Water Resources Systems - short answer type questions from AMIE exams (Summer 2019)

Answer the following in brief

Explain the term ‘planning’ in the light of water resources planning.

Reducing the frequency and/or severity of the adverse consequences of droughts, floods, and excessive pollution are common goals of many planning and management exercises. Other reasons include the identification and evaluation of alternative measures that may increase the available water supplies, hydropower, improve recreation and/or navigation, and enhance water quality and aquatic ecosystems. 

Some multiple purposes served by a river can be conflicting. A reservoir used solely for hydropower, or water supply, is better able to meet its objectives when it is full of water. On the other hand, a reservoir used solely for downstream flood control is best left empty, so it can store more of the flood flows when they occur. A single reservoir serving all three purposes introduces conflicts over how much water to store in it and discharge from it, i.e., how it should be operated. In basins where diversion demands exceed the available supplies, conflicts will exist over water allocations. Finding the best way to manage, if not resolve, these conflicts are reasons for planning.

What is a cash flow diagram?

Cash flow diagrams visually represent income and expenses over some time interval. The diagram consists of a horizontal line with markers at a series of time intervals. At appropriate times, expenses and costs are shown.

For example, consider a truck that is going to be purchased for $55,000. It will cost $9,500 each year to operate, including fuel and maintenance. It will need to have its engine rebuilt in 6 years for a cost of $22,000, and it will be sold at year 9 for $6,000. Here is the cash flow diagram:

Relative frequency function

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario.

The relative frequency formula can be given as:

Relative Frequency = Subgroup frequency/ Total frequency


Relative Frequency = f/ n


f is the number of times the data occurred in an observation
n  = total frequencies

Cumulative frequency function

The Cumulative Distribution Function (CDF) of a real-valued random variable, say “X”, which is evaluated at x, is the probability that X takes a value less than or equal to x. It is defined for both discrete and random variables.

The CDF defined for a continuous random variable is given as;

{F_X}(x) = \int_{ - \infty }^x {{f_X}(t)dt}

Probability density function

probability density function (PDF) is used to define the random variable’s probability coming within a distinct range of values, as opposed to taking on any one value. In other words, the probability density function produces the likelihood of values of the continuous random variable. Sometimes it is also called a probability distribution function or just a probability function. 

In the case of a continuous random variable, the probability taken by X on some given value x is always 0. In this case, if we find P(X = x), it does not work. Instead of this, we must calculate the probability of X lying in an interval (a, b). Now, we have to figure it for P(a< X< b), and we can calculate this using the formula of PDF. The Probability density function formula is given as,

P(a < X < b) = \int_a^b {f(x)dx}

Probability distribution function

The probability distribution function is the integral of the probability density function. This function is very useful because it tells us about the probability of an event that will occur in a given interval.

State the basic steps of Economic analysis.

  1. Explain the strategic context
  2. Establish the need for expenditure
  3. Define the objectives and constraints
  4. Identify and describe the options
  5. Identify and quantify the monetary costs and benefits of options
  6. Appraise risks & adjust for optimism bias
  7. Weigh up non-monetary cost and benefits
  8. Calculate net present values (NPVs) and assess uncertainties
  9. Assess affordability and record arrangements for funding, management, procurement, marketing, benefits realization, monitoring and ex post evaluation
  10. Assess the balance of advantage between the options and present the results and conclusions

What are the objectives of developing water resources?

Water Resources Management objectives can include promoting conditions for environmentally sustainable, economically efficient and equitably allocated use of water resources. They also include to increase the benefits and reduce the risk related to existing hydraulic infrastructure.

What is the basic difference between ‘optimization’ and ‘simulation’ in water resources planning?

Optimization techniques in water resources system management are used to reach a system of optimum  solutions, whereas simulation techniques approach the system evaluation by a trial and error method to lead to the identification of the best possible solution for the system.

What are direct and inverse problems in system analysis? Give a clear example of each.

  • Direct problem: To identify effect from causes. (Analysis of model or prediction from model.)
  • Inverse problem: To identify causes from effect. (Identify model using data.)
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