### Abstraction:

One of the cardinal issues in inundation direction is cognition of the precipitation input into catchments for hydrologists cognition of this serves to extenuate risky and environmental calamities, it is therefore imperative to adequately find precipitation input with appropriate and applicable statistical tools. The aim of this survey is to find the existent precipitation input and suggest the most appropriate method of finding precipitation input for the theoretical account catchment provided.

Standard and normally used methods of obtaining the areal precipitation input over a catchment country from rain gage measurings at the precipitation Stationss are the Arithmetical mean, Thiessen Polygon, Isohyetal, and the Hypsometric methods. These methods serve as good estimates where the topography of a catchment is level, if the gages are uniformly distributed and the single gage gimmicks do non differ extensively from the mean.

### Arithmetical mean:

This is the simplest signifier of giving a value of the mean rainfall over a certain country, and works good under the undermentioned conditions:

- When the catchment country is sampled by many uniformly spaced rain gages
- When the country has no marked diverseness in topography ( Davie, 2008 )

### Using this measuring tool to the arithmetic mean:

There are 7 rain gages with the average value being 27.14

The entire catchment country is = 456km

- 456 million square metres,
- 27mm = 0.027 metres
- So 456,000,000 tens 0.027m

§ = 12,312,000 M3

### Thiessen Polygons:

The method was devised by an American applied scientist, the method provides for the non-uniform distribution of gages by finding a weighting factor for each gage. This factor is based on the size of the country within the drainage basin that is closest to a given rain gage. These countries are otherwise known as irregular polygons.

### The method is straightforward and easy to utilize:

- The catchment is divided into polygons by lines that are equidistant between brace of next Stationss
- The lines/polygons are bisected
- Workout the country of each polygon by numbering the squares within each
- Sums up the countries
- Compare to arithmetic method to corroborate the two are the same
- Convert the single polygonal countries to million sq metres and multiply by the born-again precipitation rain gages for illustration:

o 178,000,000 x0.055 =9,790,000

Once this is done add them wholly to deduce the entire volume of precipitation input within the catchment.

### Isohyetal method

This considered one of the most accurate methods ; nevertheless as one will frequently happen the method is capable to single abilities and the cognition of the general catchment. ( Shaw, 1994 )

### The method is more complicated than the first two:

- To deduce of an accurate appraisal of the rainfall input one must foremost happen the distance between two rain gages in millimeter and finally extrapolate and generalize the line to give the next rainfall degrees, which can subsequently be plotted back onto the catchment sheet.
- i.e. method of summing up:

acquire the equidistant line between the two rain gages

take for illustration the distance in millimeter between gage A and B

### 8.5cm-convert to mm- 85mm

- happen the difference between the two rainfall gages 55-30=25
- now to work out the a & A ; frac14 ; of 85, one would split 85/100 and multiply this by 25

### & A ; religious order ; =21.25

- Which is later a & A ; frac14 ; of the equidistant line between the two rainfall gages
- This figure can be used to deduce the 2/4 point, the & A ; frac34 ; point etc. By merely duplicating the 21.25 figure you arrive at the 2/4 or 50 % point and so to acquire the 75 % point adds 21.25 to the 50 % point.

One must now spread out on the quartiles between the rainfall gages:

- This is done by utilizing the difference ( 25 ) calculated earlier.
- One-half of this gives 12.5 which when added to the first gage, or gage B ( 30mm ) you get 42.5.
- One-half of 12.5 gives 6.25, which when added to 30 gives 36.25, and so on until it matches against the next measurement line.
- ( *see auxiliary sheets to see for techniques and farther account )

-once this is done secret plan the rainfall values utilizing the next measurings and articulation lines of equal rainfall

Then advancement to number the countries between the isohyets and happen the mean the two.

Convert the single countries to million sq metres and multiply by the born-again mean precipitation values for illustration:

- 31,000,000 ten 0.059 = 1,829,000 cm3
- Do the same with all the values ; add them to acquire the entire volume of precipitation input.

### Hypsometric Method

The method uses catchment topography and the rainfall measurings to deduce of a entire leaden precipitation input. It reasonably accurate nevertheless is besides dependent on the abilities of an person, whilst pulling the hypsometric curve. The hypsometric curve allows for next precipitation values to read from the graph. The country underneath the curve of precipitation gives the country of an single gage, and can be calculated thenceforth in the same system as the old two methods:

### Analysis/Conclusion:

It is clear from the consequences that the arithmetic mean is the likely to be less accurate than the other 3 methods, this is due to the catchment holding qualities, such as topography and good distributed gages which are features that prove desirable to the other three methods.

I have averaged the precipitation inputs to acquire a more accurate figure:

### Averaged 15,027,250 Entire volume cm3

It has been really hard to detect a tendency of between the methods, nevertheless three major forms have been observed, the arithmetic mean varies much from the Thiessen weights and other two weights, demoing that on one degree the arithmetic mean is less accurate and takes the values into a much broader graduated table, whereas the other three methods are much more specific. The relation between the weights is really dispersed because the precipitation input is governed by assorted factors and complex activities, and each method besides demands certain qualities within a catchment for it to be applied suitably, take for illustration the Isohyetal method which is subjective to single abilities and cognition of the catchment country, which in this instance is non wholly possible, given the limited background information.

### Mentions:

- Davie, T. , ( 2008 ) Fundamentalss of Hydrology Volume 1 of Routledge basicss of physical geographics series, 2, illustrated, Routledge, pp28-30
- Brooks, K. N. , ( 2003 ) Hydrology and the direction of water partings, ed.3, illustrated, Wiley-Blackwell, pp30-34
- ASCE ( 1996 ) Hydrology enchiridion, Iss. 28 Vol. 28 of Time Life Complete Gardener, American Society of Civil Engineers Publications, pp 40-48
- Shaw, E.M. , ( 1994 ) Hydrology in Practice, Taylor & A ; Francis, illustrated, 3rd ed. , pp208-212