Republic of the Philippines
NUEVA ECIJA UNIVERSITY OF SCIENCE AND TECHNOLOGY
Cabanatuan City, Nueva Ecija, Philippines
CIVIL ENGINEERING DEPARTMENT
HYDROLOGY
(CE 332)
GROUP 2 (BSCE - 3B)
Advincula, Jhosua F.
Abillon, Aiko Bulanadi
Besa, Dan Robert A.
Butic, Lenih Jade
Capricho, Lesner
Cuaresma, Earl Kenneth E.
Cunanan, Reggie
Dela Cruz, Janna Marie
Dela Peña, David SanGabriel
Desiderio, Jeremy
Magnate, Jurist
Sanqui, Andrei Ruiz
Seminiano, Benjamin jr. L.
Table of Contents
I. Introductory Concepts
II. Forms of Precipitation
III. Weather Systems for Precipitation
IV. Measurement of Precipitation
V. Rain Gauge Network
VI. Preparation of Data
VII. Presentation of Rainfall Data
VIII. Probable Maximum Precipitation
UNIT 2: PRECIPITATION
I.
INTRODUCTORY CONCEPTS
PRECIPITATION
❖ Any liquid or frozen water that condenses in the atmosphere and falls to the Earth is
referred to as precipitation.
❖ It is one of the three crucial phases of the water cycle on a global scale.
❖ Precipitation is considered fresh water.
❖ "Condensation nuclei" are the dust or smoke particles in the atmosphere that act as a
surface for water vapor to condense on.
Classification of Precipitation:
❖ Orographic Precipitation - is most commonly found in coastal regions with a mountain
range.
❖ Cyclonic Precipitation - When a warm moist air mass meets a cold dry one, the warm one
rises, and the water vapor in the warm air condenses as it rises, forming clouds.
❖ Convectional Precipitation - On hot days, the sun heats the ground. That warm air rises
and cools to condense its water vapor into a liquid.
Some effects of Precipitation:
❖
❖
❖
❖
Local humidity and temperature.
Insufficient or excessive precipitation.
Organism life cycles and characteristics.
The size and frequency of fires.
Why is Precipitation Important?
❖ Precipitation is needed to replenish water on the earth. Without precipitation, this planet
would be an enormous desert. Precipitation supplies are freshwater to estuaries, which is
an essential source of dissolved oxygen and nutrients. Precipitation is crucial for sustaining
life on Earth, from providing the water we drink and the food we eat to regulating our
climate and supporting diverse ecosystems. It is an integral part of the Earth's natural
systems and has a profound impact on human societies and the environment.
II.
FORMS OF PRECIPITATION
1. Rainfall
- Drops of liquid waterfall from the clouds when
water vapor condenses around dust particles in the
clouds, forming tiny droplets that eventually get too
big for the cloud to hold so they fall, growing larger
as they collect more water on their way down. Rain
is precipitation that falls to the surface of the Earth
as water droplets. Raindrops form around
microscopic cloud condensation nuclei, such as a
particle of dust or a molecule of pollution. Even
though cartoon pictures of raindrops look like tears,
real raindrops are spherical.
Process of Rainfall
- Sunlight causes surface water to evaporate and
become water vapor, which rises due to its lighter
weight and cools as it ascends. Condensation in the
atmosphere forms small water droplets that create
clouds. These droplets combine and grow until they
become too heavy, resulting in rainfall. Before
reaching the ground, each raindrop forms from a
million tiny water droplets.
2. Snow
-Snow is ice that falls from the sky. Each snowflake
is a delicately complex arrangement of ice crystals.
A snowflake forms when water vapor sublimates, or
turns directly from a gas into its solid form, ice. Snow
is precipitation that falls in the form of ice crystals.
Snow has a complex structure. The ice crystals are
formed individually in clouds, but when they fall,
they stick together in clusters of snowflakes.
Snowfall happens when many individual snowflakes
fall from the clouds. Snow requires temperatures at
the ground to be near or below freezing—less than 0
degrees Celsius (32 degrees Fahrenheit). Snow that
falls on warmer ground melts on contact.
Process of Snow
- To form snow, two main conditions are
required: temperatures below freezing and
sufficient moisture in the air. Water vapor
changes directly into ice, forming ice crystals
around tiny particles. These crystals grow by
freezing more water vapor and colliding with
other crystals within clouds, eventually becoming
snowflakes heavy enough to fall. If they pass
through warmer air, they may melt into sleet or
rain. In slightly above-freezing, moist air, they
clump together to form large, fluffy flakes, while
in very cold, dry air, they remain powdery,
creating the ideal skiing powder.
