Rainfall is a key component of the water cycle and is measured by meteorologists and hydrologists for various applications. One of the key parameters used to characterize rainfall is the rainfall intensity, often denoted as “i” or “t”. So what does t mean in the context of rainfall?
Rainfall Intensity (t)
Rainfall intensity or t refers to the amount of rainfall per unit time, and is a measure of how hard it is raining over a given period. It is usually expressed in inches or millimeters of accumulated rainfall depth over a fixed time interval. Some common units used to express rainfall intensity include:
- Inches per hour (in/hr or in hr-1)
- Millimeters per hour (mm/hr or mm hr-1)
- Inches per minute (in/min or in min-1)
- Millimeters per minute (mm/min or mm min-1)
For example, a rainfall intensity of 1 inch per hour (1 in/hr) means that rainfall accumulated to a depth of 1 inch in that hour. Similarly, 20 mm/hr indicates 20 mm of rainfall accumulated over a 1 hour period. Higher values indicate heavier rain rates.
Using t in Rainfall Intensity Equation
In rainfall intensity equations, t is commonly used to represent the time period over which the rainfall depth accumulation is measured. Some examples of using t in rainfall intensity calculations are:
- i = d/t where,
i = rainfall intensity (in/hr or mm/hr)
d = rainfall depth over the time period (in or mm)
t = duration of time period (hr) - i = 3600 d/t where,
i = rainfall intensity (in/hr or mm/hr)
d = rainfall depth over the time period (in or mm)
t = duration of time period (min)
Here t represents the fixed time interval over which the rainfall depth d is measured. This time interval is specified based on the required resolution and data available. For hourly rainfall data, t is 1 hour while for minute-level rainfall data, t is 1 minute.
Typical Values of t Used
Some common time intervals represented by t that are used to compute rainfall intensity include:
- 1 hour – For hourly rainfall data
- 10 minutes – For high resolution 10-min rainfall data
- 5 minutes – For very high resolution rainfall data
- 1 minute – For rainfall data from tipping bucket rain gauges
- Instantaneous – For rainfall rate at a given instant from disdrometers
Hydrologists typically use hourly, 15-min or daily rainfall data to compute rainfall intensity. However, for design of urban drainage systems, high resolution 1 to 10 minute rainfall data is preferred.
Importance of Rainfall Intensity (t)
Rainfall intensity or t has several important applications in hydrology and meteorology:
- It is used to characterize rain storms – Higher t indicates more intense storms
- It is used to issue flash flood warnings when t crosses critical thresholds
- Design of urban drainage infrastructure uses rainfall t as input
- Computation of infiltration and runoff rates require rainfall intensity data
- Input for rainfall-runoff and hydrologic models to estimate streamflow
- Agricultural applications such as irrigation scheduling uses rainfall t
Thus rainfall intensity helps quantify rainfall and characterize rain storms. It is one of the most widely used rainfall parameters in hydrologic analysis and applications.
Factors Affecting Rainfall Intensity
Rainfall intensity at a location depends on several factors:
- Rainfall duration – Shorter durations have higher intensities
- Rain storm characteristics – Thunderstorms have high intensities
- Topography – Hilly regions see higher intensities
- Geography and climate – Tropical and coastal areas have high rainfall intensities
- Rainfall amount – High rainfall depths generally indicate major storms with high intensities
- Antecedent conditions – Wet soil tends to reduce infiltration and increase runoff and intensity
In addition, seasonal and inter-annual variability in rainfall patterns affects the distribution of high intensity rain storms over time.
Variation with Duration
For a given rain storm event, the rainfall intensity decreases as the time interval (t) considered increases. This is because the total rainfall depth does not increase proportionally with duration due to storms having peak intensity periods. For example, 1-hr intensity for a storm can be 30 mm/hr while the 24-hr intensity is only 10 mm/hr.
Thunderstorms
Thunderstorms tend to have very high rainfall intensities, sometimes exceeding 100 mm/hr over short intervals. This is because thunderstorms are characterized by high vertical velocities that support growth of large rain drops leading to heavy downpours.
Orographic Effects
In mountainous or hilly regions, the uplift of moisture-laden air leads to higher rainfall intensities compared to flat terrain. The orographic lifting of air masses results in greater condensation and precipitation.
Typical Rainfall Intensity Values
Typical values of rainfall intensity (t) in inches/hr observed for different rain event durations are:
| Duration | Light Rain | Moderate Rain | Heavy Rain |
|---|---|---|---|
| 5 min | 0.02 | 0.1 | 0.3 |
| 15 min | 0.08 | 0.2 | 0.8 |
| 60 min | 0.1 | 0.5 | 2 |
Light rain is typically below 0.1 in/hr while heavy downpours exceed 1 in/hr intensities. Thunderstorms often generate intensities above 2-3 in/hr over short time scales. However, these values vary across climatic regions.
For hydrologic models, mean rainfall intensities over long durations (24 hrs to few days) tend to be between 0.01 to 0.04 in/hr depending on the regional rainfall pattern.
