Lecture 5: Variability in water resources

Question 1

Define the following:

dirunal cycle
synoptic variability 
inter-onthly variability 
seasonal cycle
interannual variability 
decadal/inter decadal variability 
trends or long term changes

Answer 1

• Diurnal cycle – the variation of hydrological quantities (e.g. precipitation) over the
day as driven by the sun and the land surface energy balance
• Synoptic variability – the variation over days to weeks as forced by the weather
• Inter-monthly variability – the variation from month to month
• Seasonal (or annual) cycle – the variation over the year as driven by the sun
• Inter-annual variability – the variations between years
• Decadal/inter decadal variability – the variations between decades
• Trends or long-term changes – slowly evolving changes that happen over multiple
decades to centuries or longer

Question 2

what are some examples of temporal variability?

Answer 2

seasonal cycle of precipitation

diurnal cycle of precipitation

interannual variability, decadal variability and long term trend

Question 3

What are the controls and behaviour of variability

Answer 3

• Size – larger catchment tend to have lower variability (storage effect)
• Geology – catchments underlain by porous formations (sand and limestones) tend
to have lower variability
• Catchments underlain by crystalline rock and or clay tend to have higher variability
• Climate – catchments in humid regions tend to have lower variability
• Catchments in regions of high seasonal precipitation or snowmelt or in an arid
region tends to have higher variability

for example:- soil moisture over the southeast US- humid climate

soil moisture over the western US- dry climate

Question 4

How to reduce variability and increase water availability

Answer 4

The local river is a source of water but it is too variable – there are too many high
flows that can cause flooding and the low flows happen so often that water supply
and environmental flows cannot be sustained through the year. How do you increase
water availability and/or decrease variability?

1) Decrease variability by building a reservoir – water is stored for
low flow periods; flood water is retained
2) Extract water from natural groundwater storage reservoirs –
provides a backup to the river flows
3) Increase water availability by rain making
4) Modify loses through changing vegetation cover (less ET)

What are the implications of these
types of changes/modifications?

Question 5

What is statistical analysis of hydrological processes and water resources?

Answer 5

A goal of hydrology is to characterize a hydrological process (particularly its
variability) based on the samples of observations or model representation

• We use statistical analysis that aims to summarize or characterize the
properties of the process (population) from temporal or spatial samples and
assess the degree of uncertainty associated with this based on the laws of
probability

• Example properties are
• mean, µ
• variability or standard deviation, s
• correlation, r

• Statistical inference:
• Make an inference about the properties of a hydrological process or
water resource (the population) from the properties of samples drawn
from that population (measurements, observations)
• In practice, you have a limited series of measurements (a sample), from
which you make an assessment about the process (the population) and
its properties

Question 6

What is the time series in hydrology and water resources?

Answer 6

Time series is a time ordered sequence of discrete values of a variable separated by a
constant time interval

We are interested in the average behaviour of a system (e.g. the mean daily
streamflow), but we are very interested in the variability of the system (e.g. the
maximum daily flows, or the minimum daily flows.

digram on bb

Question 7

What are the time series analysis concept- Mean, Anomaly and Z-score?

Answer 7

1. Original time series, with
   mean (horizontal line)
2. Anomaly represents how the
   time series varies about the mean,
   calculated as Vi
   ’ = Vi – mean(V)

3. Z-score normalizes the
anomaly by the variability (stdev)
of the time series calculated as
Zi = Vi
‘ / stdev(V)

The Z-score allows you to compare
two time series with very different
means and very different variability

diagrams on blackboard

Question 8

What are time series analysis concepts- exceedance values and flow duration curves?

Answer 8

- We are interested in how the
hydrological process (e.g. streamflow)
varies from year to year, particular the
high and low values.
- The exceedance value – the rate at
which water is actually available for use
is best measured at the rate that is
available for a high percentage of time –
e.g. 95%
- A good way to show this is the duration
curve – a graph showing the fraction
(e.g. 95%) of time that the magnitude of
a given variable is exceeded.
- This is termed the exceedence
probability

Question 9

What is the time series analysis concept: auto-correlation?

