model (Walko et al. 2000), and the two-stream Harrington (1997) radiation scheme. The simulation was similar to those described in Saleeby et al. (2015), with the main difference being the increased horizontal and vertical resolution.
Figure 1 plots the surface rain rate, overlain on top of the integrated cloud liquid water, at four points during the model run. What begins as a relatively widespread layer of stratocumulus clouds develops into a more broken field of shallow cumulus clouds with light rain occurring with many of the cells. We caution that the results from this single simulation of a trade wind warm-rain event do not necessarily apply to other types of warm rain.
Four snapshots of vertically integrated cloud liquid water path (background) and surface rain rate (colored contours) from the RAMS simulation.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
As examined in Part I, it should be expected that this double moment microphysical model will not perfectly recreate the full range of DSD variability seen in warm rain, especially given the limited nature of the ATEX simulation in space and time. However, RAMS has proven successful at simulating a wide range of atmospheric phenomena in the past (e.g., Stevens et al. 2001; Jiang and Feingold 2006; van den Heever et al. 2006; Saleeby et al. 2009; Igel et al. 2013). Based on this track record, we believe the simulation can be trusted to give a general sense of how much parameters like the rain rate and rainwater content, which are targets of satellite retrievals, can realistically vary in the horizontal and vertical dimensions for shallow oceanic convection. Thus, we used surface disdrometer data in Part I to study DSD-related retrieval uncertainties, and in this paper we utilize the very-high-resolution RAMS simulation to study the uncertainties introduced by spatial heterogeneity.
b. Simulation of satellite observations
We simulate satellite observations for the same three architectures, coined A, B, and C, as in Part I. For each satellite, the vertical resolution is assumed to be 250 m, similar to the resolution of GPM and CloudSat. We assume all the instruments share the same footprint. This is not realistic but allows us to separate the effects of different measurement information content from resolution differences. We do investigate the result of changing the footprint size for each architecture in section 3. The satellite-A measurements are assumed to come from a W-band (94 GHz) radar and include TB, path integrated attenuation (PIA), and Z at each range gate. Satellite-B measurements are made up of TB at each of the 13 channels of the GPM Microwave Imager (GMI; Hou et al. 2014) and Z and PIA at Ku and Ka band (13.6 and 35.5 GHz, respectively). Satellite C combines the W-band radar measurements of satellite A with the Ku- and Ka-band measurements of satellite B, with a heightened detection sensitivity. Tables 1 and 2 show the measurements simulated for each architecture and their assumed uncertainties and detection thresholds.
Selected radar specifications for the three theoretical satellite architectures considered in this study.
Passive microwave frequencies and measurement uncertainties for the three theoretical satellite architectures considered in this study. NEDT is noise equivalent differential temperature.
From the RAMS model output, synthetic observations are generated for each satellite architecture at 15-min time steps across a total of 8 h (after 1 h of model spinup). We use the MonoRTM radiative transfer model (Clough et al. 2005), in combination with the FASTEM6 sea surface emissivity model (Kazumori and English 2015), to simulate PMW Tb. The QuickBeam radar simulator (Haynes et al. 2007) is used for the calculation of radar reflectivities. Multiple scattering is ignored, as our focus is on light rain rates for which multiple scattering effects are not expected to be large. We assume spherical hydrometeors and calculate their absorption and scattering properties using Mie theory (Mie 1908). See Part I for full details on the satellite simulation forward model.
c. Optimal estimation
The OE forward model is built upon the same radiative transfer models (i.e., QuickBeam, MonoRTM, and FASTEM6) that are used to generate synthetic satellite observations. As noted in Part I, this means that forward model errors will be less than should be expected in real life. We also assume that the elements of b—the temperature and water vapor profiles, plus the sea surface temperature and wind speed—are known perfectly by the OE algorithm. These come directly from the RAMS model output (in Part I, we show that there is only a modest impact on retrieval uncertainties when realistic ancillary assumption errors are considered). Still, there are some simplifications made in the forward model relative to the satellite simulator, which will contribute to the errors in
The assumed a priori state xa and its covariance matrix
Values used in the a priori state vector xa, along with their assumed uncertainties included in the
The
3. Uncertainties due to nonuniform beamfilling
In our first set of experiments, we examine specifically the retrieval uncertainties that arise due to horizontal sensor resolution. To create synthetic satellite observations, we take the rain DSD from the lowest 50-m level of the RAMS simulations and assume this DSD extends uniformly up to a height of 1 km. Then the CLWP is specified according to RAMS column, but the profile of cloud water is recalculated so as to match perfectly with the assumptions of the OE algorithm; that is, linearly increasing from 500 m to 2 km, with a cloud droplet effective radius, re, that increases from cloud base to cloud top and a total cloud-average re of 11 μm. Figure 2, reprinted from Part I, illustrates the cloud and rain columns assumed. We could of course use the exact profiles of cloud and rain DSDs from RAMS to simulate satellite observations (and we do this in later sections), but for this first case we focus on the same idealized retrieval framework that was used in Part I. We do this to make comparisons with Part I easier and to isolate NUBF errors that have strictly to do with horizontal sensor resolution instead of vertical structure or forward model representation errors.
