# Mass curve, hyetograph, depth-area-duration curves and intensity-duration-frequency relationship

**Presentation of Rainfall Data**

The commonly used techniques for presentation of rainfall data, suitable for interpretation and analysis in different aspects are given:

- Mass curve
- Hyetograph
- Point rainfall.

**MASS CURVE:**

It's a graph of cumulative rainfall against time (after it's been arranged in chronological order). Rainfall is measured in terms of mass-curve by float type and weighing type rain gauges, but exclusively in terms of depth by symon type rain gauges. To prepare the mass-curve, the rainfall data obtained by non-recording type rain gauge is processed (i.e. in the form of cumulative w.r.t. time). The following information about the rainfall at a specific location can be extracted using mass curves.

1. It furnishes the information on duration of occurring rainfall and its Magnitude.

2. It provides the information on starting and end times of the given rainfall.

3. Of a given storm, it enables to determine the rainfall intensity at different time intervals. The intensity of rainfall is the slope of mass curve. A mass curve is shown in figure

**HYETOGRAPH****:**

It is the plot of rainfall intensity and time interval (Fig. 3.9). For development of hyetograph, the intensity data of rainfall is extracted from the mass curve. The presentation of hyetograph is in the form of bar diagram. The range of time interval of hyetograph depends on the purpose. Normally, for urban drainage problems, a small duration is used whereas for computation of flood-flows in large catchments, the 6-h time interval is commonly used. A hyetograph furnishes following information about the rainfall

- Total depth of rainfall, which is determined by computing the area of hyetograph
- Effective rainfall depth, which is computed by converting the hyetograph into effective rainfall hyetograph. The ERH is derived by deducting average loss of rain water during rainfall (ie index)
- Predicts the extreme floods by determining the design storm.
- A hyetograph also provides the information on duration and depth of effective rainfall, both.

**POINT RAINFALL****:**

Station rainfall is another name for it. The point rainfall is the amount of rain that falls at a certain gauging station. Depending on the necessity, it is expressed in daily, weekly, monthly, seasonal, or annual terms. Rainfall data is also presented in the form of a bar graph (i.e. magnitude Vs chronological time). Because there are significant differences in point rainfall during the given time interval of the bar diagram, this type of display of point rainfall is incorrect. The moving average plot, in which mean precipitations of three or five consecutive time intervals are shown through the midpoints of the selected time intervals, helps correct this variation.

**Consistency of rainfall record:**

Consistency is assessed for the purpose of testing and correcting existing rainfall data, particularly when conditions related to the rain guard station have changed dramatically, leading the data to become inconsistent. In general, the following factors contribute to the inconsistency of rainfall data:

1. Because of a shift in the position of the train gauge station

2. Observational error's reputation

3. Whether or if there is a topographical inaccuracy or change

**Intensity-Duration-Frequency Relationship**

**Intensity-Duration Relationship**

Rainfall intensity is the inverse function of rainfall duration i.e. for longer storm duration, the rainfall intensity is less and vice-versa. It is general phenomena, that the rainfall intensity is not same throughout the storm period but varies time to time. For a shorter time, its value can be much higher than the mean rainfall intensity of the storm. For finding the rainfall intensity at any time ‘t’ during the storm, Richard (1944) developed a relationship between intensity and duration of rainfall, given as under

I/J = (T + K) / (t + K)

in which, I and I are the rainfall intensity for any time I and 7. Respectively. T is the storm duration and K is the constant. The value of K is generally taken as 1, except for extreme events. Thus, after substituting the value of ‘K’ in the equation 3.19, we have,

This equation can be used for computing the rainfall intensity for any time during rainfall, if storm duration and mean rainfall intensity of the given storm are known.

Tejwani et. Al. (1975) developed graphical relationship between one rainfall intensity and other durations rainfall intensities.

**Intensity-Duration-Frequency Relationship**

It is general characteristics of the rainfall that as the rainfall duration increases, the intensity decreases and vice-versa. On contrast, the rainfall intensity increases with increase in return period and vice-versa. The relationship amongst intensity, duration and frequency of rainfall is given as under.

Where,

I=Average rainfall intensity, cm/h.

t=duration of rainfall, hour

T= recurrence interval, years.