Answer 9

• Autocorrelation (or serial correlation) indicates how similar a time series is to
values of the same time series but lagged in time.
• Positive autocorrelation indicates that a value in the future will be similar to
the value today.
• Processes that have high autocorrelation are said to have persistence.

diagram on blackboard

Question 10

why are time series correlations useful?

Answer 10

• Positive or negative correlation can suggest that two processes (as
represented by time series of data) may be related to each other.
• Note - correlation does not imply causation (i.e. that a change in one
causes a change in another). Proof of causation needs additional
information about why the two processes may be related.
• An example use is in forecasting water resources. If two time series are
correlated it could suggest that they are related (a change in one causes
a change in another) and therefore knowing one can help you predict the
other
• Example: If I know that it is generally drier during the summer if there is
an El Nino then I could make a prediction of the upcoming summer
rainfall if I knew what the current El Nino conditions are. I can then make
a decision that would results in a benefit – e.g. plant a drought tolerant
crop or save water in a reservoir.

Question 11

what are non-stationarity of water resources processes?

Answer 11

• Implicit in the analysis of water resources is the assumption of stationarity – that there are
no long-term changes, steps or cycles in the data
• Stationarity is the assumption that a hydrological process does not change over time – i.e.
that its time series is representative of long term (i.e. future behavior)

Types of non-stationarity
1) Upward or downward
trends
2) Abrupt shifts
3) Cycles
4) Can be a change in the
mean or the variability

• Why is this important? – if
you calculate available
water (e.g. 95%
exceedence flow) or risk
of floods, based on your
data sample you may
underestimate or overestimate
the availability or
risk because the actual
process may change/shift
in the future

Question 12

What can cause non-stationarity?

Answer 12

1) What can cause non-stationarity?
• Natural – solar cycles,
teleconnections, climate
oscillations, volcanic activity
• Human – dams, land use
change, ground water pumping,
climate change, shifts in
measurement (locations/
instruments)

Question 13

How to detect non-stationarity?

Answer 13

• viual

- statistical tests

Question 14

How do you overcome non-stationairity?

Answer 14

3) How to overcome this? – you can
increase your sample size using
paleo data, regional data – or look at
model projected data to see if the
process might change

Question 15

what are the large-scale climate variability and teleconnections?

Answer 15

• Climate has average features (e.g. global distribution of precipitation and
monsoons) but also persistent, large-scale oscillations and variations that
produce climate variability at inter-annual to inter-decadal time scales
• These can lead to semi-regular fluctuations in temperature, precipitation, and
hydrology around the world, sometimes for lasting a few months
• These are called teleconnections
• Some more well-known ones are ENSO, NAO, PDO, AMO and many others
• Each of these has a characteristic time scale and regional footprint
• First identified back in the 1960s when historic time series of data were
starting to get long enough to be examined for period cycles and long-term
changes

Question 16

What are some examples of large-scale climate variations?

Answer 16

Climate variations are often characterized by indices which are time series of variables that
represent the main aspects of the climate phenomena – e.g. sea surface temperature (SSTs) or
difference in sea level pressure between two locations/regions). These indices are often
normalized, e.g. Z-score.

El Niño Southern
Oscillation
(ENSO)

North Atlantic
Oscillation
(NAO)

Pacific Decadal
Variability (PDV)

Atlantic MultiDecadal
Variability (AMV)

Question 17

What are the most iportant climate variability phenomenon?

increasing time scale of variability

Answer 17

1) MJO – Madden Julian Oscillation
2) NAO – North Atlantic Oscillation
3) ENSO – El Nino Southern Oscillation
4) PDO – Pacific Decadal Oscillation/Variability
5) AMO – Atlantic Multi-Decadal Oscillation/Variability

Question 18

What is ENSO

Answer 18

• The ENSO is the most important
driver of global climate on interannual
timescales.
• It manifests in the tropical Pacific
Ocean, in the form of anomalies in
sea surface pressure and sea
surface temperature (SST).
• The Southern Oscillation Index
(SOI) is a measure of the strength of
this, in terms of the pressure
difference between the east and
west tropical Pacific (specifically at
Tahiti and Darwin, Australia).
• This is intimately related to
temperature as well, providing an
oscillation between warm (El Niño)
and cool (La Niña) SSTs.