Schematic of the cloud and rain profiles used in the horizontal NUBF experiments only. The axes of the left qualitatively show the vertical profiles of relevant cloud DSD parameters (top part of plot; green) and rain DSD parameters (bottom part of plot; blue). The rain DSD throughout the whole column is equal to the DSD found at the lowest RAMS level, and the cloud DSD is constructed so as to give the same integrated CLWP as RAMS does.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
a. Base case uncertainties
As a baseline measure of retrieval uncertainties, and for comparison with Part I, we first simulate satellite observations at the native 100-m horizontal resolution of RAMS. Sensor noise is added, and Z values that fall below detection thresholds are eliminated, according to Tables 1 and 2. Then we use the OE algorithm to attempt to retrieve back the CLWP, RWC, and Dm for each RAMS profile from each satellite architecture. Because the forward model of the OE should in theory be able to perfectly recreate the cloud and rain profiles used to make the synthetic observations, all retrieval errors must come from one of three sources: sensor noise, fundamental nonlinearities, or insufficient information content in the satellite measurements. Fundamental nonlinearities in the retrieval problem could cause the algorithm to converge to a local minimum of Φ instead of the absolute minimum, while insufficient information content (e.g., the inability of the radars to detect small drops with reflectivities below their respective thresholds) will lead the algorithm to converge toward a priori assumptions.
Figure 3 plots the baseline pixel uncertainties in retrieved CLWP, RWP, RR, and Dm for satellite C, the most capable of the satellite architectures considered. The uncertainties are generally similar to what was seen for the base case in Part I, when the underlying DSDs came from disdrometer observations instead of a model. However, the spread in results is a bit larger, and for the lightest rain rates there is a tendency to overestimate CLWP while underestimating RWP (i.e., substitute cloud water for rainwater). This leads to a small underestimation of RR. This tendency is due to the influence of a priori assumptions about CLWP and Dm. The assumed a priori values for these parameters are higher than the average RAMS values, and at the lightest RRs there is not enough signal in the measurements to fully overcome the a priori bias. Overall (in terms of medians), retrieved CLWP is biased high by 10.8%, RWP biased low by 13.7%, RR biased low by 9.1%, and Dm biased high by 5.4%. The interquartile range (IQR) for retrieval errors for each of these parameters is between 11% and 24%.
Density plots of retrieved error in (top left) CLWP, (top right) RWP, (bottom left) column-averaged RR, and (bottom right) column-averaged Dm compared with the true value that was used to make the underlying simulated satellite observations, for satellite architecture C. This experiment considers only sensor noise and detection limits as sources of uncertainty.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
The other two satellite architectures have larger retrieval errors (their IQRs can be seen in Fig. 4). The behavior of satellite A is similar to that of satellite C, with CLWP and Dm biased high (positive) while RWP and RR are biased low (negative). The biases are slightly larger in magnitude than for satellite C, and the spread in retrieval errors is also larger. Satellite B has a distribution of retrieval errors that is unlike the other two architectures. In addition to having a much larger spread of errors, retrieved CLWP and Dm are biased low while RWP and RR are biased very high (40.3% and 34.1%, respectively). This is due in part to the fact that many of the RAMS DSDs do not generate Ku- or Ka- band reflectivities that are above the 12-dBZ reflectivity threshold of the satellite. In fact, only 56% of pixels generate valid satellite-B radar reflectivities. In the remainder of cases, satellite B has only PMW observations available to it and struggles to distinguish between cloud water and rainwater. The fact that it has a tendency to choose rainwater over cloud water is probably explained by the fact that CLWP has slightly tighter a priori bounds, so the retrieval is more likely to increase rainwater than cloud water in response to a TB signal of water in the column. For the subset of pixels for which satellite B does have valid Z, the retrieved RR is still biased high but at a more modest 22.8%.
