Methods ADR$(mm)=\frac{{\displaystyle \underset{?}{\overset{?}{}}}(A_i*P_i)}{{\displaystyle \underset{?}{\overset{?}{}}}{A}_i}$

Where $A_i$ is the polygon area $(k{m}^2),P_i$ is the rainfall $($ mm $)$ corresponding to the i polygon, and

${\displaystyle \underset{?}{\overset{?}{}}}{A}_i$ is the catchment area $(k{m}^2).$

Isohyetal Method

The average depth of rainfall over the entire catchment can be calculated using:

ADR$(mm)=\frac{{\displaystyle \underset{?}{\overset{?}{}}}(A_i*P_i)}{{\displaystyle \underset{?}{\overset{?}{}}}{A}_i}$

where in this method $A_i$ is the area between isohyets $P_i$ and $P_{i+1}(k{m}^2),P_i$ is the average rainfall

$)$ corresponding to the area $A_i$ between the isohyets, and ${\displaystyle \underset{?}{\overset{?}{}}}{A}_i$ is the total catchment area

$(k{m}^2).$

Activity

Download the answer sheet for this exercise by clicking the download button in the tool

bar.

You are given the measured data for each rainfall gauge in Table $1.$ Calculate the arithmetic mean

and write this in your summary table $($Table $3).$ Next work out the ADR based on the other two

methods.

Figure $2$: Catchment map, station locations, and isohyetal map for a storm event. Isoheytal map

corresponds to rainfall total over a $24$ hr period.

Thiessen Polygons: Sketch the polygons

To construct the Thiessen polygons, first draw dashed straight lines between the gauges. Next, find

the mid$-$points of each of these lines and draw another solid line, perpendicular to the dashed line.

These solid lines drawn perpendicular to the dashed lines will meet to form irregular polygons Figure $3$: Gridded map for polygon construction and area estimates. $9/3/24,9$:$50$ PM

Exercise $1-$ Spatial rainfall variabilty $|$Hydrology Workbook

$\frac{9}{3}\frac{?}{24},9$:$50$

Table $1$: Rainfall data for Thiessen polygon method. Use your answer sheet to edit this table!

$\backslash$table$[[$Station Number,Polygon area $(^(($m$^(2))$ :$\}),\%$ Area,Rainfall $($mm$),],[5028,,,39\mathrm{.}6,],[5035,,,74\mathrm{.}9,],[5049,,,87\mathrm{.}4,],[5038,,,73\mathrm{.}9,],[5033,,,105\mathrm{.}4,],[5089,,,106\mathrm{.}9,],[5055,,,68\mathrm{.}6,],[5050,,,62\mathrm{.}2,],[5096,,,98\mathrm{.}6,],[5082,,,101\mathrm{.}1,],[5075,,,63\mathrm{.}8,],[$CatchmentArea $=,106\mathrm{.}3,1,,$ADR $=]]$

Contoured Rainfall $($Isohyets$)$Table $2$: Iso$-$hyetal method data.

Calculate Catchment Discharge

Once we have computed ADR, we can now estimate the likely amount of runoff. Remember the

relationship between rainfall and discharge as outlined in the supporting lecture. Hint: you'll need to

choose an appropriate runoff coefficient, and calculate the stream discharge at the bottom of the

catchment $-$ remember to watch out for unit conversions!

In this exercise you are required to calculate the average rainfall $($ADR$)$ over the entire catchment

using:

a$.$ the arithmetic mean $($considering only stations within the catchment boundary$),$

b$.$ the Thiessen polygon weighting system, and

c$.$ the Isohyetal method. Rainfall data for each station in the catchment is provided in Table $1.$

Figure $1$: A depth of rain day