Raindrop size distribution and radar reflectivity-rain rate relationships for radar hydrology

The conversion of the radar reflectivity factor Z (mm6m-3) to rain rate R (mm h-1) is a crucial step in the hydrological application of weather radar measurements. It has been common practice for over 50 years now to take for this conversion a simple power law relationship between Z and R. It is the purpose of this paper to explain that the fundamental reason for the existence of such power law relationships is the fact that Z and R are related to each other via the raindrop size distribution. To this end, the concept of the raindrop size distribution is first explained. Then, it is demonstrated that there exist two fundamentally different forms of the raindrop size distribution, one corresponding to raindrops present in a volume of air and another corresponding to those arriving at a surface. It is explained how Z and R are defined in terms of both these forms. Using the classical exponential raindrop size distribution as an example, it is demonstrated (1) that the definitions of Z and R naturally lead to power law Z-R relationships, and (2) how the coefficients of such relationships are related to the parameters of the raindrop size distribution. Numerous empirical Z-R relationships are analysed to demonstrate that there exist systematic differences in the coefficients of these relationships and the corresponding parameters of the (exponential) raindrop size distribution between different types of rainfall. Finally, six consistent Z-R relationships are derived, based upon different assumptions regarding the rain rate dependence of the parameters of the (exponential) raindrop size distribution. An appendix shows that these relationships are in fact special cases of a general Z-R relationship that follows from a recently proposed scaling framework for describing raindrop size distributions and their properties

ANALISIS KEMAMPUAN RADAR NAVIGASI LAUT FURUNO 1932 MARK-2 UNTUK PEMANTAUAN INTENSITAS HUJAN [ANALYSIS OF FURUNO MARINE RADAR 1932 MARK-2 CAPABILITY TO OBSERVE RAIN RATE]

Indonesia mempunyai banyak daerah rawan banjir dan tanah longsor sehingga diperlukan sistem peringatan dini terhadap bencana tersebut. Radar cuaca merupakan salah satu alternatifnya, akan tetapi harganya mahal, sehingga diperlukan radar cuaca alternatif yang biayanya murah. Dalam penelitian ini dilakukan analisis kemampuan radar navigasi laut Furuno 1932 Mark-2 sebagai solusi radar cuaca biaya murah dengan menganalisis spesifikasinya kemudian membuat eksperimen dan pengujian untuk mencoba solusi kelemahannya melalui pengembangan sistem akuisisi dan pengolah sinyal radar. Menurut spesifikasinya, unit scanner radar memenuhi syarat untuk pendeteksian hujan, hanya membutuhkan koreksi volume untuk lebar berkas vertikal yang lebar. Sedangkan unit display-nya belum memenuhi karena plotter-nya masih satu warna dan penghilang clutter-nya menganggap hujan sebagai clutter. Dari hasil eksperimen dan pengujian dapat diketahui bahwa radar ini mampu digunakan untuk mendeteksi pergerakan hujan dengan nilai reflektivitas yang terpantau antara 15-30 dBZ. Hasil pengukuran rain gauge menunjukkan pada reflektivitas 30 dBZ tersebut terpantau hujan dengan intensitas 5,4 mm/jam. Hubungan antara (Z) dan (R) yang terdeteksi tidak sesuai dengan persamaan Marshall Palmer, karena nilai 30 dBZ menghasilkan intensitas hujan 2,7 mm/jam. Oleh karena itu dalam penelitian selanjutnya perlu dicari hubungan Z dan R yang sesuai untuk radar ini melalui kalibrasi nilai reflektivitas menggunakan data hasil pengukuran rain gauge. Kata kunci: Faktor Reflektivitas Radar, Radar Navigasi Laut, Intensitas Huja

Experimental Quantification of the Variability of the Raindrop Size Distribution at Small Scales

