Topic 7

The strength and direction of the linear relationship between two variables.

The sum of all values in a dataset divided by the number of values.

The dispersion of a dataset; it quantifies how much the values deviate from the mean.

They help in understanding the probability of occurrence of different values of hydrological variables.

A sampling method where each member of the population has an equal chance of being selected.

Streamflow or runoff.

They recognize that hydrological processes are influenced by numerous factors that are difficult to predict with certainty.

To understand and predict hydrological processes such as rainfall, streamflow, floods, and droughts.

Rainfall, catchment area, soil type.

Rainfall leads to runoff.

To analyze rainfall intensity, streamflow rates, or other hydrological variables.

A specific outcome or a group of outcomes from the sample space.

Variables such as rainfall and streamflow.

That the relationship can be represented by a straight line.

To display data points at successive time intervals.

The likelihood of an event occurring.

Hypothetical storms used in engineering to estimate the impact of rainfall on structures.

To observe trends, seasonal patterns, and anomalies in hydrological data.

Rainfall.

Sample space, events, and probabilities.

The average time interval between events of a certain magnitude or larger.

If 10 mm of rain falls uniformly over a 10-hour period, then 1 mm falls each hour.

Random variables that can take on any value within a given range.

A function that shows the probability that a random variable takes a value less than or equal to a certain value.

Recurrence interval.

Incremental precipitation.

To determine the relationship between a dependent variable and one or more independent variables.

50%.

A certain event.

An increase in rainfall typically results in increased river flow.

The probability that a hydrological variable will take a value less than or equal to a specific threshold.

The process of selecting a subset of individuals from a population to estimate characteristics of the whole population.

It allows comparison of variability between datasets with different units or scales.

A bar graph that represents the frequency distribution of a hydrological variable.

Visualizing trends, seasonality, and anomalies in continuous hydrological data over time.

A sampling method that divides the population into subgroups and samples from each subgroup.

The complete set of possible outcomes for an experiment.

The relationship between an independent variable (like rainfall) and a dependent variable (like streamflow).

Flood Frequency Analysis.

The average time interval between events of a certain intensity or size.

A consistent rate of rainfall over a specific period of time.

Rainfall - Runoff Modeling.

To assess the probability of exceeding or falling below certain hydrological thresholds.

A sampling method that involves selecting samples based on ease of access.

The amount of rain falling per unit of time is the same across the entire period.

Flood Prediction.

They are critical for water resource management, helping to quantify the availability of streamflow over time.

A given input produces the same output.

A hypothetical rainfall event characterized by specific intensity, duration, and return period, used for stormwater management infrastructure design.

To determine the point at which a system can stop operating effectively due to insufficient water supply.

Sediment Load and Streamflow.

Streamflow.

More robust predictions and better-informed decision-making under uncertainty.

An impossible event.

In hydropower generation and environmental flow assessments.

The sum of the squared differences (errors or residuals) between observed data points and predicted values.

Discrete models deal with countable outcomes, while continuous models deal with measurable outcomes.

The square root of the variance, measuring the average distance of each data point from the mean.

A standardized measure of dispersion expressed as a percentage of the mean.

To model the relationship between a dependent hydrological variable and one or more independent variables.

Stochastic models incorporate variability in input data and system responses, while deterministic models do not.

A subset of a population used for analysis.

Direct cause-and-effect relationships.

The most common values, the spread of data, and the presence of skewness or outliers.

How a hydrological variable changes over time.

The distribution and frequency of various hydrological events, such as rainfall intensities and streamflow levels.

A sampling method where samples are taken at regular intervals from the population.

They allow hydrologists to quantify uncertainties and estimate the likelihood of various hydrological events.

Streamflow (or discharge) against the percentage of time that the flow is equaled or exceeded.

A variable that takes on numerical values determined by the outcomes of a random phenomenon.

No, they do not consider randomness.

A mathematical representation of a random phenomenon.

They help in flood risk assessment and environmental protection.

To characterize the variability and availability of streamflow.

Random variables that take on a countable number of distinct values.

The frequency distribution of a dataset.

Variance = (2-4)² + (4-4)² + (6-4)² / 2 = 4.

From 0 (impossible) to 1 (certain).

They assist in assessing streamflow variability and availability.

To fit the best possible linear regression line by minimizing the sum of squared differences between observed data points and predicted values.

To predict water-related events like floods and droughts.

To design stormwater management infrastructure such as sewers, retention basins, and flood control systems.

There are no significant fluctuations in intensity.

Water Quality Analysis.

The relationship between the flow rate and the percentage of time that flow is equaled or exceeded.

Drainage channels, retention basins, and culverts.

The conditions under which a designed system ceases operation in managing stormwater or runoff.

The strength and direction of a linear relationship between two variables.

For hydrological design of infrastructure like dams, bridges, and drainage systems.

Instantaneous streamflow.

The number of rainy days in a month.

It ensures systems are designed with a margin of safety for events larger than the design storm.

The amount of rainfall in a given period.

Linear regression.

A perfect positive linear relationship.

Location and the probability of exceedance p.

The duration of the storm (hours).

Linear regression.

A rainfall event with a return period of 10 years and a duration of 1 hour.

Wind velocity.

To ensure they can manage the maximum expected rainfall and associated runoff without failure.

The system fails to manage excess runoff, potentially leading to flooding.

Rainfall intensity (mm/hr or in/hr).

No linear relationship between the variables.

To asymptotically adjust the intensity as duration t_d becomes very small.

It has a return period of 100 years, indicating a 1% chance of occurrence in any given year.

Regression predicts the value of a dependent variable based on independent variables, while correlation assesses the strength of a relationship between two variables.

A stormwater system designed to handle a 25-year storm may fail during a 100-year storm, leading to flooding.

From -1 to +1.

A perfect negative linear relationship.

For p = 1%.

Between 0.5 and 0.67.