3. Hail
-Hail forms in cold storm clouds. Hailstones form
within thunderstorm clouds when upward-moving
air keeps pellets of frozen water from falling. It
forms when very cold-water droplets freeze, or turn
solid, as soon as they touch things like dust or dirt.
The storm blows the hailstones into the upper part
of the cloud. More frozen water droplets are added
to the hailstone before it falls. Unlike sleet, which
is liquid when it forms and freezes as it falls to
Earth, hail falls as a stone of solid ice. Hailstones
are usually the size of small rocks, but they can get
as large as 15 centimeters (6 inches) across and
weigh more than a pound.
Process of Hail
-Hail begins as liquid water droplets lifted by an
updraft into the atmosphere, where they freeze into
tiny ice nuclei. These hailstones go through multiple
freeze-thaw cycles, growing larger each time. They
become too heavy for the updraft to support, and
gravity pulls them down. In a typical process, strong
updrafts in thunderstorms force hailstones upward,
where they freeze further and grow. As they collide
with other droplets, they continue to expand until
gravity overcomes the updraft, causing them to fall to
the ground. This often happens during warmer months
in thunderstorms.
4. Frost
-Frost is water vapor or water in gas form, that becomes solid.
Frost usually forms on objects like cars, windows, and plants
that are outside in air that is saturated, or filled, with moisture.
Areas that have a lot of fog often have heavy frosts. Frost
crystals, often called hoarfrost in the aggregate, form when the
invisible water vapour of the atmosphere passes into the ice
crystal phase without going through the intermediate liquid
phase. Hoarfrost lightly covers fields and rooftops under
conditions that would form dew if the temperature were above
freezing at the point of formation. Sometimes the freezing
temperature will be reached after dew has already formed,
producing frozen dew, but this usually cannot be readily
distinguished, because crystals ordinarily will start forming at
about the same time the freezing starts.
Process of Frost
-Frost is normally formed on still, clear, and cold nights. When the cool air causes water vapour
in the air to condense and form droplets on the ground. When the temperature of the ground is
below 0° C these droplets freeze into ice crystals
5. Dew
Dew is the moisture that forms at night when objects or the
ground outside cool down by radiating, or emitting, their heat.
Dew is the moisture that forms as a result of condensation.
Condensation is the process a material undergoes as it
changes from a gas to a liquid. Dew is the result of water
changing from a vapor to a liquid. The temperature at which
dew forms is called the dew point. The dew point varies
widely, depending on location, weather, and time of day.
Humid locations, such as the warm, coastal tropics, are more
likely to experience dew than arid areas. Humidity measures
the amount of water vapor in the air. Warm, humid air is full
of moisture that can condense during calm, cool nights.
Weather conditions can also influence an area’s dew point.
Strong winds, for instance, mix different layers of air,
containing different amounts of water vapor. This reduces the
atmosphere’s ability to form dew.
Process of Dew
Dew forms as temperatures drop and objects cool down. Dew forms during calm, clear nights,
when the ground surface and other exposed objects, such as tips of grass or leaves, lose heat by
radiation to the sky. If the object becomes cool enough, the air around the object will also cool.
Colder air is less able to hold water vapor than warm air. This forces water vapor in the air around
cooling objects to condense. When condensation happens, small water droplets form—dew.
6. Sleet
Sleet is a type of precipitation distinct from snow,
hail, and freezing rain. It forms under certain
weather conditions, when a temperature inversion
causes snow to melt, then refreeze. Sometimes the
weather forecast warns of “sleet,” rather than snow.
When meteorologists in the United States use this
term, they are referring to tiny ice pellets (the size
of a pea, at most) formed when falling snow melts
and then quickly refreezes. (In the United
Kingdom, sleet usually refers to a wintry mix).
These pellets typically bounce as they hit the
ground. Sleet can be dangerous, quickly coating the surface of roads and making driving
hazardous. Sleet, globular, generally transparent ice pellets that have diameters of 5 mm (0.2
inches) or less and that form as a result of the freezing of raindrops or the freezing of mostly melted
snowflakes.
Process of Sleet
Sleet forms when there is a temperature
inversion in the atmosphere. In normal
conditions, if the air temperature is at or below
freezing at cloud level, snow forms. Snowfall
occurs when the air remains cold from the clouds
to the ground. However, in a temperature
inversion, a layer of warm air interrupts the cold
air near the ground and the clouds. When snow
falls into this warm layer, it melts, and then, as it
reaches the cold air near the surface, it refreezes
rapidly, creating tiny ice pellets known as sleet..
