Precipitation & Evapotranspiration - 2 | Engineering Hydrology - Civil Engineering (CE) PDF Download

Depth-Area-Duration curves 

In designing structures for water resources, one has to know the areal spread of rainfall within watershed. However, it is often required to know the amount of high rainfall that may be expected over the catchment. It may be observed that usually a storm event would start with a heavy downpour and may gradually reduce as time passes.  Hence, the rainfall depth is not proportional to the time duration of rainfall observation.  Similarly, rainfall over a small area may be more or less uniform.  But if the area is large, then due to the variation of rain falling in different parts, the average rainfall would be less than that recorded over a small portion below the high rain fall occurring within the area.  Due to these facts, a Depth-Area-Duration (DAD) analysis is carried out based on records of several storms on an area and, the maximum areal precipitation for different durations corresponding to different areal extents.

The result of a DAD analysis is the DAD curves which would look as shown in Figure 5.

FIGURE 5. A typical Depth-Area-Duration (DAD) curve

Intensity-Duration-Frequency curves

The analysis of continuous rainfall events, usually lasting for periods of less than a day, requires the evaluation of rainfall intensities. The assessment of such values may be made from records of several part storms over the area and presented in a graphical form as shown in Figure 6. 

FIGURE 6. A typical rainfall intensity-ciuration-frequency (IDF) curve

Two new concepts are introduced here, which are:

• Rainfall intensity This is the amount of rainfall for a given rainfall event recorded at a station divided by the time of record, counted from the beginning of the event.
• Return period This is the time interval after which a storm of given magnitude is likely to recur. This is determined by analyzing past rainfalls from several events recorded at a station. A related term, the frequency of the rainfall event (also called the storm event) is the inverse of the return period. Often this amount is multiplied by 100 and expressed as a percentage. Frequency (expressed as percentage) of a rainfall of a given magnitude means the number of times the given event may be expected to be equaled or exceeded in 100 years.  

Analysis for anomalous rainfall records

Rainfall recorded at various rain gauges within a catchment should be monitored regularly for any anomalies. For example of a number of recording rain gauges located nearby, one may have stopped functioning at a certain point of time, thus breaking the record of the gauge from that time onwards. Sometimes, a perfectly working recording rain gauge might have been shifted to a neighbourhood location, causing a different trend in the recorded rainfall compared to the past data. Such difference in trend of recorded rainfall can also be brought about by a change in the neighbourhood or a change in the ecosystem, etc. These two major types of anomalies in rainfall are categorized as 

• Missing rainfall record
• Inconsistency in rainfall record

Missing rainfall record 

The rainfall record at a certain station may become discontinued due to operational reasons. One way of approximating the missing rainfall record would be using the records of the three rain gauge stations closet to the affected station by the “Normal Ratio Method” as given below:  

      (1) 

Where P₄ is the precipitation at the missing location, N₁, N₂, N₃ and N₄ are the normal annual precipitation of the four stations and P₁, P₂ and P₃ are the rainfalls recorded at the three stations 1, 2 and 3 respectively. 

Inconsistency in rainfall record 

This may arise due to change in location of rain gauge, its degree of exposure to rainfall or change in instrument, etc. The consistency check for a rainfall record is done by comparing the accumulated annual (or seasonal) precipitation of the suspected station with that of a standard or reference station using a double mass curve as shown in Figure 7. 

FIGURE 7. A typical example of inconsistent rainfall record

From the calculated slopes S0 and Sc from the plotted graph, we may write 

  (2) 

Where P_c and P₀ are the corrected and original rainfalls at suspected station at any time. S_c and S₀ are the corrected and original slopes of the double mass-curve. 

Probable extreme rainfall events 

Two values of extreme rainfall events are important from the point of view of water resources engineering.  These are:

Probable Maximum Precipitation (PMP) 

This is the amount of rainfall over a region which cannot be exceeded over at that place. The PMP is obtained by studying all the storms that have occurred over the region and maximizing them for the most critical atmospheric conditions. The PMP will of course vary over the Earth’s surface according to the local climatic factors. Naturally, it would be expected to be much higher in the hot humid equatorial regions than in the colder regions of the mid-latitudes when the atmospheric is not able to hold as much moisture. PMP also varies within India, between the extremes of the dry deserts of Rajasthan to the ever humid regions of South Meghalaya plateau.

Standard Project Storm (SPS)

This is the storm which is reasonably capable of occurring over the basin under consideration, and is generally the heaviest rainstorm, which has occurred in the region of the basin during the period of rainfall records. It is not maximized for the most critical atmospheric conditions but it may be transposed from an adjacent region to the catchment under considerations.

