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In general, for water resources planning purposes, knowledge is required of the average rainfall depth over a certain area: this is called the areal rainfall. Some exapmples where the areal rainfall is required include: design of a culvert or bridge draining a certain catchment area, design of a pumping station to drain an urbanized area; design of a structure to drain a polder, etc.
There are various methods to estimate the average rainfall over an area, areal rainfall with area A from n Point-measurements, x i.
The simplest method of obtaining the average depth is the average arithmetically the gauge amount in the area. To illustrate this method, consider point rainfall records in mm randomly distributed over a basin fig. This method yield good estimates in flat country if the gauges are uniformly distributed and the individual gauge catches do not vary widely from the mean.
These limitations can be partially overcome if topographic influences and area representatively are considered in the selection of gauge sites. Lines are drawn to connect reliable rainfall stations, including those just outside thearea. The connecting lines are bisected perpendicularly to form a polygon around each station see fig. To determine the mean, the rainfall amount of each station x i is multiplied by the area of its polygon a i and the sum of the products is divided by the total area, A.
The polygon areas are measured by plannimeter. This method is dependent on a good network , but is not good for mountanous areas. The is expressed as. Using the same data as in illustration for the average depth method, we will now illustrate the computation of areal rainfall by the Thiesen method see fig.
The Thiessen method attempts to allow for non-uniform distribution of gauges by providing a weighting factor for each gauge. The stations are plotted on a map and connecting lines form polygons around each station.
The sides of each polygon are the boundaries of the effective area assumed for the station. Multiplying the precipitation at each station by its assigned area and dividing by compute weighted average rainfall for the total area.
The results are more accurate than those obtained by simple arithmetical averaging. The greatest limitation of the Thiessen method is its inflexibility, a new Thiessen diagram being required every time there is a change in the gauge network. Also the method doesn't allow for orographic influences. It simply assumes linear variation of precipitation between stations and assigns each segment of area to the nearest station. Rainfall observations for the considered period are plotted on the map and contours of equal precipitation depth isohyets are drawn Fig.
The method takes care of non-linear distribution and detects outliers- takes care of topography-is least subjective but it is laborous. This method, when used by an experienced analyst is the most accurate method of averaging precipitation over an area. Station location and amount are plotted on a suitable map, and contours of equal precipitation isohyets are then drawn as shown in figure 2.
In this method the average precipitation for an area is computed by weighting the average precipitation between successive isohyets usually taken as the average of the two isohyetal values by the area between isohyets, totaling these products and divide by the total area see table 2. Isohyet mm. Area enclosed. Net area. Precipitation volume. The isohyetal method permits the use and interpretation of all available data and is well adapted to display and discussion.
In constructing an isohyetal map, analysts can make full use of their knowledge of orographic effects and storm morphology, and in this case the final map should represent a more realistic precipitation pattern than could be obtained from the gauge amounts alone. If linear interpolation between stations is used the results will be essentially the same as those obtained with the Thiessen method.
The grid-point method: average the estimated precipitation at all points of a superimposed grid. This approach has certain advantages over the Thiesen method but is practical only with the aid of a computer. The Kriging weights obtained are tailored to the variability of the phenomenon studied. As a result of the averaging process, and depending on the size of the catchment area, the areal rainfall is less than the point rainfall. The physical reason for this lies in the fact that a rainstorm has a limited extent.
The areal rainfall is usually expressed as a percentage of he storm-centre value: the areal reduction factor ARF. Basically the ARF is a function of: rainfall depth, storm duration, storm type, catchment size and return period.
The ARF increases comes nearer to unity with increasing total rainfall depth, which implies higher uniformity of heavy storms. It also increases with increasing duration, again implying that long storms are more uniform. It decreases with the area under consideration, as a result of the storm-centred approach. Storm type varies with location, season and climatic region.
Published ARF's are, therefore, certainly not generally applicable. From the characteristics of storm types, however, certain conclusions can be drawn. A convective storm has a short duration and a small areal extent hence, the ARF decreases steeply with distance. The same applies to orographic lifting.
Cyclone also has long duration and a large areal extent, which also leads to a more gradual reduction of the ARF than in the case of thunderstorms.
In general, one can say that the ARF-curve is steepest for a convective storm, that a cyclonic storm has a more moderate slope and that orographic storms have an even more moderate slope. The functional relationship between the ARF and return period is less clear. Bell showed for the United Kingdom that ARF decreased more steeply for rainstorms with ahigh return period.
Similar findingsare reported by Begemann for Indonesia. This is, however, not necessarily so in all cases. If widespread cyclonic disturbances, instead local convective storms, constitute the high return period rainfall,the opposite may be true.
Again, it should be observed that cyclones belong to a different statistical population from other storm types, and that they should be treated separately. If cyclones influence the design criteria of an engineering work, then one should consider a high value of the ARF. Whereas the average depth method is simple to use, its limitation lies in the fact that it assumes a uniform distribution of stations in an area, which often is not the case.
Further it assumes a flat terrain in order to minimize the variation of the point observations from the mean. The Thiesen method is more accurate than the average depth method since it takes care of the distribution of stations in an area by assigning weighting functions to each station record.
However, the method is inflexible in that a new Thiesen diagram has to be constructed each time there is a change in the station network.
It simply assumes linear variation of ppt. I stations and assigns each segment of area to the nearest station. The Isohyetal method is the most accurate method especially when used by an experienced analyst. It takes into account all the information including the physiographic features of the area under consideration. However, the method is very tedious and time consuming. Hydrological problems also require an analysis of time as well as areal distribution of storm precipitation.
Depth-area-duration DAD analysis of a storm is performed to determine the maximum amount of precipitation within various durations and over areas of various sizes. The next section outlines this method. But not appropriate for mountainous areas or if the rain gauges are unevenly distributed. The is expressed as:. Note This method yield good estimates in flat country if the gauges are uniformly distributed and the individual gauge catches do not vary widely from the mean.
Fig 2. Illustration: Using the same data as in illustration for the average depth method, we will now illustrate the computation of areal rainfall by the Thiesen method see fig. Note The Thiessen method attempts to allow for non-uniform distribution of gauges by providing a weighting factor for each gauge. Note This method, when used by an experienced analyst is the most accurate method of averaging precipitation over an area.
Note The isohyetal method permits the use and interpretation of all available data and is well adapted to display and discussion.
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