Retrieval errors as a function of horizontal resolution, for each satellite architecture. The bars show the IQR of the pixel-level retrieval error in (top) CLWP, (middle) RWP, or (bottom) RR. Errors are reported as percentage values. The satellite is indicated by the color of the lines and symbols. For satellite B, there is an additional category showing only cases in which the maximum Ku-band reflectivity in the column is greater than 12 dBZ (i.e., the detection limit of the radar on satellite B).
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
b. Effects of sensor footprint size
Next, we performed a series of experiments designed to quantify how changing the sensor footprint size changes retrieval uncertainty. The 100-m horizontal resolution maps of TB, PIA, and Z from the base case were averaged together using a boxcar filter at new resolutions of 500 m and 1, 2, and 5 km. These new synthetic satellite observations were run through the OE algorithm, and the retrieved CLWP, RWP, and RR were compared with corresponding values from RAMS at each resolution. Figure 4 shows that there is a clear trend toward a greater underestimation of RWP and RR at lower horizontal sensor resolution. Putting this in the context of previous studies such as Durden et al. (1998), this result suggests that for all three satellite architectures the NUBF effects on radar attenuation and TB, which act to cause underestimation of rainfall, outweigh the slightly positive NUBF effect on unattenuated Z. The effect is largest for satellite B, which is logical given that it includes the most Tb observations, and for many of the pixels it is operating in PMW-only mode because the reflectivites are below its detection limit. Still, even when only considering pixels that have high enough reflectivities to be seen by the satellite-B radar (dashed lines in Fig. 4), there is a substantial bias caused by NUBF. Relative to averaging retrieved RRs from the native resolution retrieval, at 5-km resolution (roughly the resolution of GPM DPR), retrieved RRs from satellite B are about 50% lower, while satellites A and C are about 40% lower. At 500-m resolution (equal to the sampling spacing planned for the upcoming EarthCARE satellite; Illingworth et al. 2015), the NUBF effect is much smaller. Retrieved RRs are biased 7% lower than native resolution for architectures B and C but only about 1% lower than native resolution for satellite A. The horizontal NUBF effect does not seem to have a large effect on the overall spread of retrieval errors; if anything, the IQR of retrieval error tends to shrink as the footprint grows larger. This is probably because averaging reduces variability.
Figure 5 shows one snapshot of surface rain rate from the RAMS simulation and the RR retrieved by satellite C from this time assuming a sensor field of view of 1 km. It is clear that the higher-end values of the rain rate are not as well captured by the retrieval. While some of this is an inevitable result of averaging to a lower spatial resolution, the retrieved values are biased low even after this averaging is accounted for. However, Fig. 5 also makes clear that the RAMS simulation used for this study features strong gradients in rain rate over sub-kilometer scales. For other types of warm-rain environments, where precipitation might be more uniform, NUBF biases would likely be lower than those presented here.
(top left) Surface rain rate from RAMS at 4 h 30 min after model initialization. (top right) Satellite-C retrieved surface rain rate at RAMS resolution assuming a constant profile of Dm in the retrieval and no surface clutter. (bottom left) Satellite-C retrieved surface RR if reflectivity values below 1 km are not included in the observations vector. (bottom right) Satellite-C retrieved surface RR if the footprint size is assumed to be 1 km.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
4. Uncertainties due to vertical variability
a. Assumptions about vertical structure
In the next set of experiments, actual hydrometeor profiles from RAMS were used to simulate satellite observations instead of assuming the simplified vertical structure of Part I and section 3 of this paper. To isolate the effect of assumptions about vertical structure, without the effect of NUBF, we first used RAMS profiles at their native horizontal resolution. All pixels with a surface RR greater than or equal to 0.1 mm h−1 were included (over 10 000 pixels in total), and the columns were sampled every 250 m in the vertical to match the vertical resolution of the satellite radars. As before, random measurement noise was added to the simulated measurements before trying to retrieve back the true CLWP, RWP, and profiles of RR and Dm using each satellite architecture.
