ESTRATEGIA PARA LA CONSOLIDACIÓN DE INSTALACIONES PORTUARIAS EFICIENTES

events are associated with stationary flow, and form stable and active bands of precipitation which are parallel to the direction of the wind and can last for several hours (Miniscloux et al., 2001; Godart et al., 2011). Typically, deep-convective events are temporally shorter, show more intermittency (“patchiness”), and have higher rain rates than shallow-convective events (Godart et al., 2011). Orographic rainfall is a complex process (Houze, 2012) and precipitation rates in mountainous regions remain poorly known as a result (Roe, 2005).

The Hydrological Cycle in the Mediterranean Experiment2(HyMeX, Drobinski et al., 2014;

Ducrocq et al., 2014) is a long-term, multi-disciplinary, international project that brings together teams of scientists with the common goal of providing better understanding of the complex water cycle of the Mediterranean. It has a particular emphasis on extreme and high- impact weather events such as HPEs. The main study region for this thesis was in Cévennes, France, in which an instrument network was deployed as part of HyMeX. The Cévennes region lies to the southeast of the Massif Central, and forms a large south-easterly facing slope to the sea, dissected by deep and narrow northwest to southeast valleys (Miniscloux et al., 2001; Godart et al., 2011). It is one of the five rainiest areas in the region (Nuissier et al., 2008). Rain occurs particularly during the autumn - there is a well defined precipitation maximum in October (Frei and Schär, 1998). The region is subject to HPEs (Ricard et al., 2012) and ORBs (Godart et al., 2011), with an average 7.6 days per year with rainfall over 150 mm (between 1967 and 2006, Ricard et al., 2012). Data from two autumn field campaigns in this region were used in this work.

1.5 Thesis outline

The work in this thesis follows a logical arc, from collection of accurate DSD data from a network of disdrometers, to technique development for the study of the variability of the DSD using spatial interpolation and stochastic simulation, to analysis of DSD variability in the horizontal and vertical. Here, a brief overview of the following chapters is provided. Each chapter has been adapted from a published or submitted research article.

Chapter 2 relates to collection of the high-quality and accurate point measurements of the DSD. Most of the DSD data used in this thesis were collected by a network of Parsivel disdrometers, which is introduced in this chapter. Like any instrument, disdrometers have collection errors that must be taken into account when their data are used. In particular, these disdrometers classify drops into “bins” of drop size, and may misestimate the number of drops in each class. In Chapter 2 we present a method for the correction of disdrometer data recorded using Parsivel disdrometers, that uses a 2DVD as a reference. In the first part of the method, drop velocities are corrected with reference to a theoretical model of raindrop terminal velocity. Second, raw disdrometer measurements are filtered to remove particles that are unlikely to be real drops. Third, concentrations per Parsivel diameter class are corrected such that on average they match those recorded by the 2DVD. The correction method improves the match

of DSD moments between the Parsivel and the 2DVD, and test results are shown in which, in the majority of cases, the Parsivel-derived rain rate was closer to that of a collocated rain gauge after the correction was applied. The corrected Parsivel data were then used for technique development and analyses of DSD variability.

In Chapter 3, we present a new method for spatial interpolation and stochastic simulation of experimental DSD spectra. Disdrometers such as Parsivels provide non-parametric ex- perimental DSD spectra in which concentrations are provided per drop diameter class. In a network of disdrometers, the DSD is measured at discrete point locations with varying inter-measurement distance. Our interpolation and simulation approach uses geostatistics to estimate or simulate the DSD, in the same non-parametric classes, at unmeasured points in space. Careful processing is required in order to comply with the assumptions of the geosta- tistical technique. Non-stationarity of the DSD field is taken into account using the dry-drift (Schleiss et al., 2014a), which we show exists on DSD concentrations. Principal component analysis is used to find uncorrelated components of the DSD, which are then interpolated or simulated for the requested points. A back-transformation process produces the estimates of the DSD. Results of leave-one-out testing show low bias on the estimated DSDs.

In Chapter 4, the data correction and DSD stochastic simulation techniques are brought together to investigate the small-scale variability of the DSD. In this chapter we report on a study in which simulated high-resolution grids of DSDs, conditional on measurements, were used to test the effects of DSD variability on areal rainfall retrieval. DSD variability is studied over two scales that were chosen for their similarity to areal scales used in rainfall products.