Question 19

What is the ENSO mechanism?

Answer 19

In a normal year, the Trade winds
blow westwards pushing warm
surface water towards Indonesia
and Australia. The warm water
causes lots of convection and
precipitation

In an El Niño year, the Trade
winds die down, and warm surface
waters shift eastwards bringing
more rain to the central and
eastern Pacific, and drier
conditions to the western Pacific

In a La Niña year the opposite
happens. The eastern Pacific
cools and dries, and the western
Pacific gets warmer and wetter

Question 20

Describe the ENSO time series

Answer 20

Various ENSO indices have been proposed and
many of then are calculated based on sea surface
temperature (SST) in the tropical Pacific, by
averaging over different regions and calculating
anomalies or Z-scores (e.g. the Nino 3.4 index)

Question 21

Where does the ENSO teleconnection impact?

Answer 21

• The regions of the world affected by the
ENSO, stretch well beyond the local area
of the tropical Pacific.
• Warmer SSTs during El Niño force
convection to migrate eastwards,
bringing wetter conditions to the central
Pacific and drier conditions to Indonesia
and northern Australia.
• Further afield, El Niño brings reduced
rainfall in southwestern Africa, but wetter
conditions in parts of the US, and in East
Asia weakens the monsoon, causing
warmer conditions.
• La Niña generally drives the opposite
teleconnection, although La Niña and El
Niño are not perfectly symmetrical.

Question 22

What are some examples of ENSO impacts

Answer 22

• Fires burning on the Indonesian island of Sumatra,
  September 24, 2015. (NASA Earth Observatory)
• Total emissions from Indonesian fires
  compared to other years and to fossil
  fuel emissions for various countries

Question 23

What was the EL NINO monster

Answer 23

The El Niño in 2015/2016 was one of the three most extreme since 1950. Strongly contrasting
effects and weather events were seen in different parts of the world.

Question 24

What is the Madden-Julian Oscillation?

Answer 24

• The MJO was first discovered in the early 1970s by Dr. Roland Madden
and Dr. Paul Julian when they were studying tropical wind and pressure
patterns in the west central equatorial Pacific.

• Unlike ENSO, which is stationary, the MJO is an eastward moving disturbance of clouds,
  rainfall, winds, and pressure that traverses the planet in the tropics and returns to its initial
  starting point in 30 to 60 days, on average.

• The MJO can have dramatic impacts in the mid-latitudes,
contributing to extreme events.
• There can be multiple MJO events within a season, and so
the MJO is best described as intraseasonal tropical climate
variability (i.e. varies on a week-to-week basis).

Question 25

What are the NAO and AO

Answer 25

• In the northern hemisphere, the North Atlantic Oscillation (NAO) is characterized by a yearto-year
seesaw in the difference in pressure between the Icelandic Low and the Azores High
pressure regions.
• These modes are particularly strong in the northern
hemisphere winter, although summertime
manifestations are apparent.
• The variations are actually part of an extended pattern
throughout the northern hemisphere and are better
known as the Arctic Oscillation (AO), or Northern
Annular Mode (NAM).
• The AO manifests as anomalies of different size
between the Arctic and mid-latitudes, at around 40oN.

Question 26

What are the NAO teleconnections?

Answer 26

The phases of the NAO deflect the jet stream further north or south in the Atlantic Ocean, changing
the strength of westerly winds and storm tracks, and affecting the climates of North America and
Europe.
•If the Icelandic low and Azores subtropical high are stronger than normal, then the NAO is positive
• results in more and stronger storms crossing the Atlantic on a more northerly track
• eastern US will experience mild and wet winter conditions
• If the Icelandic low and Azores subtropical high are weaker than normal, then the NAO is negative
• results in fewer and weaker storms crossing the Atlantic
• eastern US experiences more cold-air outbreaks and snowy weather conditions

Question 27

What is an example of the NAO teleconnection with European streamflow?

