Precipitation-Gauge Network 沉淀物估算网络.ppt

Precipitation Gauge Network Precipitation varies both in time and space Sound hydrologic/hydraulic designs require adequate estimation of temporal/ spatial precipitation patterns. The density of rain gauge network depends on (1) purpose of the study; (2) geographic configuration of the study region; (3) economic consideration. Rain Gauge Density in HK Rain gauge density in HK is: Daily 13.6 km2/gauge Autographic/ Automatic 11.0 km2/gauge Rain gauge density is significant higher in Hong Kong Island and much sparse relatively in New Territory (see figure). TypeNumber of StationsLocation Map HKO Automatic Weather Station Rain Gauges18Figure 2 GEO Rain Gauge Stations - Telemetered86Figure 2 DSD Rain Gauge Stations - Telemetered9Figure 2 HKO Conventional Rain Gauge Stations51Figure 3 HKO Automatic Reporting Rain Gauges21Figure 2 Conventional Raingauge Locations in HK Telemetered Raingauge Network in HK World Meteorological Organization (WMO) Suggestion A minimum density for precipitation gauge network: (at least 10% are automatic recording gauges) I: Flat region of temperature, Mediterranean IIa: Mountain region of temperate, Mediterranean speed at which mechanical devices work (such as tipping bucket gages); exposure angle; Px = rainfall amount to be estimated ; Pi = rainfall amount at index station i ; ai = weighting factor for index station i . Sometimes, we may want to impose ai 0 for all i = 1, 2, n Px? P2 P1 P3 P4 Arithmetic Average/Normal Ratio Methods Arithmetic Average Method: Normal Ratio Method: or where Ni = Average annual total rainfall at station i. Inverse Distance Method Inverse Distance Method: , i = 1, 2, , n where Di = distance from index station i to the point of estimation. Issue: How to determine the “best“ value for “b“? Px? P2 P1 P3 P4 Modified Methods Modified Normal Ratio Method: i = 1, 2, , n Issue: How to determine the “best“ value for “b“? Modified Inverse Distance Method: i = 1, 2, , n where Ei = elevation difference between the i-th index station and the point of estimation. a,b = constant Issue: How to determine the “best“ values for “a“ and “b“? Optimization Methods Minimize (Min. Absolute Deviation, MAD, Criterion) Subject to ai 0, i = 1, 2, , n; Uj, Vj 0, j =1, 2, , J where Pij = rainfall amount for the j-th storm event at the i-th index station; J = total number of storm events; Uj, Vj = over- and under-estimation for event j The above MAD objective function can be replaced by the least square criterion as Minimize Any other goodness-of-fit criteria we can use? Isohyetal/ Kriging Methods Isohyetal Method: Estimate point rainfall depth by first construct equal rainfall contour map (see HK annual total rainfall isohyetal maps) Kriging Method: - A geostatistical method originally developed in mining engineering by Krige. - The method is appropriate for dealing with random field having non-repeated observation at different locations in space. - Preserve the spatial correlation structure of observed data. - Optimal weight factors, ais , are determined to minimize the mean-squared-error at the point of estimation. - The by-product of the method is to produce error map of estimation. Areal Rainfall Analysis Rainfall gauges provides point measurements of rainfall amount (in terms of depth). In some hydrologic applications, spatial variation or average depth of precipitation over a given area is needed. Equivalent Uniform Depth (EUD): Depth of water that would result if all of the precipitation received were uniformly distributed over the designated area. Methods for Estimating Mean Areal Rainfall: - Basic Idea : where P = EUD ; Pi = rainfall depth at station i ; ai = weighting factor for station i , 0 ai 1 , and n = total number of stations (or gauges) Arithmetic Average Method : where n = number of rain gauges within the designated area. Thiessen Polygon Method: Attempt to define the area represented by each gage in order to weigh the effects of non-uniform rainfall distribution. Procedure : (1) Connecting lines of gages are drawn. (2) Draw perpendicular bisectors of these connecting lines. (3) Determine the area of each polygon , Ai , where = total area of interest (4) Limitations : (1) Inflexible new polygon is needed if there is any change in the number of gages or the position of gages. (2) Does not consider orographic influences. Arithmetic Average/Thiessen Polygon Methods Isohyetal Method/Others Isohyetal Method The method is generally considered to be the most accurate scheme to compute the EUD of rainfall over a drainage area. Procedure : (1) Contours of equal precipitation (isohyet) are constructed. (2) Areas between successive isohyets are measured, Ai. (3) Average precipitation depth between isohyets are computed, Pi. (4) The basinwide EUD of rainfall is The procedure is subjective in the sense of interpolating precipitation depth between gages. Usually, linear interpolation is used. The accuracy of the analysis heavily depends on the analysts skill. Other Methods: Trend Surface Analysis, Kriging Method, Hypsometric Method (see Shaw, 1994, p.211), and Multiquadric Method (see Shaw, 1994, p.212). Examples Depth-Area Relation Area (km2)2550100200 ARF1.000.960.910.85 The DAD analysis is devised to determine the greatest precipitation amounts for various size areas and durations over different regions and for certain seasons. The resulting DAD relationship is primarily to be used for determining a hypothetical storm event for designing hydraulic structures. Area-Reduction Factor (