Stratiform and Convective Radar Reflectivity–Rain Rate Relationships and Their Potential to Improve Radar Rainfall Estimates

Abstract

The variability of the raindrop size distribution (DSD) contributes to large parts of the uncertainty in radar-based quantitative rainfall estimates. The variety of microphysical processes acting on the formation of rainfall generally leads to significantly different relationships between radar reflectivity Z and rain rate R for stratiform and convective rainfall. High-resolution observation data from three Micro Rain Radars in northern Germany are analyzed to quantify the potential of dual Z–R relationships to improve radar rainfall estimates under idealized rainfall type identification and separation. Stratiform and convective rainfall are separated with two methods, establishing thresholds for the rain rate-dependent mean drop size and the α coefficient of the power-law Z–R relationship. The two types of dual Z–R relationships are tested against a standard Marshall–Palmer relationship and a globally adjusted single relationship. The comparison of DSD-based and reflectivity-derived rain rates shows that the use of stratiform and convective Z–R relationships reduces the estimation error of the 6-month accumulated rainfall between 30% and 50% relative to a single Z–R relationship. Consistent results for neighboring locations are obtained at different rainfall intensity classes. The range of estimation errors narrows by between 20% and 40% for 10-s-integrated rain rates, dependent on rainfall intensity and separation method. The presented technique also considerably reduces the occurrence of extreme underestimations of the true rain rate for heavy rainfall, which is particularly relevant for operational applications and flooding predictions.

On the Relationships Between Radar Reflectivity and Rainfall Rate and Kinetic Energy Resulting From a Weibull Drop Size Distribution

“…The expression in Equation 23b is close to the one computed by Sauvageot (1994) for the Marshall and Palmer (1948) data, i.e., [Z(R) = 295R 1.47 ]. It has the same power but a higher constant compared to the expression fitted by Kirsch et al (2019) to the whole set of data (global data) measured in northern Germany between 2013 and 2015 using a Micro Rain Radar, i.e., [Z(R) = 180R 1.41 ]. Expressions similar to Equations 23a and 23b are widely used and were fitted to many rainfall events reported in the literature over the years (Sauvageot, 1994).…”

“…where d is the equivalent spherical diameter of the drop, N is the number concentration (mm −1 m −3 ), N 0 is the intercept parameter (mm −1 m −3 ), μ is a dimensionless shape parameter, and Λ is the slope parameter (mm −1 ). Neglecting the upward vertical component of the air velocity, R (mm h −1 ) is defined as (Kirsch et al, 2019;Steiner et al, 2004)…”

“…Therefore, radar methods can be harnessed to improve flash flood warning and forecasting, and water resources management (Morin et al, 2005). The radar reflectivity, Z (mm 6 m −3 ), can be evaluated as (Kirsch et al, 2019; Steiner et al, 2004) …”

“…Capitalizing on the exponential model introduced by Marshall and Palmer (1948), a widely used expression relies on the standard gamma distribution (Narayana Rao et al, 2006; Smith et al, 2009; Takeuchi, 1978; Ulbrich, 1983; Willis, 1984): where d is the equivalent spherical diameter of the drop, N is the number concentration (mm −1 m −3 ), N 0 is the intercept parameter (mm −1 m −3 ), μ is a dimensionless shape parameter, and Λ is the slope parameter (mm −1 ). Neglecting the upward vertical component of the air velocity, R (mm h −1 ) is defined as (Kirsch et al, 2019; Steiner et al, 2004) where V is the terminal fall velocity in still air of the drops according to their respective diameter (m s −1 ).…”

“…The vast majority of related studies show strong evidence for a statistical relationship between both quantities in the general form of a power law (Kirsch et al, 2019; Sauvageot, 1994): where the multiplicative factor κ and the exponent β are empirical constants depending on the DSD parameters. The combination of the parameters κ and β represents the microphysical processes that shape the DSD and determine its variation in space and time.…”