Other factors leading to precipitation other than natural conditions:
Human activity can create precipitation. Urban heat islands, which are areas around major
cities that are much warmer than their surroundings, lead to increased and more intense rainfall
near cities.
Global warming also causes changes in global precipitation. When the planet is hotter,
more ice evaporates in the atmosphere. That eventually leads to more rainy precipitation. It usually
means wetter weather in parts of North America, for example, and drier conditions in tropical areas
that are usually humid.
III.
WEATHER SYSTEMS FOR PRECIPITATION
WEATHER SYSTEMS
-
Weather Systems are simply the movement of warm and cold air across the globe.
These movements are known as low-pressure systems and high-pressure systems.
High-pressure systems are rotating masses of cool, dry air. Therefore, they are usually
associated with clear skies. On the other hand, low-pressure systems are rotating masses of
warm, moist air. They usually bring storms and high winds.
WEATHER SYSTEM FOR PRECIPITATION
-
For the formation of clouds and subsequent precipitation, it is necessary that the moist air
masses cool to form condensation. This is normally accomplished by adiabatic cooling of
moist air through a process of being lifted to higher altitudes. Some of the terms and
processes connected with the weather systems associated with precipitation are given
below. The following list includes some of the words and concepts related to the weather
systems that cause precipitation.
WEATHER FRONT
- A weather front is a transition zone between two different air masses at the Earth's surface.
Each air mass has unique temperature and humidity characteristics. Often there is
turbulence at the front, which is the borderline where two different air masses come
together. The turbulence can cause clouds and storms.
- Fronts move across the Earth's surface over multiple days. The direction of movement is
often guided by high winds, such as Jet Streams. Landforms like mountains can also
change the path of a front. When a front passes over an area, it means a change in the
weather. Many fronts cause weather events such as rain, thunderstorms, gusty winds, and
tornadoes.
There are four different types of weather fronts: cold fronts, warm fronts, stationary fronts, and
occluded fronts.
1. COLD FRONTS
-A cold front forms when a cold air mass
pushes into a warmer air mass. Cold fronts can
produce dramatic changes in the weather. They
move fast, up to twice as fast as a warm front.
As a cold front move into an area, the heavier
(more dense) cool air pushes under the lighter
(less dense) warm air, causing it to rise up into
the troposphere. Lifted warm air ahead of the
front produces cumulus or cumulonimbus
clouds and thunderstorms.
-As the cold front passes, winds become gusty.
There is a sudden drop in temperature, and also
heavy rain, sometimes with hail, thunder, and lightning. Atmospheric pressure changes from
falling to rising at the front. After a cold front move through your area, you may notice that the
temperature is cooler, the rain has stopped, and the cumulus clouds are replaced by stratus and
stratocumulus clouds or clear skies.
-On weather maps, a cold front is represented by a solid blue line with filled-in triangles along it,
like in the map. The triangles are like arrowheads pointing in the direction that the front is moving.
Notice on the map that temperatures at the ground level change from warm to cold as you cross
the front line.
2. WARM FRONTS
-A warm front forms when a warm air mass
pushes into a cooler air mass, as shown in the
image to the right (A). Warm fronts often bring
stormy weather as the warm air mass at the
surface rises above the cool air mass, making
clouds and storms. Warm fronts move more
slowly than cold fronts because it is more
difficult for the warm air to push the cold, dense
air across the Earth's surface. Warm fronts often
form on the east side of low-pressure systems
where warmer air from the south is pushed
north.
-You will often see high clouds like cirrus, and cirrostratus, and middle clouds like altostratus
ahead of a warm front. These clouds form in the warm air that is high above the cool air. As the
front passes over an area, the clouds become lower, and rain is likely. There can be thunderstorms
around the warm front if the air is unstable.
-On weather maps, the surface location of a warm front is represented by a solid red line with red,
filled-in semicircles along it, like in the map on the right (B). The semicircles indicate the direction
that the front is moving. They are on the side of the line where the front is moving. Notice on the
map that temperatures at ground level are cooler in front of the front than behind it.
3. STATIONARY FRONT
-A stationary front forms when a cold front or
warm front stops moving. This happens when
two masses of air are pushing against each
other, but neither is powerful enough to move
the other. Winds blowing parallel to the front
instead of perpendicular can help it stay in
place.
-A stationary front may stay put for days. If the
wind direction changes, the front will start
moving again, becoming either a cold or warm
front. Or the front may break apart.