Reliable quantitative precipitation estimation is crucial to better understand and eventually prevent water-related natural hazards (floods, landslides, avalanches, ...). Because rainfall is highly variable in time and space, precipitation monitoring and forecasting is a complex task. In addition, the variability of rainfall at small scales (for instance within the radar pixel) is still poorly understood. Knowledge of the rain drop size distribution (DSD) is of primary concern for precipitation estimation and in particular weather radar. To better understand the variability of the DSD at small scales, a network of optical disdrometers (Parsivel) has been designed and set up. The instruments are fully autonomous in term of power supply and data transmission. The network of 16 disdrometers has been deployed over a typical operational weather radar pixel (1 × 1 km2) in Lausanne, Switzerland, for 16months collecting DSD data at a high temporal resolution (30 s). The sampling uncertainty associated with Parsivel measurements has been quantified for different quantities related to the DSD, using a 15-month data set collected by two collocated disdrometers. Using a geostatistical approach, and in particular variograms, the spatial structure of quantities related to the DSD has been quantified. The analyses have been conducted on 36 rainfall events that have been grouped according to three types of rainfall (i.e., convective, transitional and frontal). It shows a significant variability, i.e., larger than the one induced by the sampling process, of the different quantities of interest. The observed spatial structure is significant for temporal resolution below 30 min from which it is difficult to distinguish between the natural variability and the one induced by the sampling process. The impact of the observed variability of the DSD on radar rainfall estimators is investigated focusing on two different radar power laws (the classical Z-R law for conventional radar and the R-Kdp law for polarimetric radar). The parameters of the power laws are estimated at different spatial scales: at the single station scale, at the aggregate of stations scale (aggregate of point measurements) and at the pixel area scale (average over all the stations). First, it shows clear distinct groups of power law parameters according to the type of rainfall. Moreover, the observed variability of these parameters is significantly larger than the variability induced by the sampling process of the instruments. The observed variability in power law parameters can be responsible for deviation in terms of rain amounts at the single station scale ranging from -5 to +15% the one estimated at the pixel (average) scale. The original contributions in this work are: (1) the design and deployment of an innovative network of autonomous disdrometers Parsivel over a typical operational weather radar pixel (1 km2), (2) the quantification of the sampling uncertainty associated with Parsivel measurements, (3) the quantification of the spatial variability of different quantities related to the DSD within this typical radar pixel and (4) the quantification of the influence of this spatial variability of the DSD on radar rainfall estimation (for conventional and polarimetric radar). For illustration, the results are important: (i) to illustrate the added value of the network of disdrometer that has been designed and the interest for various environmental fields (meteorology, hydrology, risks of water-related natural hazards, ...), (ii) for a better knowledge of the spatial variability of the DSD at different scales which should helps improving radar rainfall estimation, (iii) for the quantification of the errors associated with the extension of relationships derived at a specific location to larger domains (e.g., pixel) and (iv) for the ground validation of numerical weather model