First, we let the retrieval algorithm assume the same simplistic uniform raining column scenario used in section 3. The column extended from the surface up to the point at which the W-band reflectivity first exceeded −10 dBZ (even for satellite B, which does not actually include a W-band radar). The OE algorithm then retrieved a single RWC and a single Dm value for the entire column (i.e., the column average). As can be seen in Fig. 6, these assumptions led to a retrieval algorithm that performed poorly for all satellite architectures. All of the retrieved values tracked in the figure were strongly negatively biased (with the one exception of CLWP for satellite C), and the variability was also large. The uniform raining column assumption seems to make the retrieval too sensitive to the uppermost part of the column, where drop sizes and RRs are low for the RAMS simulation. On the other hand, we also tested a version of the retrieval algorithm that attempted to retrieve RWC and Dm at every level of the raining column. This version performed slightly better; however, estimates of the surface RR were biased low by between 35% and 45% for all three satellites, and the IQR of retrieval errors was still large. This result indicates that assuming a more complex vertical structure is not always wise. If there is not enough independent information in the measurements to constrain what one is trying to retrieve (as appears to be the case here, even for satellite C), the ill-posed nature of the inversion problem will lead to suboptimal results. One possible approach to reduce errors due to vertical variability would be to add correlations between vertical levels to the
Next, we conducted two experiments in which a full profile of RWC was retrieved, but Dm was constrained. In the first (blue lines in Fig. 6), as a compromise between the two experiments above, Dm was retrieved as a single column-averaged value. For the triple-frequency satellite C, this led to good results, with the bias in retrieved CLWP, RWP, and surface RR all being close to zero. A map of results from one time step can be seen in Fig. 5. For the other two satellites, there was a tendency to overestimate rainwater at the expense of cloud water. All three satellites tended to underestimate the surface Dm, which is likely because the Dm at the surface is usually larger than the column average. In the other experiment (red lines in Fig. 6), the RWC profile was retrieved and the profile of Dm was calculated based on the AB12 relationship. For the surface RR metric, this set of experiments had the lowest biases and IQR values. However, the retrieval had a tendency to substitute cloud water for rainwater higher up in the column. An examination of the RAMS profiles revealed that the AB12 RWC–Dm relationship was especially inappropriate for the RAMS profiles at these heights. In Fig. 8, for instance, it can be seen that RWC tends to be higher at 1000 m than at the surface whereas Dm tends to be much lower, contradicting the AB12 RWC–Dm relationship.
Each bar shows the IQR (as a percentage value) in CLWP, RWP, surface RR, or surface Dm, for a given experiment and satellite architecture. The satellite is indicated by the letter on the x axis. The experiment being considered is indicated by the color of the bars. In the purple experiment, only a column-average RWC and Dm are retrieved; in the gold experiment RWC and Dm are retrieved at each valid radar range gate. Blue and red show the results when a profile of RWC is retrieved and Dm is either retrieved as a column average (blue) or prescribed according to AB12 (red). The cyan and magenta experiments use the same retrieval setup as blue and red (respectively) but are run on synthetic satellite observations that account for vertical nonuniform beamfilling.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
b. Vertical NUBF
For the same reasons that horizontal inhomogeneity can lead to biases in radar retrievals of rain, vertical inhomogeneity also increases retrieval uncertainty (it is much less of a concern for observables that lack vertical resolution, like TB or PIA). To quantify the effect of vertical NUBF, we repeated the exercise of section 4a but, instead of sampling the RAMS profiles at every 250 m, we simulated radar reflectivity at the 50-m resolution of the RAMS model and then averaged the Z to the 250-m resolution of the radars. We performed retrievals using either the variable RWC/constant Dm approach or assuming the AB12 RWC–Dm relation. These two methods were chosen because they gave the smallest biases in retrieved values of the four methods tested in section 4a. The error distributions from these experiments are also shown in Fig. 6 (in cyan and magenta). Including vertical NUBF effects had the tendency to reduce retrieved RWP and RR across all satellite architectures, with satellites B and C affected a little bit more strongly. These patterns are consistent with the effects of horizontal NUBF that were seen in section 3. When comparing the profiles of retrieved rain from this experiment with those from section 4a (not shown), we find that most of the missing rainwater comes from the top of the column. This suggests that vertical NUBF effects are most problematic when the top of the raining column lies in the middle of the radar range gate. Such a scenario results in measured radar reflectivities that correspond to rain amounts that are lower than the truth.
