The effect of rainfall measurement uncertainties on rainfall-runoff processes modelling
Purpose:
A modelling of surface runoff and pipeflow processes comprises uncertainties in model structure, model constants and parameters and model inputs. Rainfall data are crucial input for all tasks concerning the analysis of urban drainage during wet weather period.
The most common measuring equipment to obtain the information about the precipitation intensity is tipping bucket rain gauge. However, its measuring principle introduces significant errors. Therefore, the need of static and dynamic calibration was studied by several previous studies (e.g. Niemczynowicz, 1986). The static one was found necessary whereas the dynamic one less important, because it affects high precipitation intensities only (Fankhauser, 1998). The quantification of uncertainty has been recommended for futher reasearch by Krajewski et.al. (1998).
Further, the propagation of measurement errors and uncertainty through runoff - pipe flow model is investigated. Apparently uncertainty analysis of rainfall and its propagation through a runoff models have been already studied (e.g. Lei 1996), but not with respect to measuring facilities.
To assess credibility of measured rainfall data including its interference with urban drainage modelling tasks was the general goal of the project. First, the following characteristics of the rain gauges were determined: i) static error in bucket volume and uncertainty of its determination; ii) dynamic error caused by rain gauge mechanical function (tipping) and uncertainty of its determination; iii) the uncertainty of correct horizontal levelling.
Second, the propagation of rainfall measurement errors and uncertainties throughout the runoff - pipeflow model was studied. The effect on different flow characteristics is studied as well as its magnitude for differently sized catchments.
Methods:
The set of 18 rain gauges with 500 cm2 collecting area and the resolution 0.1 mm of rain depth was used in the study. The static and the dynamic errors were studied using laboratory calibration setup. The uncertainty of the errors determination was quantified by the methods of system analysis. Dynamic error curves were constructed for intensities range 0.5 to 50 μm/s. Finally, the individual errors and the uncertainties were combined into the overall error and the uncertainty of rainfall measurement represented by relationship between the intensity and the measurement error expressed by probability density function (PDF).
The quantification of the rainfall measurement uncertainty on the runoff - pipe flow simulation is undergoing at present. Three scenarios have been defined:
1. Rainfall data corrected by static error only.
2. Rainfall data corrected by static and dynamic errors.
3. Rainfall data corrected by overall error and uncertainty.
The system behaviour for two different rain events (short intensive storm and long rain event with high rain depth) is analyzed. In the scenarios 1 and 2 the identically corrected data are used for simulation, in the third scenario a number of hyetograph generations is done according to PDF. All generations are simulated and the results are statistically treated in order to obtain PDF of simulated outputs. The influence on the following characteristics is going to be quantified: i) the instantaneous values of the water depth h, the velocity v and the discharge Q in sewer system; ii) the values of the peak discharge Qmax and the hydrograph volume V of the flood wave in sewer system; iii) the reservoir characteristics of two serial stormwater retention ponds.
Dumping of the measurement error and the uncertainty influence along the catchment size is going to be studied as well.
Results:
It was found that “correct” adjustment of the bucket volume (static calibration) is limited by drop size produced by buret tube. The error was evaluated up to +/-2%. Hovewer, the uncertainty rises in field conditions, because drops at the outflow from the syphon are three times larger than that from the burette. It produces the increase of the error to +/-6%. The dynamic calibration showed similar trends for the majority of rain gauges. However, the difference in the gradient of dynamic error curves was observed. The uncertainty from horizontal levelling was proved to be small.
The catchment Prague - Kosik, served by storm sewer system, has been chosen as an experimental area. The propagation of rainfall measurement error and uncertainty through the runoff - pipeflow model is carried out and the results will be presented in the paper.
Conclusions:
As a consequence of the presented project a methodology of measurement, processing and using of rainfall data will be created.
References:
Fankhauser R. (1998). Influence of Systematic Errors from Tipping Bucket Rain Gauges on Recorded Rainfall Data. Water Science & Technology, Vol. 37, No. 11, pp. 121-129.
Lei J. H. (1996). Uncertainty Analysis of Urban Rainfall - Runoff Modelling. A Dissertation, NTNU Trondheim, Norway.
Krajewski W.F., Kruger A., Nespor V. (1998). Experimental and Numerical Studies of Small-Scale Rainfall Measurement and Variability. Water Science & Technology, Vol. 37, No. 11,
pp. 131-138.
Niemczynowicz J. (1986). The Dynamic Calibration of Tipping-Bucket Raingauges. Nordic Hydrology, Vol. 17, pp. 203-214.