Answer 27

Large positive z-scores
denote more than
average river discharge
in a NAO-positive year

Large negative z-scores
denote less than
average discharge in a
NAO-positive year

Thickness of lines is
proportional to
yearly average river
discharge.

Question 28

What is the NAO teleconnection with snow in the alps?

Answer 28

A negative NAO tends
to shift storms
southwards bringing
more snow to the Alps
- very important for
the ski industry

The NAO has
generally been
positive over the past
few months with
forecasts saying that
it will change to
negative through
March

Question 29

what is the pacific decadal variability?

Answer 29

• Also called the Pacific Decadal
Oscillation (PDO)
• The PDV is similar to the ENSO
but manifests in the northern
Pacific Ocean and varies across
much longer timescales of 20 to 30
years (Mantua et al, 1997).
• It is quantified by the variability in
sea surface temperatures and sea
level pressure in the north Pacific.
• Different phases of the PDO have
persisted for several decades,
most notably the ‘cold’ or ‘negative’
phase of 1890–1924 and 1947–
1976, and the ‘warm’ or ‘positive’
phase of 1925–1946, and from
1977 until recent times.

Question 30

what are the PDV/ PDO teleconnections?

Answer 30

• The impacts of the PDO are somewhat similar to those of the ENSO.
• Over North America, for example, the positive phase of the PDO is associated with wetter
conditions in the southwestern US, and warmer winter and spring temperatures in the
northwest, accompanied by lower precipitation extending to the Great Lakes region.
• The PDO exerts a modulating influence on the ENSO, therefore changing the strength and
persistence of the ENSO’s effects around the world. For example, the impact of the ENSO
on the East Asian winter monsoon is only robust when the PDO is in its cold phase (Wang
et al, 2008).

Question 31

What is the atlantic multi-decadal variability (AMV,AMO)

Answer 31

• On the other side of the world, the Atlantic Multidecadal
Variability (AMV) (also called Atlantic Multidecadal
Oscillation (AMO)) describes changes in
surface temperatures in the North Atlantic over
periods of several decades.
• It is thought to be a factor in the frequency of Atlantic
hurricanes and may be influenced by anthropogenic
warming.

Question 32

what are the AMV/AMO teleconnections?

Answer 32

• The AMO is related to temperature
and precipitation fluctuations over
the northern hemisphere. The
figure shows the regions that are
impacted, in particular North
America and Europe.
• The warm phase of the AMO is
associated with dry conditions in
the Midwest and southwest of the
US, whereas wetter conditions
prevail in the southeast and
northwest (Enfield et al, 2001).
• There is also evidence from
climate models and palaeoclimate
data that the AMO is associated
with climate over North Africa,
India and northeastern Brazil
(Zhang and Delworth, 2006;
Shanahan et al, 2009).

Question 33

what are the AMO and tropical cyclones?

Answer 33

diagram on bb

Question 34

what is hydrological/ water reosurces forecasting?

Answer 34

• Forecasting availability of water or extreme events (droughts, floods) over
the next weeks, months or years

Question 35

Why is the forecasting important?

Answer 35

Why is it important?
• Water resources management can be improved or optimized
• Flood warnings, drought early warning

Question 36

what is the basis of forecasts?

Answer 36

What is the basis of forecasts?
• Forecasting water resources relies on the inertia in the climate system
(the tendency for aspects of the system to persist in a certain state) and
teleconnections between these states and the variable of interest (e.g.
streamflow at a certain locations).
• These sources of predictability can be the ocean, soil moisture, snow
pack, …, each of which persist at different time scales
Climate variability, such as ENSO, is very important for forecasting at
seasonal time scales

Question 37

what is the difference between deterministic and probablistic predictions?

Answer 37

• Deterministic process is exactly defined, e.g. a single forecast
• Probabilistic process captures the uncertainty

Question 38

what are the types of hydrological forecasting?

