J.N.M. Stricker

Rainfall measurement using radio links from cellular communication networks

We investigate the potential of radio links such as employed by commercial cellular communication companies to monitor path-averaged rainfall. We present an analysis of data collected using two 38-GHz links during eight rainfall events over a 2-month period (October?November 2003) during mostly stratiform rainfall in the Netherlands. Comparisons between the time series of rainfall intensities estimated using the radio links and those measured by a nearby rain gauge and a composite of two C band weather radars show that the dynamics of the rain events is generally well captured by the radio links. This shows that such links are potentially a valuable addition to existing methods of rainfall estimation, provided the uncertainties related to the reference signal level, signal level resolution, wet antenna attenuation, and temporal sampling can be resolved.

A consistent rainfall parameterization based on the exponential raindrop size distribution

Abstract There exists an impressive body of experimental evidence confirming the existence of power law relationships between various rainfall related variables. Many of these variables (such as rain rate, radar reflectivity factor and kinetic energy flux density) have a direct relevance for hydrology and related disciplines (hydrometeorology, soil erosion). There is one fundamental property of rainfall which ties all these variables together, namely the raindrop size distribution. It is the purpose of this article to explain (1) that there exist two fundamentally different forms of the raindrop size distribution, (2) how various hydrologically relevant rainfall variables are related to both these forms, and (3) how the coefficients of power law relationships between such rainfall variables are determined by the parameters of these two forms of the raindrop size distribution. The classical exponential raindrop size distribution is used as an example of a family of raindrop size distributions. Three groups of rainfall related variables are considered, namely properties of individual raindrops (size, speed, volume, mass, momentum and kinetic energy), rainfall integral variables (raindrop concentration, raindrop arrival rate, liquid rainwater content, rain rate, rainfall pressure, rainfall power and radar reflectivity factor) and characteristic sizes (median-volume diameter, volume-weighted mean diameter and mean-volume diameter). Six different consistent sets of power law relationships between these rainfall related variables and rain rate are presented, based on different assumptions regarding the rain rate dependence of the parameters of the raindrop size distribution.

Hydrometeorological application of a microwave link: 1. Evaporation

A method to estimate areal evaporation using a microwave link (radio wave scintillometer) in combination with an energy budget constraint is proposed. This radio wave scintillometry-energy budget method (RWS-EBM) is evaluated for its applicability in different meteorological conditions and for its sensitivity to various variables (the structure parameter of the refractive index of air C n 2, the total available energy R n - G, the wind velocity u, the effective average vegetation height h 0, and the correlation coefficient between the temperature and humidity fluctuations r TQ ). The method is shown to be best suited for use in wet to moderately dry conditions, where the latent heat flux is at least a third of the total available energy (i.e., Bowen ratio =2). It is important to accurately measure the total available energy and the wind velocity as the RWS-EBM is most sensitive to these variables. The Flevoland field experiment has provided the data, obtained with a 27-GHz radio wave scintillometer (over 2.2 km), a large-aperture scintillometer (also 2.2 km), and four eddy covariance systems, which are used to test the RWS-EBM. Comparing 92 daytime measurements (30-min intervals) of the evaporation estimated using the RWS-EBM to that determined in alternative manners (eddy covariance and two-wavelength scintillometry) leads to the conclusion that the method provides consistent estimates (coefficient of determination r 2 = 0.85 in both cases) under relatively wet conditions.

Towards a stochastic model of rainfall for radar hydrology: testing the poisson homogeneity hypothesis