-Because a stationary front mark the boundary between two air masses, there are often differences
in air temperature and wind on opposite sides of it. The weather is often cloudy along a stationary
front, and rain or snow often falls, especially if the front is in an area of low atmospheric pressure.
On a weather map, a stationary front is shown as alternating red semicircles and blue triangles.
Notice how the blue triangles point in one direction, and the red semicircles point in the opposite
direction.
4. OCCLUDED FRONT
-Sometimes a cold front follows right behind a
warm front. A warm air mass pushes into a
colder air mass (the warm front), and then
another cold air mass pushes into the warm air
mass (the cold front). Because cold fronts move
faster, the cold front is likely to overtake the
warm front. This is known as an occluded front.
-At an occluded front, the cold air mass from
the cold front meets the cool air that was ahead
of the warm front. The warm air rises as these
air masses come together. Occluded fronts
usually form around areas of low atmospheric
pressure.
-There is often precipitation along an occluded front from cumulonimbus or nimbostratus clouds.
Wind changes direction as the front passes and the temperature either warms or cools. After the
front passes, the sky is usually clearer, and the air is drier. On a weather map, shown to the right,
an occluded front looks like a purple line with alternating triangles and semicircles pointing in the
direction that the front is moving. It ends at a low-pressure area shown with a large ‘L’ on the map
and begins at the other end when cold and warm fronts connect.
CYCLONE AND ANTICYCLONE
Cyclone- A cyclone is a pattern of winds (or air mass) that circulates a low-pressure system. It
rotates counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
It is typically associated with wet and stormy weather.
Anticyclone- An anticyclone is a pattern of winds (or air mass) that circulates a high-pressure
system. It rotates clockwise in the Northern Hemisphere and counterclockwise in the Southern
Hemisphere. It is typically associated with dry and fair weather.
DIFFERENCES BETWEEN CYCLONE AND ANTICYCLONE
Cyclone
Anticyclone
Also known as Lows
Also known as Highs
Circulates a low-pressure system
Circulates a high-pressure system
Winds converge towards the center of the
storm
Winds diverge away from the center of the
storm
Winds circulate counterclockwise in the
Northern Hemisphere
Winds circulate clockwise in the Northern
Hemisphere
Cyclone
Anticyclone
Winds circulate clockwise in the Southern
Hemisphere
Winds circulate counterclockwise in the
Southern Hemisphere
Associated with wet and stormy weather
conditions
Associated with dry and fair-weather
conditions
Commonly occurs in the Tropics and
Subtropics
Commonly occurs in the northern parts of
North America and Asia
CONVECTIVE AND OROGRAPHIC PRECIPITATION
Convective Precipitation
Convective precipitation is a type of rainfall that occurs when warm, moist air rises and
cools, forming clouds and raindrops. It is usually intense and short-lived, and often associated with
thunderstorms. Convective precipitation is often caused by the sun’s energy heating the surface of
the Earth. Convective precipitation is showery by nature. This type of precipitation occurs in
varying intensities.
Orographic Precipitation
Orographic precipitation is defined as snow, rain, or other precipitation, which is formed
when moist air is lifted as it moves over a range of mountains. As the air rises and cools, the
orographic clouds form and serve as the precipitation source, where most falls upwind of the
mountain ridge. Moving air masses have a chance to strike barriers such as mountains. Once they
strike, they rise up causing condensation and precipitation. The precipitation that occurs is greater
on the windward side of the barrier when compared to the leeward side of the barrier.
DIFFERENCE BETWEEN CONVECTION AND OROGRAPHIC PRECIPITATION
Convection Precipitation
Orographic Precipitation
Convection precipitation is when warm
and moist air rises and cools, forming
clouds and rain.
Orographic precipitation is when moist air
is forced to rise over mountains or hills,
causing clouds and rain on the windward
side.
Convection Precipitation
Orographic Precipitation
Occurs due to thermal convection
currents caused by insolation heating of
the ground surface.
Occurs due to the accent of air from
highland.
It is usually intense and short-lived
It is usually steady and persistent.
IV.
MEASUREMENT OF PRECIPITATION
A.
Rainfall
-Precipitation is expressed in terms of depth (in meter, m) or in terms of volume (m^3). In the
case of snow or hail, equivalent water depth is considered. Rainfall is measured with the help
of an instrument known as a rain gauge. Terms such as pluviometer, hyetometer, and
ombrometer are also used to designate a rain gauge.
