WEIGHING GAUGES MEASUREMENT ERRORS AND THE DESIGN RAINFALL FOR URBAN SCALE APPLICATIONS

WEIGHING GAUGES MEASUREMENT ERRORS AND THE DESIGN RAINFALL FOR URBAN SCALE APPLICATIONS by M. Colli (1), L.G. Lanza (1),(2) and P. La Barbera (1) (1) University of Genova, Dep. of Construction, Chemical and Environmental Engineering 1 Montallegro, 16145 Genoa, Italy (matteo.colli@unige.it) (2) WMO/CIMO Lead Centre on Precipitation Intensity, Genoa, Italy ABSTRACT Investigation of the accuracy and precision of a modern Weighing Gauge (WG) under non steady-state reference flowrate conditions is addressed as the first objective of the present work. The preliminary development and validation of the laboratory equipment for the generation of variable time step reference flowrates is shown. The generator is characterized by a sufficiently short time response with respect to the expected weighing gauge behavior in order to ensure effective comparison of the measured vs. reference flowrates at very high resolution in time. Preliminary tests were conducted on the WG instrument by imposing different generation conditions: a finite step and a double step flowrate generation. The main goal of this initial phase was to characterize the time varying response of the instrument also providing an interpretation based on the dynamic system theory. The second part of the work was devoted to the simulation of biased WG time series under non-steady flowrates with a time resolution of one minute. The internal structure and variability of the generated events was based on 22 years of one-minute RI observations recorded at the meteorological station of Villa Cambiaso (University of Genoa). The influence of the measurement accuracy on the relevant extreme events statistics was analyzed by comparing the original intensity-duration-frequency (IDF) curves with those obtained after the simulation. Keywords: rainfall, measurements, accuracy, weighing gauges 1 INTRODUCTION Extreme events statistics are proven to be highly affected by the on-site Rainfall Intensity (RI) measurement accuracy (see e.g. La Barbera et al., 2002; Molini et al., 2005). The correct construction of synthetic hyetographs that are representative of rain events relevant to urban scale applications requires high temporal resolution of the recorded RI series. Measurement accuracy requirements for rainfall intensity gauges under operational use are becoming tighter after the recent Field Intercomparison of Rainfall Intensity Gauges promoted by WMO (the World Meteorological Organisation) demonstrated the achievable accuracy of a number of commercially available instruments. Various measuring principles had been involved in the WMO intercomparison exercises and extensively tested, first under controlled laboratory conditions (see Lanza and Stagi, 2009) and then at a field test site in the period 2007-2009 (see Lanza and Vuerich, 2009). During these intercomparisons the performance of Weighing type Gauges (WG) has been proved to be comparable and under some circumstances higher than traditional Tipping Bucket Rain gauges (TBR) under steady-state reference flowrate conditions (Lanza et al., 2005; Lanza & Stagi, 2009; 2012). Meanwhile the tests under real-world conditions (Vuerich et al., 2009; Lanza & Vuerich, 2012) showed a noticeable increase of uncertainty in the WG measurements as summarized in Fig. 1 with comparable or even lower performance than suitably calibrated TBRs. The most relevant bias concerning weighing type instruments is due to the response time of the acquisition system and the derived systematic delay in assessing the exact weight of the volume of cumulated Colli and Lanza, Weighing gauges measurement errors and the design rainfall for urban scale applications 1