Rainfall Intensity Patterns
Within a storm event, the rainfall intensity varies with time and is not constant. The hyetograph or time variation of rainfall intensity typically shows a peaked pattern with higher intensities concentrated in the rising and peak section of the storm. Let’s look at typical rainfall intensity patterns.
Thunderstorms
Thunderstorm intensities demonstrate a sharp rising limb as the storm builds followed by a peak and then declining intensities. The entire event lasts for short durations, typically less than 1 hour. The peak 5-15 minute intensities can be extremely high, sometimes 10-30 times the hourly intensities.
Orographic Storms
In mountain regions, as moist winds are uplifted over high terrain, rainfall intensities tend to increase steadily to a peak and then decline gradually. Such orographic rainfall events have durations ranging from few hours to a day.
Frontal Storms
Rain storms caused due to fronts tend to have prolonged moderate intensities spanning over 6-12 hours. Multiple peaks in intensities are common as bands of rain pass over the region.
Tropical Cyclones
Tropical cyclones produce extreme rainfall intensities but over relatively short periods within rain bands. The peak intensities match those of thunderstorms. However, tropical cyclone rains last longer for a half to few days.
Measurement of Rainfall Intensity
Rainfall intensity is generally measured using rain gauges that can record rainfall depth at high resolution over short intervals. Some instruments used include:
- Tipping bucket rain gauges – Resolution up to 0.01 inches per tip
- Weighted gauge – 1 minute resolution
- Optical rain gauges – Can measure intensity up to 0.001 in/hr
- Disdrometers – Very high resolution for drop spectrum
- Weather radars – Estimate rainfall over large domains
Rainfall data from multiple rain gauges is used to derive areal average intensities overcatchment scales for hydrologic modeling.
Tipping Bucket Rain Gauges
Tipping bucket rain gauges are the most widely used instruments for rainfall intensity monitoring. They have a resolution between 0.01 to 0.2 mm per tip. By recording the time interval between tips, high resolution rainfall intensities can be computed. 1 minute intensities are commonly derived from tipping bucket data.
Optical Rain Gauges
Optical rain gauges estimate rainfall intensity based on the impact of raindrops on an optical sensing surface. They provide very high resolution intensities up to 0.001 in/hr and are suitable for urban hydrologic applications.
Weather Radar
Weather radar networks estimate rainfall intensity over large areas based on the returned signal from raindrop scattering and calibrated using ground observations. Radar rainfall data provides spatial patterns of storm intensity.
Design Rainfall Intensity
In hydrologic design such as storm sewers, storage reservoirs, flood control structures etc., an appropriately high rainfall intensity is used. This design intensity represents the maximum rainfall expected during a storm of specified return period or probability of occurrence.
Design rainfall intensities are computed through frequency analysis of long-term observed annual maximum rainfall intensities at various durations ranging from 5 min to 24 hours. Statistical distributions are fit to these extremes to derive the design intensities for a given return period.
Rainfall Depth-Duration-Frequency
Design intensities at various durations are generally expressed through depth-duration-frequency (DDF) relationship for a location compiled in the form of tables or charts. DDF curves provide the design rainfall depth for a given duration and return period.
Higher design intensities are used for small catchments and urban drainage, while lower intensities are adequate for larger rural basins for streamflow estimation.
Estimating Rainfall Erosivity
Rainfall intensity or t is also used to compute rainfall erosivity – a measure of the ability of rain to cause soil erosion. Erosivity is directly related to the kinetic energy of rainfall and runoff.
The rainfall erosivity factor R is computed as:
R = EI30
Where E is the rainfall energy (J/m2) and I30 is the maximum 30-minute rainfall intensity (mm/hr). This highlights the importance of high resolution rainfall data in estimating the erosion potential of storms.
Role in Rainfall-Runoff Modeling
Rainfall intensity input is critical in all rainfall-runoff models used for streamflow prediction. The infiltration rates and resulting surface runoff are directly dependent on rainfall intensity. For event-based models, the time distribution of rainfall represented through a hyetograph is required. In continuous simulation models, long rainfall records at hourly or daily resolution are provided as input to the models.
Accurate measurement and estimation of rainfall intensities is essential for reliable streamflow estimation and flood forecasting.
Limitations of Rainfall Intensity
While rainfall intensity is a widely used rainfall parameter, it has some limitations:
- Point rainfall intensities have limited representation for large basins
- Sparse rain gauge networks cannot capture spatial variability
- Uncertainties in high resolution rainfall estimates
- Indirect estimates from radar have biases
- High data requirements for continuous monitoring
However, with advances in radar quantitative precipitation estimation and dense rain gauge networks, the rainfall intensity estimates are continually improving.
Conclusion
In summary, rainfall intensity denoted by t represents the amount of accumulated rainfall over a fixed time period. It is a key parameter used to characterize rain storms, design infrastructure, estimate erosion, model hydrologic processes and issue flood forecasts and warnings. While intensities are not uniformly distributed during storms, a peak intensity period represents the critical storm value. Advances in monitoring technology and hydrologic techniques continue to improve the measurement and application of rainfall intensity data.