Rain gauges can be classified into two categories:
1. Non Recording rain gauges - a most common type of rain gauge used by meteorological
department that only shows how much rain has fallen. This type of rain gauge cannot tell you
when the rain began when it stopped, the intensity of the rain, or how much the intensity of
the rain varied throughout the storm.
2. Recording rain gauges - can give permanent automatic rainfall records without any bottle
reading. In this type of rain gauge, no man is required to measure or read the amount of
rainfall from the rain gauge.
While installing Rain gauges, the following guidelines are to be adhered to:
i)
A rain gauge must be surrounded by an open fenced area of at least 5.5 m x 5.5 m.
ii)
No object should be near the instrument than 30 m or double the height of the
obstruction, whichever is greater.
iii)
The ground should be perfectly leveled so that the instrument must represent a
horizontal surface.
iv)
A rain gauge must be seated near to the ground as far as possible to reduce the wind
effect but it must be sufficiently high to prevent flooding action.
Three main parts of a rain gauge:
1. FUNNEL
-Pour rainwater into the cup below.
2. INNER MEASURING TUBE
-holds inches of water.
3. OUTER/OVERFLOW CYLINDER
-catches the excess water from the inner
measuring tube.
B.
Snowfall
A snow gauge is an instrument used by hydrologists and
meteorologists to determine the quantity of snow precipitation during a
certain period of time.
Snowfall records are as follows:
Depth of Snowfall
•
To determine the depth of snow, a ruler or yardstick is commonly
used if there is no equipment available in the area. Snow depth sensor is
used to measure snow depth with high accuracy and reliability.
Water Equivalent of Snow
•
The device used to accumulate the snow is a Federal Snow
Sampler (formerly known as Mt. Rose Sampler). SLR or Snow to Liquid
Ratio estimates the water equivalent of snow. 10:1 is generally used as a
ratio (10% as the liquid content).
V.
RAIN GAUGE NETWORK
It is evident that in order to obtain a representative representation of a storm over a
catchment, the number of rain gauges should be as great as feasible, i.e., the catchment area per
gauge should be modest. This is because the catching area of a rain gauge is relatively small in
comparison to the overall extent of a storm. On the other hand, the number of gauges that must be
maintained is limited in part by economic concerns and in part by other considerations such as
geography, accessibility, etc. In order to gather somewhat reliable information about the storms,
one looks for the optimal density of gauges.
It goes without saying that there should be a lot of rain gauges, with each gauge's catchment area
being as tiny as feasible, in order to have a good picture of a storm over a catchment. This is so
because a rain gauge's catching area is so little compared to a storm's total extent. On the other
hand, economic factors significantly and other variables, such as geography, accessibility, etc., to
a lesser extent, limit the number of gauges that must be maintained.
Importance of Rain Gauge Network
❖
❖
❖
❖
Analyzing storms
Fixing design flood
Forecasting flood in a river
Reservoir regulation
Three types of the most widely used recording rain gauges:
1. Tipping bucket rain gauge - The filling gauges work by catching
the falling rain in a funnel-shaped collector that is attached to a
measuring tube. The area of the collector is 10 times that of the tube;
thus, the rain gauge works by magnifying the liquid by a factor of 10.
2. Weighing bucket rain gauge - The receiving funnel leads to one of
two small buckets. The filling of one bucket occurs at one-hundredth of
an inch. The result is a “tipping” of the liquid into the outer shell of the
gauge, triggering the second bucket to take its place.
3. Siphon rain gauge - These gauges are very precise in measuring
rainfall intensity as the weighing mechanism at the bottom of the
collector can be used to measure depth and time simultaneously.
Towards this, the World Meteorological Organization (WMO) recommends the following
densities:
● In flat regions of temperate, Mediterranean, and tropical zones
o Ideal – 1 station for 600 – 900 km2
o Acceptable – 1 station for 900 – 3000 km2
● In mountainous regions of temperate, Mediterranean and tropical zones
o Ideal – 1 station for 100 – 250 km2
o Acceptable – 1 station for 25 – 1000 km2
● In arid and polar zones: 1 station for 1500 – 10000 km2 depending on the feasibility.
Ten percent of the rain gauge station should be equipped with self-recording gauges to
know the intensities of rainfall.
TRIVIA
Radar Measurement of Precipitation - short term of “radio detecting and ranging”.
- is a detection system that uses radio waves to locate objects.
The Indian Meteorological Department has a well-established radar network for detecting
thunderstorms, along with some cyclone-warning radars on the country’s east coast.