precipitation. This delay assumes a relevant role in case high resolution RI time series are sought from the instrument, as is the case of many hydrologic and meteo-climatic applications. The WMO Lead Centre on Precipitation Intensity activity aims at investigating the accuracy and precision of rainfall intensity gauges based on various measuring principles and the attention is focused here on the weighing type gauges. The OTT Pluvio2 weighing gauge (WG) is here investigated since it demonstrated very good performance under previous constant flow rate laboratory calibration efforts (Lanza et al., 2005). One of the most significant results of the last field intercomparison is the evidence that the dynamic response seems to impact quite heavily on the accuracy of WG measurements under real world/time varying rainfall conditions (Vuerich et al., 2009). An overall comparison of the performance of the involved rain gauges is provided in Figure 1 in terms of the percentage relative deviations of one-minute RI measurements. Figure 1 Overall measurement comparison from the WMO Field Intercomparison of Rainfall Intensity Gauges in terms of percentage relative deviations between each tested instrument and the reference system (the grey shaded graph indicates the sample size in terms of the number of available minutes of measurement). The weighing type gauge are highlighted in red. Following up such in-field results a laboratory dynamic rainfall generation system has been arranged and validated in order to evaluate the WG dynamic response under non-steady rainfall intensity conditions with a proper accuracy on the assessment of the actual values. 2 THE DYNAMIC RESPONSE OF WEIGHING GAUGES Tests conducted with a variable one-step and two-step RI generation allowed to determine the dynamic response of the OTT Pluvio2 weighing gauge, a modern rain gauge already employed as a reference sensor for the ongoing WMO Solid Precipitation InterComparison Experiment in-field campaign. The RI generator is based on joint operation of two precision pumps working on different flow rate ranges and managed by a programmable control system. Complete characterization of the RI generator accuracy and response time was achieved as a result of dedicated test sessions involving a 2-D video validation technique (Colli and Lanza, 2012). In particular, the maximum average relative residual error of the pumps Colli and Lanza, Weighing gauges measurement errors and the design rainfall for urban scale applications 2

is equal to 0.7 % meanwhile the time employed by the whole system to reach 63.2 % of the reference RI (time constant) is always lower than 200 msec. Table I - Operative range of the low flow rates Q ref generation system, average of the generation residual percentage relative errors avg(e res) and of its standard deviation st.dev(e res) Qref avg(eres) st.dev(eres) Qref avg(eres) st.dev(eres) ml/min % % ml/min % % 0.35 0 1.9 25.03 3.7 0.3 0.75 0 0.8 40.28-0.6 0.7 1.56 0.1 0.2 56.98-0.3 0.4 3.16-0.1 0.3 90.35 0.4 0.4 6.38-0.1 0.1 134.57 0.8 0.2 12.78-0.3 0.1 178.65 1.1 0.1 18.11 0.4 0.1 241.82 0.2 0 This characterization allowed highlighting a strong similarity between the WG Intensity RT indications and the response of a first order linear dynamic system, under a step forcing input. In particular, being α the ratio between the rainfall intensities generated during the first and second step (Figure 2a), a linear trend is obtained for the WG measurement at the end of the second step, here normalized with the actual value, as a function of α (Figure 2b). The same behavior is performed by a dynamic system with a null dead time d and time constant τ equal to 22.2 seconds; the best fit between the proposed conceptualization and the observed WG measurements is proposed in Figure 2b. The more the RI value between two consecutive intervals is similar (α 1), the best accurate is the theoretical description of the WG dynamical behavior. 120 100 80 RI [mm/h] RI II RI ref Ri m 1.40 1.20 1.00 RI II m/ RI II ref [-] 60 40 RI I 0.80 0.60 0.40 WG I ord. lin. dyn. sys. 20 0 0 60 120 180 t [sec] 0.20 0.00 α [-] 0 0.5 1 1.5 2 2.5 Figure 2 a) Dynamic response of the weighing gauge RI measurements (black line) superimposed to the double steps RI generation (grey histogram); b) ratio between the measured (RI II m) and reference rainfall intensity (RI II ref) as a linear function of α (square dots) obtained for both the observed WG measurements and their theoretical interpretation. 3 SIMULATION OF A REAL WORLD SCENARIO With the purpose of quantify the influence of the WG dynamic response on rainfall design statistics, the historical series recorded at the Villa Cambiaso meteorological station (University of Genova) using a traditional tipping bucket rain gauge has been corrected for systematic mechanical errors and modified following the RI(α) relation of the first order dynamic system. The original TBR measurements are available at one-minute time resolution allowing the simulation of 21 years long WG virtual records and to derive annual maxima statistics at the fine temporal scales typical of the urban basins hydrological response. It s important to stress the point that the original TBR data set corrected for systematic mechanical errors is here Colli and Lanza, Weighing gauges measurement errors and the design rainfall for urban scale applications 3