5. Uncertainties due to surface clutter height
Surface clutter causes retrieval uncertainties because it masks variability in the lowest part of the atmospheric column. For a given radar, the higher the surface clutter extends up above the surface, the more range gates there are that will have to be disregarded in the retrieval algorithm and the larger the overall retrieval uncertainty. To quantify this effect, the experiments of section 4a were repeated, except that radar observations from the lowest levels of the column were omitted. The simulated surface clutter extended up to 500, 1000, or 1500 m. For the purposes of calculating TB and PIA, the OE algorithm assumed that the profiles of RWC and Dm were constant from the lowest observable radar range bin down to the surface. We ran two sets of experiments, either with a constant Dm assumed throughout the column (but RWC retrieved as a profile above the surface clutter), or with the AB12 RWC–Dm relation. The IQR of the retrieved RR error at the top of the surface clutter, for each surface clutter height, is plotted in Fig. 7, and an example of a satellite-C retrieval assuming a surface clutter height of 1 km is shown in Fig. 5. While the spread in retrieval uncertainty does not necessarily increase as the surface clutter depth increases, there is a tendency for the RR to be underestimated above the surface. At 1 km in height, the retrieved RR is biased low by between 20% and 50%. The underestimation effect is slightly lower for satellite A.
Median and IQR of retrieved RR error, if surface clutter is assumed to extend up to various heights. The different satellite architectures are represented by the different colors. The heights considered are 0, 500, 1000, and 1500 m for all architectures; the error bars are slightly offset from these heights to make the differences between the satellites easier to see. (left) The experiments were run with the OE algorithm assuming a constant Dm profile; (right) the experiments prescribed an RWC–Dm relationship according to AB12.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
Of course, even if an RR retrieval is unbiased at 1 km above the surface, retrieval of the surface RR will be subject to additional uncertainties because the RR can change between the surface and the top of the surface clutter. This could be due to evaporation, collision–coalescence, or both. Retrieval algorithms may or may not try to model these processes to give a more accurate surface rain rate, but even if they do their microphysical models will not perfectly represent reality. Rather than test specific microphysical models (since the microphysical models used by RAMS are already known), we examine the difference between the rain characteristics in RAMS at each of these heights in comparison with the rain characteristics at the surface, to give a worst-case scenario of the types of the errors that could be expected in a warm-rain retrieval algorithm because of surface clutter.
Figures 8a–c show the RAMS distributions of RWC, Dm, and RR at the surface, 500 m, 1 km, and 1.5 km. RWC and RR tend to be highest at 1 km, probably due to evaporation that occurs below this level. The distribution of Dm, on the other hand, broadens and shifts toward higher values as one approaches the surface. As seen in Fig. 8d, most pixels feature a small difference in RR between the top of the surface clutter and the surface, but there is a long positive tail. About 30% of profiles have a difference between the 1-km RR and the surface RR that is larger than 0.2 mm h−1.
Histograms of various DSD characteristics from the RAMS simulations, colored by height: (a) log base 10 of rainwater content (g m−3), (b) mass-weighted mean diameter (mm), (c) log base 10 of rain rate (mm h−1), and (d) difference (mm h−1) between RR at a given height and the RR at the surface underneath.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
6. Combined uncertainties for an AOS-like satellite
In our last experiment, we performed retrievals combining all of the sources of uncertainty previously considered: sensor noise and detection thresholds, nonuniform beamfilling, algorithm assumptions about the cloud and rain structure, and surface clutter. We simulated observations for an AOS-like satellite based on the “minimum desired capabilities” specified in Revision E of NASA’s Science and Applications Traceability Matrix (SATM) for the AOS mission (available at https://science.nasa.gov/science-pink/s3fs-public/atoms/files/ACCP_SATM_Rel_E_TAGGED.pdf). The SATM specifies W-band and Ka-band radar observations with a minimum detectable radar reflectivity of −25 and 5 dBZ, respectively; horizontal resolution of 2 km; vertical resolution of 250 m; and measurements extending down to 500 m. Note that these Z thresholds are slightly higher than the ones used for satellite C in previous experiments, and that the satellite lacks a Ku-band radar (lower thresholds and a Ku-band are included under “desired enhanced capabilities” in the SATM). For comparison, we also performed retrievals using the rough characteristics of CloudSat and GPM. All three sets of parameters are given in Table 4.
