PRECIPITATION. Assignment 1

Transcription

1 Assignment 1 PRECIPIAION Due: Monitoring of precipitation is based on an almost worldwide network of measuring stations (point measurements). However, for the investigation of fundamental questions in engineering hydrology, knowledge of precipitation in relation to area (areal rainfall) is needed. Areal rainfall is of importance for eample as input parameter for catchment-scale water balances, in flood analysis or for the synthesis of design floods. herefore, areal rainfall has to be derived from the available point measurements of precipitation. he precipitation measurement stations should ideally be distributed according to the spatial variability of the precipitation (e.g. denser network in mountainous regions). For small catchments (A < 10 km 2 ) areal rainfall is often determined solely based on data from one pluviometer. For larger catchments at least three stations should be available for determining the areal rainfall. Introduction to the Study Area In four assignments the Dischmabach catchment, upstream of gauge Kriegsmatte (Figure 1), will be investigated and different hydrological methods will be applied. Dischmabach is located mainly within the municipality of Davos in canton Graubünden (Switzerland). It discharges into the Albula, which is a tributary to the river Rhine. Figure 1: Dischmabach catchment ( Pegelauslass = gauge; source: GoogleMaps) HS 17, Hydrology I, Assignment 1 Page 1

2 ask 1 (Characterisation of the study area) Use - a website which is run by the Swiss Federal Office for the Environment (BAFU) - to get familiar with the study area. Answer the following questions: 1.1 What is the area of the catchment? 1.2 How long is the Dischmabach from its source to the gauge Kriegsmatte? 1.3 How high are the highest and the lowest points in the catchment? 1.4 What are the two dominant landuses in the study area? 1.5 Which percentage of the catchment area is covered by glaciers? 1.6 What statements can be made concerning the retention capacity and the permeability of the ground in the catchment? 1.7 What was the average discharge in the period from at the gauge Kriegsmatte? 1.8 How high was the highest observed flood at the gauge Kriegsmatte? ask 2 (Methodology) In the lectures you got to know several methods to derive the areal rainfall for a catchment. Amongst others, these were: hiessen-polygons, Isohyets and the arithmetic average. Figure 2 schematically depicts two catchments with differing catchment characteristics. C B D A B D A C Catchment I Lowland catchment Hardly any height difference Landuse: predominantly forest Area: 98,5 km 2 E E Catchment II Alpine catchment Large elevation differences Bounded at the east and west by mountain ridges Landuse: steep slopes, partially pasture Area: 14,6 km 2 Figure 2: Schematic maps of the catchments I and II with location of available rain gauges (A-E) HS 17, Hydrology I, Assignment 1 Page 2

3 2.1 Briefly describe the aforementioned methods and contrast their advantages and disadvantages. 2.2 Which of the aforementioned methods for the computation of the areal rainfall can be applied in the case of catchments I and II, respectively? Which rain gauges would you include in your computations? Eplain your decisions. ask 3 (Computation of the Areal Rainfall) In and around the catchment Dischmabach the precipitation depth is measured in the five rain gauges A-E with a tipping-bucket (Figure 3; enlarged in the appendi Figure 4). For a rainfall event of August 2010 the measurement data are provided in a half-hourly resolution (able 1). Figure 3: Map of the Dischmabach catchment with locations of the pluviometers A, B, C, D and E able 1: Data of the rain gauges A-E (Precipitation in mm) Pluviometer A B C D E 18: : : : : : : : : : : : : HS 17, Hydrology I, Assignment 1 Page 3

4 3.1 Apply the hiessen-polygon-method to determine the areal rainfall in the study area. Use the raster to determine the areas that can be allocated to the different rain gauges. For this purpose, estimate the number of squares for each polygon (e.g. for each polygon count all squares that lie completely within and estimate the sum of the remaining parts). he sum of squares of all polygons is equivalent to the total area of the catchment (task 1.1). 3.2 Plot the areal rainfall over time (unit of areal rainfall = mm). ask 4 (DDF-Curve) For the station of Davos a DDF-chart (DDF = Depth Duration Frequency) using precipitation data from 1978 to 2007 shall be developed. his depicts the relationship between duration of rainfall, maimum precipitation amount and probability of occurrence. he latter is described using the recurrence period. DDF-charts are the basis for many hydraulic constructions, e.g. in flood protection, bridge planning, urban water management as well as urban and regional planning. Given are maimum values of annual precipitation data from 1978 until 2007 for durations of 1, 3, 6, 12 and 24 hours (Appendi able 2). he data are assumed to be Gumbel distributed How can you verify that the rainfall data are assumed as Gumbel distributed? Name two different methods For the different time durations calculate the mean value m and the variance s of the sample Estimate the parameters of the Gumbel distribution u and for every time duration (1, 3, 6 12 and 24 hours) using the method of moments. 4.4 Calculate the precipitation amount for every time duration and the period of recurrence for (R) 2, 10 and 50 years. 4.5 Create a DDF-chart that contains the different return periods of 2, 10 and 50 years. Use a power function to describe the single curves and give the equations of the fitted functions. 4.6 Plot a precipitation event with a recurrence period of 10 years and a duration of 4.5 hours into the same chart. Estimate the precipitation depth either by reading it from the chart or by using the fitted equation. 1 Hint: All necessary mathematical equations can be found in the formulary on the course web page. HS 17, Hydrology I, Assignment 1 Page 4

5 4.7 Which problem do you see in estimating etreme rainfall events with very large recurrence periods (> 100 years) using a DDF-curve based on the data in able 2 (Appendi)? HS 17, Hydrology I, Assignment 1 Page 5

6 - Appendi - Figure 4: Map of the Dischmabach catchment with locations of the pluviometers A, B, C, D and E HS 17, Hydrology I, Assignment 1 Page 6

7 able 2: Maimum annual precipitation depth of different years and durations for the station of Davos Ma precipitation Duration [h] depth [mm] HS 17, Hydrology I, Assignment 1 Page 7