The relationship between wave characteristics and precipitation intensity is represented by,
The average resonant force, r is the distance from the radar to the target, and C is optimal
Continuous. Radar Echo Factor Z associated with rainfall intensity I (in mm/hour) is
In this case, a and b are numerical constants by calibrating the radar. One may, thus, be
obtained
Satellite measurement of precipitation - is a method of using satellites to observe
and estimate the amount and distribution of rain and snow on Earth.
The Global Precipitation Measurement mission is an international network of satellites.
-In satellite measurements, rainfall is estimated by correlating satellite-derived data and observed
precipitation data. These relationships can be developed for a portion of the electromagnetic
spectrum using either the cloud life history or the cloud indexing method.
Precipitation History in
the Philippines
Dec - Jan – Feb
June - July- Aug
Mar - Apr- May
Sep - Oct - Nov
1991 2020
Precipitation in the Philippines increased to 2826.17 mm in 2021 from 2529.66
mm in 2020.
VI.
PREPARATION OF DATA
Preparation of Data
The process involves cleaning, organizing, and transforming raw data into a format that is
suitable for analysis. Proper data preparation is essential to ensure the accuracy, reliability, and
validity of research findings.
Estimation of Missing Data
Estimating missing data involves filling in or making educated guesses about values that
are not available in a dataset. This is a common step in data preparation and analysis when
dealing with incomplete datasets. There are various techniques for estimating missing data,
depending on the nature of the data and the research context.
Simple Arithmetic Average
❖ The simple arithmetic average (mean) can be used as a straightforward method to fill in
missing values. This method involves calculating the average precipitation value from the
available data for a particular location over a certain time period and then using that average
to estimate the missing values. if the normal annual precipitation at various stations is
within 10% of the normal precipitation at station, x, as follows:
1
Px = 𝑀 [𝑃1 + 𝑃2+. . . +𝑃𝑚]
Example:
Suppose you are analyzing annual precipitation data for a city, but your dataset has some missing
values. You have precipitation data for the past 10 years, but three years are missing (years 2015,
2017, and 2019).
Here's your available data:
● Year 2010: 42 inches
● Year 2011: 38 inches
● Year 2012: 45 inches
● Year 2013: 50 inches
● Year 2014: 47 inches
● Year 2016: 40 inches
● Year 2018: 43 inches
● Year 2020: 49 inches
To estimate the missing values (2015, 2017, and 2019) using the simple arithmetic average,
(1) Calculate the average of the available data:
Average = (42 + 38 + 45 + 50 + 47 + 40 + 43 + 49) / 8 = 354 / 8 = 44.25 inches
(2) Use this average value to estimate the missing annual precipitation for the missing years:
● Year 2015: 44.25 inches (estimated)
● Year 2017: 44.25 inches (estimated)
● Year 2019: 44.25 inches (estimated)
So, you have estimated the missing precipitation values for the years 2015, 2017, and 2019 as
44.25 inches each, using the simple arithmetic average method.
While this method is straightforward and easy to apply, it has limitations. It assumes that the
missing values are similar to the observed values, which may not always be the case. Additionally,
it doesn't take into account potential trends or seasonality in the data.
❖ Normal Ratio Method -The Normal Ratio Method is a statistical technique used to
estimate missing data in situations where you have some information about the distribution
or relationship between variables. This method assumes that the ratio of precipitation (or
another variable of interest) at one location to that at another location remains relatively
constant over time. The normal ratio method gives Px as:
𝑁𝑥
𝑁1
𝑁2
𝑁𝑚
Px = 𝑀 [ 𝑃1 + 𝑃2 +. . . + 𝑃𝑚 ]
Example:
Imagine you have two weather stations, Station A (target station) and Station B (reference station),
and you want to estimate missing annual precipitation data for Station A for the year 2012.
Station A (Target Station):
Known Precipitation Data:
● Year 2011: 24 inches
● Year 2013: 28 inches
Missing Data for 2012.
Station B (Reference Station):
Known Precipitation Data:
● Year 2011: 22 inches
● Year 2012: 26 inches
● Year 2013: 25 inches
To estimate the missing annual precipitation data for Station A (2012) using the Normal Ratio
Method:
(1) Calculate the normal ratio for the available year (2011) as follows:
Normal Ratio (2011) = Precipitation at Station B (2011) / Precipitation at Station A (2011)
Normal Ratio (2011) = 22 inches / 24 inches = 0.92
(2) Apply the calculated normal ratio to estimate the missing data for 2012:
Estimated Precipitation at Station A (2012) = Normal Ratio (2011) * Precipitation at
Station A (2011) Estimated Precipitation at Station A (2012) = 0.92 * 24 inches = 22.08
inches
So, using the Normal Ratio Method, you estimate that the missing annual precipitation data for
Station A in the year 2012 is approximately 22.08 inches based on the relationship between the
two stations.