Comparison of key characteristics for the CloudSat and AOS simulation experiments described in section 6.
Synthetic observations were first generated at the native resolution of RAMS, and then averaged to the horizontal and vertical resolutions given in Table 4. Radar observations below the surface clutter height were eliminated. The CLWP and the RWC profile were retrieved for each synthetic satellite pixel (sampled from the RAMS grid at every 500 m) using the AB12 DSD assumptions. Figure 9 shows the surface RR from RAMS (at 2-km resolution), plotted against the RR at 500 m retrieved by the OE algorithm, which is assumed to be the same as the surface RR. There is a tendency to underestimate the RR, especially for heavier precipitation, which is perhaps to be expected given the effects of NUBF. The overall negative bias is −18.6%, with an IQR of 55.4% that is considerably larger than the base-case IQR for satellite C of 15.7% calculated in section 3 and seen in Fig. 3. The SATM also specifies a desired uncertainty for the precipitation rate profile of 100%. Taking this to mean a 100% positive bias or a 50% negative bias, relative to RAMS, 81.4% of synthetic AOS-like retrievals fall within these bounds. The desired uncertainty range is shown by the dashed red lines in Fig. 9.
RAMS surface RR (mm h−1), at 2-km resolution, plotted against (left) retrieved RR or (right) retrieved RR percentage error from an AOS-like satellite as described in the text. The red dashed lines represent the desired uncertainty limits specified in the NASA SATM.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
Results for the CloudSat-like satellite are shown in Fig. 10. It did not perform as well as the AOS-like satellite, with a greater negative bias in retrieved RR, a larger IQR, and only 63.9% of cases falling within the desired uncertainty bounds. This shows that the extra Ka-radar frequency of AOS, along with (to a lesser extent) the reduced surface clutter and radar-derived TB noise, markedly improves retrieval performance. We tested adding a Ku-band radar with a minimum detectable reflectivity of 10 dBZ to the theoretical AOS satellite (not shown), but there was little improvement in retrieved RR. This suggests that there is not much extra information in the Ku band if one already has the Ka band, at least for the very light rain considered in this study.
As in Fig. 9, but for a CloudSat-like satellite.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
As seen in Fig. 11, the GPM-like satellite underestimated the true rain rate in almost all cases. This is not surprising given the lower spatial resolution of this satellite, and the fact that most of the raining cells in this simulation are less than 5 km in width. Thus, NUBF effects are significant. The underestimation was seen both for cases when radar reflectivities above 12 dBZ were present in the column, as well as for cases for which the satellite only has passive measurements to use. In our experiment, only 6% of cases fell within desired uncertainty limits. Note that the GPM mission is intended mostly to measure precipitation that is both heavier and more widespread than the precipitation in our simulation, so this result should not be taken as an indictment of the GPM mission as a whole. Still, it could help to explain why GPM has been found to measure less warm rain than CloudSat in terms of both frequency and amount (Battaglia et al. 2020; Behrangi and Song 2020; Schulte and Kummerow 2022).
RAMS surface RR, at 5-km resolution, plotted against retrieved surface RR from a GPM-like satellite. Blue symbols represent cases in which the maximum reflectivity in the column (above the surface clutter) is below 12 dBZ, so the retrieval algorithm is relying only on the radiometer observations plus a priori assumptions. The red symbols are cases in which the maximum reflectivity is above 12 dBZ, so there is at least some radar information.
Citation: Journal of Applied Meteorology and Climatology 62, 2; 10.1175/JAMC-D-22-0051.1
7. Discussion and conclusions
Our analysis reiterates previous findings that NUBF is an important source of error in satellite precipitation estimates. We found that, for the shallow isolated warm rain generated in our simulation, NUBF effects led to a 40%–50% negative bias in retrieved RR at the coarsest resolution tested (5 km). While the effect was largest for light rain retrieved by satellite B, it was significant for all cases, suggesting that beamfilling had similar effects on both the active and passive measurements. Retrieval biases were much more modest (less than 10%) at 500-m horizontal resolution. This seems like a good, if ambitious, target for future satellite radars, particularly those operating at higher frequencies for which smaller footprints are more feasible. Vertical NUBF errors were found to be smaller, though they still tended to lead to the underestimation of RR. Assumptions made about the profile of rainwater were even more important. Assuming a uniform profile of rain led to severe negative biases; however, trying to retrieve both RWC and Dm at each level also led to poor retrieval performance due to insufficient information content. The optimal solution seems to land somewhere in the middle; that is, retrieving a profile of RWC but making simplifying assumptions about the profile of Dm.