assumed to be the most representative estimate of the actual RI. In Figure 3, the depth-duration-frequency curves obtained from the WG reconstructed measurements are reported for return periods T equal to 5, 10, 20, and 50 years, and superimposed to the original curves to allow direct comparison with both the original and corrected TBR measurement statistics. 500 450 400 350 TBR corrected WG statistics TBR uncorrected T= 50 years T= 20 years RAINFALL DEPTH (mm) 300 250 200 T= 10 years T= 5 years 150 100 50 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 DURATION (hours) Figure 3 Superposition of the depth-duration-frequency curves evaluated for the WG simulations, and for the original uncorrected and corrected TBR observations at return periods T equal to 5, 10, 20 and 50 years. The representation of the gain in the estimation of the return period T WG/T TBRcorr as a function of the duration d points out the impact of WG non corrected measurements on urban design (see Figure 4). A strong biasing effect is evident for event durations shorter than one hour, where the WG reconstructed observations produce a general overestimation of the return period (T WG/T TBRcorr > 1) with a peak value equal to T WG/T TBRcorr = 2.1 retrieved for a duration of one minute and T TBRcorr =50 years. 3.5 3.0 2.5 2.0 T WG / T TBR corr (-) T=5 years T=10 years T=20 years T=50 years 1.5 1.0 0.5 0.0 0.010 0.100 1.000 DURATION (hours) 10.000 100.000 Figure 4 Gain in the estimation of the return period T WG/T TBRcorr for assigned durations evaluated for the WG reconstructed measurements at T TBRcorr = 5, 10, 20 and 50 years Colli and Lanza, Weighing gauges measurement errors and the design rainfall for urban scale applications 4

4 CONCLUSIONS Recent in-field and laboratory efforts involving modern weighing gauges have proven that the instrumental dynamic response is largely responsible for the observed lack of accuracy when non steady rainfall conditions are sought. The present work provides a first outlook of the errors involved in using annual maxima statistics based on WG observations without proper correction of the dynamic response issue. It has been shown that rainfall events with duration between one minute and one hour are affected by significant overestimation of the return period T from 10 to 100% (1.1 < T WG/T TBRcorr < 2.1) with potential consequences on hydrologic applications in urban basins that are supposed to cope with rapid hydrological responses (d < 1 h). On the contrary, good performance ( 1 < T WG/T TBRcorr < 1.1) are obtained for those applications that do not require the analysis of short duration events (d > 1 h). The WG data used in the present work were obtained from reconstruction via a numerical simulation based on real in-field observations from a different sensor and by interpreting the WG behavior as a first order linear dynamic system. The next step of this investigation will be focused on the laboratory generation of the same real world annual maxima at hourly and sub-hourly time scales so as to perform the extreme events analysis on effective WG measurements and to validate the present findings. 5 REFERENCES CIMO, (2008). Guide to Meteorological Instruments and Methods of Observation, WMO-No. 8, 7th ed., World Meteorological Organization Colli, M., L.G. Lanza, (2012) Weighing gauge performance under laboratory simulation of real world precipitation events, TECO 2012, Session 1 Instrument intercomparisons and testbeds, Brussels, Belgium, 16 October 2012 La Barbera P., Lanza L.G. and Stagi L. (2002). Influence of systematic mechanical errors of tipping-bucket rain gauges on the statistics of rainfall extremes. Water Sci. Techn., 45(2), 1-9. Lanza, L.G. and E. Vuerich (2009). The WMO Field Intercomparison of Rain Intensity Gauges. Amos. Res., 94, 534-543. Lanza, L., Leroy, M., Alexandropoulos, C., Stagi, L. and Wauben, W. (2005). Laboratory Intercomparison of Rainfall Intensity Gauges. World Meteorological Organisation Instruments and Observing Methods Rep. No. 84, WMO/TD No. 1304. Lanza, L.G. and L. Stagi (2009). High resolution performances of catching type rain gauges from the laboratory phase of the WMO Field Intercomparison of Rain Intensity Gauges. Atmos. Res., 94, 555-563. Molini, A., Lanza, L.G., La Barbera, P. (2005). The impact of tipping bucketmeasurement errors on design rainfall for urban-scale applications.hydrol. Process. 19 (5), 1073 1088. Vuerich, E., Monesi, C., Lanza, L.G., Stagi, L. and E. Lanzinger (2009). WMO Field Intercomparison of Rainfall Intensity Gauges. World Meteorological Organisation Instruments and Observing Methods Rep. No. 99, WMO/TD No. 1504, pp. 286. Colli and Lanza, Weighing gauges measurement errors and the design rainfall for urban scale applications 5