The methods to obtain PMP and SPS are involved and the interested reader mayfind help in text books on hydrology, such as the following:

• Mutreja, K N (1995) Applied Hydrology, Tata McGraw Hill
• Subramanya, K (2002) Engineering Hydrology, Tata McGraw Hill 

Evapotranspiration

As discussed earlier, evapotranspiration consists of evaporation from soil and water bodies and loss of water from plant leaves, which is called transpiration. It is a major component of the hydrologic cycle and its information is needed to design irrigation projects and for managing water quality and other environmental concerns. In urban development, evapotranspiration calculations are used to determine safe yields from aquifers and to plan for flood control. The term consumptive use is also sometimes used to denote the loss of water molecules to atmosphere by evapotranspiration. For a given set of atmospheric conditions, evapotranspiration depends on the availability of water. If sufficient moisture is always available to completely meet the needs of vegetation fully covering the area, the resulting evapotranspiration is called potential vapotranspiration (PET). The real evapotranspiration occurring in a specific situation is called actual evapotranspiration (AET). 

Measurement of evapotranspiration

There are several methods available for measuring evaporation or evapotranspiration, some of which are given in the following sub-sections.

Potential E vapotranspiration ( PET)

• Pan evaporation The evaporation rate from pans filled with water is easily obtained. In the absence of rain, the amount of water evaporated during a period (mm/day) corresponds with the decrease in water depth in that period. Pans provide a measurement of the integrated effect of radiation, wind, temperature and humidity on the evaporation from an open water surface. Although the pan responds in a similar fashion to the same climatic factors affecting crop transpiration, several factors produce significant differences in loss of water from a water surface and from a cropped surface. Reflection of solar radiation from water in the shallow pan might be different from the assumed 23% for the grass reference surface. Storage of heat within the pan can be appreciable and may cause significant evaporation during the night while most crops transpire only during the daytime. There are also differences in turbulence, temperature and humidity of the air immediately above the respective surfaces. Heat transfer through the sides of the pan occurs and affects the energy balance.

Notwithstanding the difference between pan-evaporation and the evapotranspiration of cropped surfaces, the use of pans to predict ETo for periods of 10 days or longer may be warranted. The pan evaporation is related to the reference evapotranspiration by an empirically derived pan coefficient:

ET_o = K_p E_pan

Where

ET_o reference evapotranspiration [mm/day],

K_p pan coefficient [-],

E_pan pan evaporation [mm/day]. 

• Evapotranspiration gauges The modified Bellani plate atmometer has been offered as an alternative and simpler technique to combination-based equations to estimate evapotranspiration (ET) rate from green grass surface. 

Actual Evapotranspiration (AET) 

• Simple methods
  • Soil water depletion method  Evapotranspiration can be measured by using soil water depletion method.  This method is usually suitable for areas where soil is fairly uniform.  Soil moisture measured at various time intervals.  Evapotranspiration can be measured from the difference of soil moisture at various time levels.
  • Water balance method  The method is essentially a book-keeping procedure which estimates the balance between the inflow and outflow of water. In a standard soil water balance calculation, the volume of water required to saturate the soil is expressed as an equivalent depth of water and is called the soil water deficit. The soil water balance can be represented by: 

 Ea = P - Gr + ΔS – Ro

Where,  Gr = recharge;

P = precipitation;

Ea = actual evapotranspiration;

ΔS = change in soil water storage; and

Ro = run-off. 

• Complex methods
  • Lysimeters  A lysimeter is a special watertight tank containing a block of soil and set in a field of growing plants. The plants grown in the lysimeter are the same as in the surrounding field. Evapotranspiration is estimated in terms of the amount of water required to maintain constant moisture conditions within the tank measured either volumetrically or gravimetrically through an arrangement made in the lysimeter. Lysimeters should be designed to accurately reproduce the soil conditions, moisture content, type and size of the vegetation of the surrounding area. They should be so hurried that the soil is at the same level inside and outside the container. Lysimeter studies are time-consuming and expensive.
  • Energy balance method The energy balance consists of four major components: net radiation input, energy exchange with soil, energy exchange to heat the air (sensible heat) and energy exchange to evaporate water (latent energy). Latent energy is thus the budget involved in the process of evapotranspiration:
  • Net Radiation -Ground Heat Flux = Sensible Heat + Latent Energy The energy balance method of determining Evapotranspiration can be used for hourly values during daylight hours but accurate night time values are difficult to obtain.  Eddy diffusion equations can be used and combinations of these procedures can be used also to calculate evapotranspiration.  The method used is governed often by the data available, the accuracy needed, and the computational capability.
  • Mass transfer method This is one of the analytical methods for the determination of lake evaporation. This method is based on theories of turbulent mass transfer in boundary layer to calculate the mass water vapour transfer from the surface to the surrounding atmosphere. 

Estimation of Evapotranspiration 

The lack of reliable measured data from field in actual projects has given rise to a number of methods to predict Potential Evapotranspiration (PET) using climatological data. The more commonly used methods to estimate evapotranspiration are the following:

• Blaney-Criddle m ethod
• Modified Penman Method  
• Jansen-Haise m ethod
• Hargreaves method
• Thornwaite method

Some of the more popular of these methods have been discussed in detail in lesson 5.4 “Estimating irrigation demand”. Interested readers may consult Modi, P N (2000) Water Resources Engineering for detailed discussions on this issue.