For this RAMS simulation, RRs tend to be lower at the surface than slightly above the surface, at 500–1000 m. This is due to evaporation below cloud base. The surface RR was at least 0.2 mm h−1 lower than the rain rate above in about 30% of cases, meaning that surface clutter could potentially cause significant biases for light rain if one’s target variable is surface rain intensity or frequency. This finding is consistent with prior studies (e.g., Rapp et al. 2013). We also found, however, that our retrieval tended to underestimate the RR at the top of the surface clutter, a partially compensating error. It is not immediately clear whether other precipitation retrieval algorithms should be expected to be subject to this sort of effect.
Combining all error sources, we tested the performance of an AOS-like satellite using NASA’s minimum desired capabilities and found that the combined uncertainty would be sufficiently low to make the theoretical instrument useful for advancing the study of warm rain. The retrieval error fell within the desired uncertainty range over 80% of the time, as compared with only 64% of cases for a corresponding CloudSat-like simulation. Still, retrieved RR was biased low by almost 20% with a large spread in retrieval errors, particularly at the lightest RRs. The overall negative bias should probably not be a surprise, since even in the base case (section 3) there was a bias, and because most of the individual sources of uncertainty that we studied individually tended to reduce the retrieved RR. In practice, this bias could hopefully be greatly reduced. While it is beyond the scope of this paper, a NUBF correction model such as that proposed by Short et al. (2015) would improve retrieval accuracy. It would be important to train such a model using a globally representative collection of statistics, rather than just a single case study. The effects of surface clutter can be mitigated either by radar technological advances that reduce surface interference, incorporating better evaporation models, or both. Retrieval performance could also likely be improved by making more careful assumptions about the cloud drops in the column.
In contrast to the simulations from Part I, in which assuming the AB12 DSD relationship led to large positive biases in retrieved RR, in this study we found that this assumption performed reasonably well. This could be because this study was based on modeled raindrops, whereas Part I was based on actually measured drops that tended to be larger. Another possible explanation is that the positive AB12 bias found in Part I was counteracted by the large negative bias of NUBF, leading to reasonable performance overall. More work is needed to determine whether the RWC–Dm relationship from AB12 is actually appropriate for warm rain.
It is important to note that the results from this study should not be taken to definitively characterize the errors that affect any current or future precipitation-measuring satellite. We have made several implifying assumptions, and a thorough error analysis would rely on additional model simulations from varying meteorological regimes. Our model simulation has a small domain size and simulates only one type of warm rain—that of small raining cells embedded in a mixed field of broken stratocumulus and shallow cumulus clouds. Some of the errors considered here, in particular the nonuniform beamfilling, would likely be considerably smaller for a more homogeneous large-scale cloud deck. There is an urgent need for more high-resolution (on the order of 100 m) model simulations capturing a wide variety of precipitation environments to be used in preparation for the AOS mission. As one example, RAMS model simulations covering much larger domains are planned as part of first phase of the Investigation of Convective Updrafts Mission (INCUS; van den Heever et al. 2022). These simulations should prove very valuable in characterizing the uncertainties not only for INCUS algorithms, but also for AOS retrievals. Even with the limitations of our current study, we believe that by examining the relative impact of different types of uncertainties on three different satellite architectures, we can better understand why current satellite precipitation estimates disagree, and better plan for future missions.
Acknowledgments.
We are grateful to the NASA FINESST program, which funded this work (Award 80NSSC19K1325). We also thank the members of the NASA ACCP Science Impact Team (SIT) for helpful feedback and guidance as the study was being formulated. Three anonymous reviewers greatly improved the quality and clarity of the paper.
Data availability statement.
RAMS source code and related documentation can be downloaded online (http://vandenheever.atmos.colostate.edu/vdhpage/rams.php). The composite ATEX sounding used to initialize the model is included in Stevens et al. (2001).
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