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Abstract
The raindrop size distribution (RDSD) is defined as the relative frequency of raindrops per given diameter in a volume. This paper describes a mathematically consistent modeling of the RDSD drawing on probability theory. It is shown that this approach is simpler than the use of empirical fits and that it provides a more consistent procedure to estimate the rainfall rate (R) from reflectivity (Z) measurements without resorting to statistical regressions between both parameters. If the gamma distribution form is selected, the modeling expresses the integral parameters Z and R in terms of only the total number of drops per volume (N
T
), the sample mean [m = E(D)], and the sample variance [σ
2 = E(m − D)2] of the drop diameters (D) or, alternatively, in terms of N
T
, E(D), and E[log(D)]. Statistical analyses indicate that (N
T
, m) are independent, as are (N
T
, σ
2). The Z–R relationship that arises from this model is a linear R = T × Z expression (or Z = T
−1
R), with T a factor depending on m and σ
2 only and thus independent of N
T
. The Z–R so described is instantaneous, in contrast with the operational calculation of the RDSD in radar meteorology, where the Z–R arises from a regression line over a usually large number of measurements. The probabilistic approach eliminates the need of intercept parameters N
0 or 
Abstract
The raindrop size distribution (RDSD) is defined as the relative frequency of raindrops per given diameter in a volume. This paper describes a mathematically consistent modeling of the RDSD drawing on probability theory. It is shown that this approach is simpler than the use of empirical fits and that it provides a more consistent procedure to estimate the rainfall rate (R) from reflectivity (Z) measurements without resorting to statistical regressions between both parameters. If the gamma distribution form is selected, the modeling expresses the integral parameters Z and R in terms of only the total number of drops per volume (N
T
), the sample mean [m = E(D)], and the sample variance [σ
2 = E(m − D)2] of the drop diameters (D) or, alternatively, in terms of N
T
, E(D), and E[log(D)]. Statistical analyses indicate that (N
T
, m) are independent, as are (N
T
, σ
2). The Z–R relationship that arises from this model is a linear R = T × Z expression (or Z = T
−1
R), with T a factor depending on m and σ
2 only and thus independent of N
T
. The Z–R so described is instantaneous, in contrast with the operational calculation of the RDSD in radar meteorology, where the Z–R arises from a regression line over a usually large number of measurements. The probabilistic approach eliminates the need of intercept parameters N
0 or
Abstract
To date, the assimilation of satellite measurements in numerical weather prediction (NWP) models has focused on the clear atmosphere. But satellite observations in the visible, infrared, and microwave provide a great deal of information on clouds and precipitation. This special collection describes how to use this information to initialize clouds and precipitation in models. Since clouds and precipitation often occur in sensitive regions for forecast impacts, such improvements are likely necessary for continuing to acquire significant gains in weather forecasting.
This special collection of the Journal of the Atmospheric Sciences is devoted to articles based on papers presented at the International Workshop on Assimilation of Satellite Cloud and Precipitation Observations in Numerical Weather Prediction Models, in Lansdowne, Virginia, in May 2005. This introduction summarizes the findings of the workshop. The special collection includes review articles on satellite observations of clouds and precipitation (Stephens and Kummerow), parameterizations of clouds and precipitation in NWP models (Lopez), radiative transfer in cloudy/precipitating atmospheres (Weng), and assimilation of cloud and precipitation observations (Errico et al.), as well as research papers on these topics.
Abstract
To date, the assimilation of satellite measurements in numerical weather prediction (NWP) models has focused on the clear atmosphere. But satellite observations in the visible, infrared, and microwave provide a great deal of information on clouds and precipitation. This special collection describes how to use this information to initialize clouds and precipitation in models. Since clouds and precipitation often occur in sensitive regions for forecast impacts, such improvements are likely necessary for continuing to acquire significant gains in weather forecasting.
This special collection of the Journal of the Atmospheric Sciences is devoted to articles based on papers presented at the International Workshop on Assimilation of Satellite Cloud and Precipitation Observations in Numerical Weather Prediction Models, in Lansdowne, Virginia, in May 2005. This introduction summarizes the findings of the workshop. The special collection includes review articles on satellite observations of clouds and precipitation (Stephens and Kummerow), parameterizations of clouds and precipitation in NWP models (Lopez), radiative transfer in cloudy/precipitating atmospheres (Weng), and assimilation of cloud and precipitation observations (Errico et al.), as well as research papers on these topics.
Abstract
The focus of this chapter is progress in hydrology for the last 100 years. During this period, we have seen a marked transition from practical engineering hydrology to fundamental developments in hydrologic science, including contributions to Earth system science. The first three sections in this chapter review advances in theory, observations, and hydrologic prediction. Building on this foundation, the growth of global hydrology, land–atmosphere interactions and coupling, ecohydrology, and water management are discussed, as well as a brief summary of emerging challenges and future directions. Although the review attempts to be comprehensive, the chapter offers greater coverage on surface hydrology and hydrometeorology for readers of this American Meteorological Society (AMS) monograph.
Abstract
The focus of this chapter is progress in hydrology for the last 100 years. During this period, we have seen a marked transition from practical engineering hydrology to fundamental developments in hydrologic science, including contributions to Earth system science. The first three sections in this chapter review advances in theory, observations, and hydrologic prediction. Building on this foundation, the growth of global hydrology, land–atmosphere interactions and coupling, ecohydrology, and water management are discussed, as well as a brief summary of emerging challenges and future directions. Although the review attempts to be comprehensive, the chapter offers greater coverage on surface hydrology and hydrometeorology for readers of this American Meteorological Society (AMS) monograph.