The first scale, 5 × 5 km2, is the ground footprint size of the Global Precipitation Measurement

(GPM) satellite weather radar. The second scale, 2.8×2.8 km2, is the size of a pixel in the

operational Consortium for Small-scale Modelling (COSMO) numerical weather model. The error introduced by assuming that a point measurement represents an areal measurement is quantified by areal size, and the retrieval algorithms for both GPM and COSMO are evaluated with respect to whether their pixel-scale results are representative of the sub-pixel process. In Chapter 5 we move to investigation of the double-moment normalisation of the DSD. Normalisation allows for the compact representation of the DSD and is also useful for the investigation of DSD variability, but it relies on the idea that the normalised DSD is the same everywhere. We show that the double-moment normalisation method of Lee et al. (2004) is effective at collapsing the DSD into a mean shape. We show the results of tests on the invariance of the double-normalised DSD in three climatic regions, through both horizontal and vertical displacement of the normalised DSD. This is the first test of the invariance of the normalised DSD in the vertical and the first over a large horizontal range of up to 100 km in one region. The normalised DSD trained in one region is shown to be applicable to another region more than 7000 km away.

In Chapter 6, the assumption that the normalised DSD is invariant is used to develop a new technique for the retrieval of the DSD from polarimetric radar data. The assumption

1.5. Thesis outline

of an invariant normalised DSD means that the goal of the new technique is essentially to recover two moments of the DSD from radar information, because with these values the whole DSD can be reconstructed at any point using double-moment normalisation. We show how moments three and six of the DSD can be recovered from polarimetric variables, and show results of testing the retrieval technique against a state-of-the-art method. The technique performs as well or better than the existing technique. Further, we introduce a new method for the treatment of noisy radar variables that substantially improves the performance of both techniques when they are applied to real radar data.

In Chapter 7, we turn from the study of small-scale variability of rain to that of snow, and present an investigation into the multifractal properties of snowfall at high temporal and spatial resolutions. Universal multifractal (UM) analysis is a method for describing the spatio- temporal variability of a process over many scales. We applied it to high-resolution snowfall data collected in the Swiss Alps with a 2DVD and cut into time series, reconstructed vertical columns, and small-scale snowflake accumulation maps. This is the first application of full UM to vertical columns of snowfall structure, and to snowfall-only accumulation maps and time series at such high resolution.

In the final chapter, Chapter 8, conclusions are drawn and perspectives for future research are explored. The work in the thesis is summarised and put into perspective.

2

Correction of Parsivel drop size distri-

bution measurements

This chapter is adapted from:

• T. H. Raupach and A. Berne. Correction of raindrop size distributions measured by Parsivel disdrometers, using a two-dimensional video disdrometer as a reference. Atmo-

spheric Measurement Techniques, 8(1):343–365, 2015. doi: 10.5194/amt-8-343-2015. URL

http://www.atmos-meas-tech.net/8/343/2015/. Distributed under Creative Commons Attribution 3.0 License.

• T. H. Raupach and A. Berne. Corrigendum to “Correction of raindrop size distributions measured by Parsivel disdrometers, using a two-dimensional video disdrometer as a reference” published in Atmospheric Measurement Techniques, 8, 343-365, 2015. Atmos. Meas. Tech., 2015. doi: 10.5194/ amt-8-343-2015-corrigendum. URL http://www. atmos-meas-tech.net/8/343/2015/. Distributed under Creative Commons Attribution 3.0 License.

This work was completed by T. Raupach under the supervision of A. Berne. Research, analyses, and writing are by T. Raupach. For data acknowledgements, see Appendix A.

2.1 Introduction

In order to study rainfall microstructure effectively, we require accurate measurements of the DSD. Disdrometers are instruments that measure the DSD at a point location. There are various types, but in this chapter we are concerned with the OTT Hydromet particle size and velocity (Parsivel) disdrometer, and the two-dimensional video disdrometer (2DVD) from Joanneum Research. The original Parsivel was by PM Tech Inc. OTT Hydromet purchased the rights to the instrument and redesigned it in 2005; the result was the first-generation Parsivel.

The second-generation Parsivel2was introduced in 2011, and provided improvements over

the first-generation model (Tokay et al., 2014). The Parsivel is a laser optical disdrometer that uses a sheet of light through which drops fall. The diameter and velocity of a drop is then determined by sensing the shadow it casts and for how long it casts it (Löffler-Mang and Joss, 2000). Parsivels bin drops into classes of velocity and diameter and record the number of drops measured per class over an integration time. Parsivel disdrometers have been shown to be susceptible to errors in the recorded drop concentrations, particularly for small and large drops (Krajewski et al., 2006; Tokay et al., 2013). The Parsivel measurement technique assumes properties of the precipitation that are far more appropriate for rain than for solid precipitation; for example, that particles will be spheroidal, have a horizontal orientation of their major axis, and that only one particle will be in the beam at once (Yuter et al., 2006; Battaglia et al., 2010). The Parsivel is, however, a low cost, durable, and reliable instrument that makes it particularly well-suited for deployment in networks to study the small-scale variability of the DSD (e.g. Tapiador et al., 2010; Jaffrain et al., 2011).