K, a, b and d = constants, depend on the geographical locations of the area.

The value of recurrence interval can be computed by using the following formula

T = 1/p

For other places, they have also determined the values of K, a, b and d.

**Depth-Area-Duration Relationship**

**Depth-Area Relationship**

The depth-area relationship is very important for determining the variations in rainfall depth with respect to the variation in area of watershed during a given storm. In this regard, Horton developed a mathematical model for predicting the average rainfall depth, based on the highest amount of rainfall and area of watershed. The model is given as under:

P= P_{o }e^{-KA^n}

Where,

P= average rainfall depth, cm

P_{o}= highest rainfall depth occurred at the storm centre, cm

A = area of the watershed, km²

K and n= constants for given region. Dhar Bhattacharya (1975) determined the values of K and for North

India on the basis of 42 severe most storms. The values are:

S No. |
Duration |
K |
n |

1. |
One day |
8.256 x 10 |
6.614 x 10 |

2. |
Two days |
9.877 × 10 |
6.306 x 10 |

3. |
Three days |
1.745 × 10 |
5.961 × 10 |

**Depth-Area-Duration Relationship**

The depth-area-duration connection is particularly important for determining the rainfall depth throughout storm duration over the watershed owing to any storm. From the storm's centre to its perimeter, this relationship is derived by showing the steadily decreasing average rainfall depth over a progressively greater watershed area. In other words, the depth-area-duration curve is calculated by graphing the average rainfall depth against the equivalent area up to the enclosing isohyets. The following is a description of the derivation procedure:

- Find out 1-day, 2-days. 3-days up to 5 consecutive days maximum average rainfall.
- Prepare the isohyetal map of maximum average rainfall for 1- to 5-days rainfall durations, separately for each day.
- Divide each isohyetal map into different zones, representing the centre of main storm.
- Determine the enclosed area by each isohyet. It is determined by using the planimeter or any suitable method, Measurement of area is started from centre of the storm of each zone.
- Calculate the rainfall volume between two isohyets. It is determined by multiplying the enclosed area between them and mean of the two adjacent isohyet value.
- Compute the total rainfall volume by adding the incremental volume to the previous accumulated rainfall volume.
- Find out the average rainfall depth over the area, which is obtained by dividing the total rainfall volume computed in step (6) with the total area of isohyetal map.
- Determine the average rainfall depth for each zone by repeating the procedure up to step 7 and then combine the enclosed area by the common isohyets.
- Plot the values of highest average rainfall depth and corresponding area and join all the points by smooth curve. The obtained curve is the depth area-duration curve for maximum rainfall of a particular period.

**Maximum Depth-Area-Duration Curves**

Many hydrological studies involving the estimation of severe floods require data on the maximum quantity of rainfall over various time periods and over various region sizes. DAD analysis is the creation of a link between maximum depth-area-duration for a region and is a key part of hydro-meteorological research. For further information on DAD analysis, see References 2 and 9. The storm's isohyetal maps and mass curves are compiled. A depth-area curve for a specific storm duration is created. Following that, several durations and the greatest depth of rainfall in these durations are observed based on a study of the rainfall mass curve. During a given duration D, the maximum depth-area curve is calculated by assuming that the area distribution of rainfall for shorter durations is similar to the whole storm. The technique is then repeated for other storms, yielding the maximum depth-area envelope curve for duration D. DAD curves are the name for these curves.

The preparation of DAD curves necessitates a significant amount of computer effort as well as regional meteorological and topographical data. Detailed information about past strong storms is required. The development of design storms for use in computing the design flood in the hydrological design of big buildings such as dams requires DAD curves.

**CONCLUSION: **

So, based on the conclusion of this article, we can conclude that in order to study rainfall and its measurement and analysis, we must first understand a few basic terminologies and key links between rainfall intensity, frequency, and depth. The mass curve depicts cumulative rainfall over time, but the hyetograph depicts rainfall intensity over time intervals. Rainfall at a single location is referred to as point precipitation. Further hydrology calculations are made easier by understanding the link between intensity and duration, intensity duration frequency, and depth area duration.

**Frequently Asked Questions**

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