Procedures for improved weather radar data quality control

[eng] Weather radar data and its downstream products are essential elements in weather surveillance and key parameters in the initialisation and validation of hydrological and meteorological models, among other downstream applications. Following the quality standards established by the European and global weather radar networking referents, the present thesis aims for the improvement of the base data quality control in the regional weather radar network operated by the Meteorological Service of Catalonia, the XRAD. This objective is accomplished through the analysis, development and implementation of new or existing procedures and algorithms for radar data quality assessment and improvement. Attending to the current radar technology and to the already implemented quality control procedures for the XRAD, the work is focused on the continuous evaluation of the radar system calibration status and on the correction of Doppler velocity data. The quality control algorithms and recommendations presented are easily translatable to any other operative weather radar networking environment. A Sun-based, fully automatic procedure for online monitoring the antenna alignment and the receiver chain calibration is adapted and operationally implemented for the XRAD. This Sun-monitoring technique was developed at the Royal Netherlands and Finnish Meteorological Institutes and is included in the quality control flow of numerous weather radar networks around the world. The method is modified for a robust detection and characterisation of solar interferences in raw data at all scan elevations, even when only data at relatively short ranges is available. The modified detection algorithm is also suitable for detecting interferences from wireless devices, which are stored for monitoring their incidence in the XRAD. The solar interferences detected, in turn, are input observations for the inversion of a two-dimensional Gaussian model that yields estimates of the calibration parameters of interest. A complete theoretical derivation of the model establishes its validity limits and provides analytical estimates of the effective solar widths directly from radar parameters. Results of application of this Sun-monitoring methodology to XRAD data reveal its ability to determine the accuracy of the antenna pointing and to detect changes in receiver calibration and radar system operation status. In order to facilitate the usage of the Sun-monitoring technique and the interpretation of its estimates, the methodology is reproduced under controlled conditions based on the distributions of solar observations collected by two of the XRAD radars. The analysis shows that the accuracy of the estimated calibration parameters is conditioned by the precision, number and distribution of the solar observations which constitute key variables that need to be controlled to ensure reliable estimates. In addition, the Sun-monitoring technique is compared under actual operative conditions with two other common techniques for quantifying the antenna azimuth and elevation pointing offsets. Pointing bias estimates gathered in a dedicated short-term campaign are studied in a direct inter- comparison of the methods that reflects the advantages and limitations in each case. The analysis of the bias estimates reported by the methods in the course of a one-year period reveals that the performance of the techniques depends on the antenna position at the time of the measurement. After this study, a reanalysis of the Sun-monitoring method results is proposed, which allows to additionally quantify the antenna pedestal levelling error. Finally, a post-processing, spatial image filtering algorithm for identification and correction of unfolding errors in dual-PRF Doppler velocity data is proposed. The correction of these errors benefits the usage of radar velocity data in downstream applications such as wind- shear and mesocyclone detection algorithms or assimilation in numerical weather prediction models. The main strengths of the proposed algorithm, in comparison with existing correction techniques, are its robustness to the presence of clustered unfolding errors and that it can be employed independently of post-processing dealiasing algorithms. By means of simulated dual-PRF velocity fields, the correction ability of the algorithm is quantitatively analysed and discussed with particular emphasis on the correction of clustered errors. The quality improvement in real dual-PRF data brought out by the new algorithm is illustrated through application to three selected severe weather events registered by the XRAD.[cat] Seguint els estàndards de qualitat establerts per a les xarxes de radars meteorològics de referència a nivell europeu i global, la present tesi té com a objectiu la millora del control de qualitat de les dades de la xarxa regional de radars meteorològics operada pel Servei Meteorològic de Catalunya (la XRAD). Atenent als procediments de control de qualitat ja implementats per a la XRAD, el treball es centra en l'avaluació contínua de l'estat del calibratge del sistema radar i en la correcció de les dades de velocitat Doppler. Es presenta l'adaptació i aplicació d’un procediment totalment automàtic basat en el Sol, que permet la quantificació remota dels errors d'alineació de l'antena i de calibratge en recepció del radar a la XRAD. El mètode ha estat modificat per a la detecció i caracterització robusta d'interferències solars a les dades primàries de radar. Les interferències solars són utilitzades per a la inversió d'un model físic que proporciona estimacions dels paràmetres de calibratge d'interès. L'algoritme de detecció modificat també és adequat per a la identificació d'interferències procedents de dispositius electrònics externs. Aquestes interferències són emmagatzemades per al seguiment de la seva incidència a la XRAD. La metodologia solar esmentada es modelitza en condicions controlades a partir de la distribució de les observacions solars recollides per dos dels radars de la XRAD. L'anàlisi mostra que la precisió, el nombre i la distribució de les observacions solars constitueixen variables clau que necessiten ser controlades per garantir estimacions fiables dels paràmetres de calibrage. A més, la tècnica solar es compara, sota condicions operatives reals, amb altres dues tècniques habitualment emprades per a la quantificació de l'error d'apuntament de l'antena. A partir d'aquest estudi, es proposa un nou mètode d'anàlisi de les interferències solars, el cual permet quantificar l'error d'anivellament del pedestal de l'antena. Finalment, es desenvolupa i valida un algoritme de filtrat d'imatges per a la identificació i correcció dels errors característics que es donen lloc a les dades dual-PRF de velocitat Doppler. Els punts forts de l'algoritme proposat, en comparació amb les tècniques de correcció existents, són la seva robustesa en la correció d'errors agrupats i que pot emprar- se amb independència dels algoritmes de dealiasing. La millora de la qualitat de les dades reals de velocitat s'il·lustra mitjançant l'aplicació de l’algoritme a tres episodis de temps sever enregistrats per la XRAD

Improved Data Uncertainty Handling in Hydrologic Modeling and Forecasting Applications