Test for Consistency of Record
Testing for the consistency of records in recording precipitation data is crucial to ensure the
accuracy and reliability of weather data, particularly when dealing with datasets from multiple
sources or over extended periods. Here are some common tests and checks specific to precipitation
data:
1. Range Checks: Perform range checks to ensure that recorded precipitation values fall
within plausible limits. For example, check that precipitation values are non-negative
(since precipitation cannot be negative) and do not exceed reasonable upper bounds.
2. Temporal Consistency: Check for temporal consistency by verifying that precipitation
values follow expected patterns over time. This includes checking for seasonality and
ensuring that daily or monthly totals do not show sudden, unrealistic spikes or drops.
3. Spatial Consistency: If working with data from multiple weather stations or geographic
locations, check for spatial consistency. Compare precipitation values at nearby stations
for the same time periods to identify significant discrepancies. Stations in close proximity
should generally record similar precipitation amounts.
4. Duplicate Records: Identify and remove or flag duplicate records. Duplicate entries for the
same time period can lead to data inaccuracies.
5. Data Entry Errors: Examine the data for common data entry errors, such as typographical
mistakes or transposition errors. These errors can result in incorrect precipitation values.
6. Missing Data: Check for missing data and decide on an appropriate method for dealing
with missing values, such as imputation techniques or interpolation methods.
7. Consistency with Historical Records: Compare the recorded precipitation data with
historical weather records for the same location. Ensure that the data is consistent with
historical trends and patterns.
8. Quality Control Flags: Some weather datasets include quality control flags or codes that
indicate potential issues with the data. Review these flags and take appropriate actions
based on their meanings.
9. Visual Inspection: Visualize the data using graphs or charts to identify unusual patterns or
outliers. For example, a time series plot can help you spot irregularities in precipitation
data.
10. Data Source Verification: If you are merging data from different sources, verify that the
data sources are consistent in terms of units, measurement methods, and recording
practices.
11. Extreme Events: Pay special attention to extreme precipitation events, such as heavy
rainfall or storms. Ensure that these events are accurately recorded and that they align with
historical records or nearby station data.
12. Data Resolution: Be aware of the temporal resolution of your data (e.g., daily, hourly, or
minute-by-minute) and ensure that you use the appropriate methods to aggregate or analyze
the data at the desired temporal scale.
DOUBLE-MASS CURVE TECHNIQUE
A double mass curve technique is a graphical method used in hydrology and meteorology
to analyze and assess the consistency and relationship between two sets of data, typically involving
time-series data. This technique is particularly useful for comparing and understanding the
variations in two related variables, such as precipitation and streamflow. It helps identify trends,
patterns, and potential discrepancies in the data.
The procedure of Double-Mass Curve Technique
❖ Assume that station X is the location where inconsistent rainfall records are observed.
❖ In the neighborhood of station X that is causing problems, a group of 5 to 10 base stations
is chosen.
❖ The data on the annual or monthly mean precipitation at station X as well as the average
precipitation for the entire set of base stations over a long period of time is arranged in
reverse chronological order, i.e. the latest record as the first entry and the oldest record as
the last entry in the list.
❖ Based on the latest record, the accumulated precipitation at station X (i.e∑𝑃𝑋 ) and the
accumulated values of the average precipitation (i.e.⅀𝑃𝑎𝑣 )for the group of base stations are
calculated.
❖ For several consecutive time periods, a plot of (∑𝑃𝑋 )vs. (∑𝑃𝑎𝑣 ) is created.
❖ A clear break in the slope of the generated plot denotes a change in the precipitation regime
of station X.
❖ The data of the precipitation at station X after the period of the change of the regime are
corrected using the relation:
Where:
𝑴
𝑷𝒄𝒙 = (𝑷𝒙 )(𝑴 𝒄 )
𝒂
𝑷𝒄𝒙 = Corrected precipitation at station X.
𝑷𝒙 = Original recorded precipitation at station X.
𝑴𝒄 = Corrected slope of the double mass curve.
𝑀𝑎 = Original slope of the double mass curve.
Double-Mass Curve
The record is consistent if the slope of a double-mass curve is constant. If the slope of a
double mass curve does not remain constant, the record is inconsistent and must be adjusted. In
this way, the station X older records are brought into the new regime. The more homogeneous the
base station records are, the more accurate the corrected values at station X will be. A change in
slope is considered significant only if it lasts for more than five years.