Abstract In order to investigate to what extent rainfall fluctuations observed with different types of instruments reflect the properties of the rainfall process itself and to what extent they are merely instrumental artefacts we are in the process of developing a stochastic model of rainfall. The starting point for the development of the model has been the notion that at the spatial and temporal scales associated with many types of surface rainfall measurements, rainfall is a discrete process describing the arrival of raindrops of different sizes at the ground. A fundamental question is whether this raindrop arrival process can be considered a homogeneus (Poisson) process or whether it behaves as a clustering (or possibly even scaling) process, as has recently been proposed in the litereture. We have tested the classical Poisson homogeneity hypothesis in rainfall on a 35 min time series of 10 s raindrop size spectra collected with a 50 cm2 disdrometer. The rain rates calculated from the spectra indicated roughly uncorrelated fluctuations around a constant mean rain rate of about 3.5 mm h−1. Two types of analysis of the drop counts were carried out, a global analysis taking into account all drops regardless of their size and an analysis considering the drop counts in the 16 0.21 mm diameter intervals separately. The first type of analysis revealed that evene for the more or less stationary time series under consideration the total raindrop arrival rate was overdispersed with respect to the homogeneous Poisson process. The second type of analysis demonstrated that this rejection of the homogeneity hypothesis could be attributed entirely to raindrops with diameters smaller than 1.14 mm. Although these drops account for 66% of the raindrop concentration in the air and 55% of the raindrop arrival rate at the ground, they only account for 14% of the rain rate and 2% of the radar reflectivity factor (on the basis of the mean drop size distribution during the experiment). In order words, although clustering may be a significant phenomenon for the smallest raindrops, the analyzed data seem to indicate that for moderate rain rates the arrival rate fluctuations of the raindrops which contribute most to the rain rate and radar reflectivity factor behave according to Poisson statistics.

Dependence of rainfall interception on drop size – a comment

In a series of three articles Calder, Hall and colleagues have recently presented an extension of Calder’s original stochastic model of rainfall interception. In their model, the dependence of rainfall interception on raindrop size is explicitly taken into account. All raindrops are assumed to have the same characteristic size, the so-called median-volume raindrop diameter D0, which is taken to be a power law function of the rain rate R. However, the D0–R relationship used in their model results from an erroneous interpretation of the general theory of the raindrop size distribution recently proposed by Sempere Torres and colleagues. As a result, this relationship is not consistent with the postulated underlying raindrop size distribution. Moreover, it seriously underestimates D0 for a given R as compared to the consistently derived D0–R relationships and to the D0–R relationship reported in a classical article on the subject of raindrop size distributions. This may seriously affect the model results presented by Calder, Hall and colleagues.

Application of X- and S-band radars for rain rate estimation over an urban area

Abstract The potential of ground-based radar systems operating at X-band for rainfall estimation over urban areas is investigated. To this end, rainfall measurements from the X-band weather surveillance radar SOLIDAR are compared against those from the colocated S-band research radar DARR and a line configuration of 4 tipping bucket rain gages located at ranges between 5 and 10 km from the radar site. The analysis is restricted to 1 rainfall event with a duration of approximately 2 h, a maximum instantaneous rainfall intensity of about 20 mm h −1 and a cumulative rainfall amount of around 5 mm. Attention has been paid to a careful quality check of the data, particularly with respect to the effects of synchronization errors in the rain gage measurements and the effects of ground clutter in the radar measurements. It is demonstrated that the radar measurements compare well to each other, but that both radars fail to capture a rainfall peak observed by all rain gages. It is argued that this lack of agreement may be due to the fact that such local phenomena are lost in the radar data as a result of the fairly large amount of range averaging employed (600 m). This indicates that such resolutions, although necessary for achieving acceptable signal-to-noise ratios, may already be too coarse for urban hydrological applications. For the event considered the effects of attenuation on the X-band radar data are small.

Estimation of path-average evaporation and precipitation using a microwave link

The potential of a 27 GHz microwave link for measuring both evaporation and precipitation is investigated. For the estimation of evaporation a combination of the microwave link (radio wave scintillometer) and an energy budget constraint is proposed. This Radio Wave Scintillometry-Energy Budget Method (RWS-EBM) has been tested using data from an experiment with a 27 GHz radio wave scintillometer over 2.2 km and four eddy covariance (EC) systems. Comparing one day of measurements (30- minute intervals) of the evaporation estimated using the RWS-EBM to those measured by eddy covariance systems leads to the conclusion that the method provides consistent estimates under relatively wet conditions. In the case of precipitation, analyses show that the specifc attenuation of an electromagnetic signal at 27 GHz varies nearly linearly with the rainfall intensity, which is ideal for line-integrating instruments. Data from an experiment with a 4.89 km microwave link and a line configuration of seven tipping-bucket raingauges are used to test whether this instrument is indeed suitable for the estimation of path-average rainfall. Results from this experiment show that the attenuation due to wet antennas can have a significant effect on the retrieved rainfall intensity. However, when a two-parameter wet antenna correction function is applied to the link data, comparisons with the raingauge data show that the instrument is indeed well-suited for the measurement of path average rainfall.