In hydrologic modeling and forecasting applications, many steps are needed. The steps that are relevant to this thesis include watershed discretization, model calibration, and data assimilation. Watershed discretization separates a watershed into homogeneous computational units for depiction in a distributed hydrologic model. Objective identification of an appropriate discretization scheme remains challenging in part because of the lack of quantitative measures for assessing discretization quality, particularly prior to simulation. To solve this problem, this thesis contributes to develop an a priori discretization error metrics that can quantify the information loss induced by watershed discretization without running a hydrologic model. Informed by the error metrics, a two-step discretization decision-making approach is proposed with the advantages of reducing extreme errors and meeting user-specified discretization error targets. In hydrologic model calibration, several uncertainty-based calibration frameworks have been developed to explicitly consider different hydrologic modeling errors, such as parameter errors, forcing and response data errors, and model structure errors. This thesis focuses on climate and flow data errors. The common way of handling climate and flow data uncertainty in the existing calibration studies is perturbing observations with assumed statistical error models (e.g., addictive or multiplicative Gaussian error model) and incorporating them into parameter estimation by integration or repetition with multiple climate and (or) flow realizations. Given the existence of advanced climate and flow data uncertainty estimation methods, this thesis proposes replacing assumed statistical error models with physically-based (and more realistic and convenient) climate and flow ensembles. Accordingly, this thesis contributes developing a climate-flow ensemble based hydrologic model calibration framework. The framework is developed through two stages. The first stage only considers climate data uncertainty, leading to the climate ensemble based hydrologic calibration framework. The framework is parsimonious and can utilize any sources of historical climate ensembles. This thesis demonstrates the method of using the Gridded Ensemble Precipitation and Temperature Estimates dataset (Newman et al., 2015), referred to as N15 here, to derive precipitation and temperature ensembles. Assessment of this framework is conducted using 30 synthetic experiments and 20 real case studies. Results show that the framework generates more robust parameter estimates, reduces the inaccuracy of flow predictions caused by poor quality climate data, and improves the reliability of flow predictions. The second stage adds flow ensemble to the previously developed framework to explicitly consider flow data uncertainty and thus completes the climate-flow ensemble based calibration framework. The complete framework can work with likelihood-free calibration methods. This thesis demonstrates the method of using the hydraulics-based Bayesian rating curve uncertainty estimation method (BaRatin) (Le Coz et al., 2014) to generate flow ensemble. The continuous ranked probability score (CRPS) is taken as an objective function of the framework to compare the scalar model prediction with the measured flow ensemble. The framework performance is assessed based on 10 case studies. Results show that explicit consideration of flow data uncertainty maintains the accuracy and slightly improves the reliability of flow predictions, but compared with climate data uncertainty, flow data uncertainty plays a minor role of improving flow predictions. Regarding streamflow forecasting applications, this thesis contributes by improving the treatment of measured climate data uncertainty in the ensemble Kalman filter (EnKF) data assimilation. Similar as in model calibration, past studies usually use assumed statistical error models to perturb climate data in the EnKF. In data assimilation, the hyper-parameters of the statistical error models are often estimated by a trial-and-error tuning process, requiring significant analyst and computational time. To improve the efficiency of climate data uncertainty estimation in the EnKF, this thesis proposes the direct use of existing climate ensemble products to derive climate ensembles. The N15 dataset is used here to generate 100-member precipitation and temperature ensembles. The N15 generated climate ensembles are compared with the carefully tuned hyper-parameter generated climate ensembles in ensemble flow forecasting over 20 catchments. Results show that the N15 generated climate ensemble yields improved or similar flow forecasts than hyper-parameter generated climate ensembles. Therefore, it is possible to eliminate the time-consuming climate relevant hyper-parameter tuning from the EnKF by using existing ensemble climate products without losing flow forecast performance. After finishing the above research, a robust hydrologic modeling approach is built by using the thesis developed model calibration and data assimilation methods. The last contribution of this thesis is validating such a robust hydrologic model in ensemble flow forecasting via comparison with the use of traditional multiple hydrologic models. The robust single-model forecasting system considers parameter and climate data uncertainty and uses the N15 dataset to perturb historical climate in the EnKF. In contrast, the traditional multi-model forecasting system does not consider parameter and climate data uncertainty and uses assumed statistical error models to perturb historical climate in the EnKF. The comparison study is conducted on 20 catchments and reveal that the robust single hydrologic model generates improved ensemble high flow forecasts. Therefore, robust single model is definitely an advantage for ensemble high flow forecasts. The robust single hydrologic model relieves modelers from developing multiple (and often distributed) hydrologic models for each watershed in their operational ensemble prediction system