EXAMPLE:
SOLUTION:
● Get cumulative of group and cumulative of m:
GRAPH:
Continuation of Solution:
● To get the adjusted values of M and the Cumulative of Adjusted Values of M:
SOLUTION OF DATA:
FINAL GRAPH:
VII.
PRESENTATION OF RAINFALL DATA
What is Rainfall Data?
Rainfall data generally are collected using electronic data loggers that measure the rainfall
in 0.01-inch increments every 15 minutes using either a tipping-bucket rain gage or a collection
well gauge.
Why is rainfall data important?
Rainfall data is necessary for the mathematical modeling of extreme hydrological events,
such as droughts or floods, as well as for evaluating surface and subsurface water resources and
their quality.
Commonly used methods of Presentation of Rainfall Data
1. Mass curve rainfall
❖ The mass curve of rainfall is a plot of the accumulated precipitation against time, plotted
in chronological order. Records of float type and weighing-bucket type gauges are of this
form.
❖ It is very useful in extracting the information on the duration and magnitude of a storm.
Also, intensities at various time intervals in a storm can be obtained by the slope of the
curve.
2. Hyetograph
❖ A hyetograph is a graphical representation or a tool used by hydrologist to illustrate the
distribution of rainfall intensity over time.
❖ A hyetograph can help engineers to know the maximum flow rate that a drainage system
must be able to handle and this type of information is important for prevention of flooding
in urban areas.
❖ It is a critical tool for analyzing and predicting the effects of the rainfall to the environment
and infrastructure. Such as in different fields like engineering, hydrology and agriculture.
3. Point Rainfall
• Also known as station rainfall
•
•
Point Rainfall is the amount of rain that falls at a certain gauging station and is expressed
in daily, weekly, monthly, seasonal, or annual terms.
Presented in the form of a bar graph
VIII.
PROBABLE MAXIMUM PRECIPITATION (PMP)
-
The Probable Maximum Precipitation (PMP) is an estimate of the maximum possible
rainfall in a specific area during an extreme weather event. It is crucial for designing and
ensuring the safety of large water infrastructure projects like dams, reservoirs, and flood
control systems, allowing engineers to prepare for the worst weather conditions.
❖ In the design of major hydraulic structures such as spillways in large dams the hydrologist
and hydraulic engineer would like to keep the failure probability as low as possible, i.e.,
virtually zero.
❖ In order to prevent heavy damage to life, property, economy, and national morale in the
design and analysis of structures, the maximum possible precipitation is used.
❖ There is a physical upper limit to the amount of precipitation that can fall over a specified
area in a given time.
Maximum Intensity-Duration Relation
Maximum Intensity-Maximum Depth-Duration Relation
Maximum Intensity-Duration and Maximum Depth-Duration Curves
❖ Defined as the greatest or extreme rainfall for a given duration that is physically possible
over a station or basin.
❖ It also can be defined as rainfall over a basin that would produce a flood flow with virtually
no risk of being exceeded.
There are Two Approaches Used in PMP
i.
Meteorological methods
Meteorological method – This method is applicable in a large area of a certain land like countries
or states. The gathering of data uses satellites from the atmosphere and uses atmospheric devices
to compute the PMP.
ii.
Statistical study of rainfall data
Statistical studies indicate that PMP can be defines as
PMP = 𝑷 + Kσ
Where:
𝑷 = mean of annual maximum rainfall series
σ = standard deviation of the series
K = a frequency factor which depends upon the statistical distribution of the series,
number of years of record and the return period.
World’s Greatest Observed Rainfall
❖ Based upon the rainfall records available all over the world, a list of world’s greatest
recorded rainfalls of various duration can be assembled.
❖ When this data is plotted on a log-log paper, an enveloping straight line drawn to the plotted
points obeys the equation.
Pm = 42.16 D0.475
Where:
Pm = extreme rainfall depth in cm
D = duration in hours
Sample Problem:
In a catchment there are six rain gauge stations with average depth of rainfall of 92.8 cm
and standard deviations of the rainfall values recorded in these rain gauge stations is 30.7 cm. For
a 10% degree of error in the measurement of mean rainfall, the optimum number of stations
required is.
Given:
𝑷 = 92.8 cm
σ = 30.7 cm
E = 10%
Solution:
Cv = σ/𝑷 x 100
Cv = 100 x 30.7/92.8
Cv = 33.08%
Cv = coefficient of variation
Optimum number of rain gauge
n= (Cv/E)2
n = (33.08/10)2
n = 10.94 or 11
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