The 2DVD1uses two perpendicular high-speed line-scan cameras, each with an opposing

light source, to measure particles from orthogonal angles and thus record their shape (e.g. Thurai and Bringi, 2005; Thurai et al., 2007) as well as their size and velocity (Kruger and Krajewski, 2002; Schönhuber et al., 2008). Information on each individual particle that falls through the measurement area of the 2DVD is recorded. A particle’s fall speed is determined by the difference in time between its detection in the two camera planes, which are offset vertically by 6.2–7 mm. Thus, the 2DVD uses no literature-derived estimates for raindrop shape or velocity; these parameters are measured directly (Schönhuber et al., 2008). Some drawbacks of the 2DVD have been noted. In particular, drops with diameters smaller than 0.2 mm have been found to be unreliably measured (Tokay et al., 2001); Tokay et al. (2013) recommend taking 0.3 mm as a minimum measured diameter in 2DVD data due to underestimation of drop counts below this diameter. In earlier designs of the instrument, the reliability of mea- surements decreased with increasing wind speed (Nešpor et al., 2000). This has subsequently been addressed through design improvements (Schönhuber et al., 2007).

Several comparisons between 2DVD and Parsivel disdrometers have been reported on in the literature. In experimental trials the 2DVD has been found to produce better matches to rain 1_{The 2DVD was called the two-dimensional video distrometer by Schönhuber et al. (2008), to emphasise that}

the instrument collects information on the distribution of particles. To avoid confusion we use the standard spelling of disdrometer.

2.1. Introduction

gauges than Joss and Waldvogel (Tokay et al., 2001) and Parsivel (Thurai et al., 2011; Tokay et al., 2013) disdrometers. Krajewski et al. (2006) showed that PM Tech Parsivel disdrometers measured higher numbers of small drops (0.2 to 0.4 mm) than the 2DVD and generally re- ported higher rain rates. In a study in Alabama, USA, using first-generation Parsivels, Tokay et al. (2013) found that Parsivel disdrometers were less sensitive to small drops than the 2DVD, and that they overestimated the numbers of drops over 2.44 mm in diameter, while under- estimating the numbers of drops under 0.76 mm in diameter. Furthermore, they found that Parsivels measured fall velocities lower than the expected terminal fall speeds for drops larger than 2.44 mm in diameter. Tokay et al. (2013) concluded that inhomogeneous laser beams in first-generation Parsivel disdrometers were the cause of the misestimation of drop counts. Thurai et al. (2011) found that first-generation Parsivels recorded higher mass-weighted mean

diameter and rain rate than 2DVD, mostly when the rain rate exceeded 20 mm h−1.

Disdrometers can record erroneous measurements due to wind turbulence, splashing, mis- matching between cameras (in the case of the 2DVD), multiple drops appearing at the same time, margin-fallers, or external interference from, for example, insects or spiderwebs. Mini- mal data treatment for disdrometer measurements usually involves removing outlier points by reference to expected terminal fall velocity (e.g. Tokay et al., 2001; Kruger and Krajewski, 2002; Thurai and Bringi, 2005). For example, Tokay et al. (2013) removed drops exceeding ±50 % of the expected terminal fall speed, while Jaffrain and Berne (2011) used a threshold of ±60 % of the expected fall speed. This existing approach removes particles that are obviously erroneous, but it has some shortcomings. By only removing measurements, it does not allow for the fact that the disdrometer may underestimate the number of drops falling. Most importantly, the treatment is based solely on bulk variables such as rain rate, and does not test whether the resulting DSDs after the correction are physically viable.

In this chapter, we present a correction method for DSD measurements provided by Parsivel disdrometers, using a 2DVD as a reference instrument. The correction is designed to ensure that the DSDs recorded by Parsivel disdrometers are accurate, in terms of both the raw DSD and its moments. The correction method adjusts two properties of the recorded DSDs. First, drop velocities per diameter class are shifted such that the mean velocity per diameter class aligns with the theoretical terminal drop velocity for raindrops of that diameter; these raw measurements can then be screened for implausible measurements. Second, per-diameter- class volumetric drop concentrations are scaled such that they match, in a statistical way, the concentrations measured by a collocated 2DVD.

The rest of this chapter is organised as follows: the data used are described in Section 2.2, where we introduce the Parsivel network that provided data for most of the work in this thesis. Measurement of the DSD and the instruments we are concerned with in this work are discussed in Section 2.3. The correction is introduced in Section 2.4. The results of the correction applied to the data are shown in Section 2.5 for first-generation Parsivels, and in

Section 2.6 for Parsivel2. The application of the technique to another climatology is addressed