Answer 38

• Statistical: pros (easy to use; based on real data; simple), cons (empirical so no
direct physical basis)
• Dynamical (physically-based model): pros (physical basis, can be used for
attribution), cons (skill dependent on model)

Question 39

What are the different time scales of forecasts?

Answer 39

• Short-term forecasts (1-2 weeks) based on weather model forecasts, such as
those you see on the BBC weather forecast
• Sub-seasonal or inter-seasonal forecasts (2 weeks to 3 months) based on
medium range weather models or seasonal climate models
• Seasonal forecasts (3-6 months) based seasonal climate models
• Long-range forecasts (1 year) based seasonal climate models
• Decadal Forecasts (5-10 years) based decadal climate models

Question 40

give some examples of how forecats can be used?

Answer 40

Some examples of how a short-term to seasonal hydrological forecast could be used to better
manage water resources:

• Flood forecasts can provide alerts to communities

• Reservoir management
• A reservoir can release water if a flood is forecast
• A reservoir can save water if a drought is forecast

• Energy management – hydropower, thermoelectric plants

• Agriculture
• Crop yield forecasting helps manage storage and food security
• Selection of crop type based on drought tolerance
• Agricultural water use can be optimized – irrigation can be scheduled
• When to plant for optimal yield
• Recreation summer/winter
• Long-term planning

Question 41

what is regression analysis in statsitical forecasting?

Answer 41

What is it?
• Regression analysis involves identifying the relationship between a
dependent variable and one or more independent variables.
• A model of the relationship is hypothesized, and estimates of the parameter
values are used to develop an estimated regression equation.
• Various tests are then employed to determine if the model is satisfactory.
• If the model is deemed satisfactory, the estimated regression equation can
be used to predict the value of the dependent variable given values for the
independent variables.
Reasons to use Regression Analysis
• To model phenomenon in order to better understand it and possibly make
decisions
• To model phenomenon to predict values at other places or times
• To explore hypotheses
We can model, examine, and explore temporal relationships, and make
predictions. A regression model is a form of statistical prediction model

Question 42

explain linear regression?

Answer 42

Used to analyze (simple) linear relationships among variables
(one can also do non-linear regression)
• Regression analyses attempt to demonstrate the degree to which one or more
variables potentially promote positive or negative change in another variable.

• The general form of a linear regression model is:
y = b0 + b1x1 + b2x2 + ….. + bnxn + e

y = variable you are trying to predict (e.g. streamflow)
x = explanatory (or independent) variable
b = coefficients (or weights) that represent the strength and type (positive or
negative) of the relationship x has to y
e = random error or residuals. This is the unexplained part of the dependent
variable y.

Question 43

what is simple linear regression?

Answer 43

• In practice this generally involves
fitting a linear model (line) to data
from two variables that we think
are related somehow (e.g. rainfall
and streamflow)

y = b0 + b1x + e

where b0 is the y-axis intercept and
b1 is the slope of the line
• Linear regressions can be fit in
Excel using Ordinary Least
Squares Regression method which
minimizes the sum of the squared
residuals

Question 44

What is linear regression and correlation?

Answer 44

• Correlation and regression analysis are related in the sense that both deal with
relationships among variables.
• The correlation coefficient is a measure of linear association between two
variables.
• Linear relationships are positive or negative

Question 45

what are dynamical/ physical model forecasts?

Answer 45

Numerical weather/climate
prediction uses mathematical
models of the atmosphere and
oceans to predict the weather
based on current weather
conditions (also known as initial
conditions in the model).

Mathematical equations
represent the laws of physics,
including for example, Isaac
Newton’s laws of motion

These models, based on the
same physical principles, can be used to generate either shortterm
weather forecasts or
longer-term climate
predictions/change;

Question 46

How are weather/ climate models run?

Answer 46

1) The model is initialized with actual
observations of the atmosphere, land
and ocean using a method called data
assimilation

2) A model consists of representations
of different aspects of the climate
system that are coupled together in the
model

3) The model is run from the initial conditions
into the future. We do not know the exact state
of the atmosphere at the start of the forecast
so the model is run multiple times with slightly
different initial conditions to produce an
ensemble of forecasts.

Question 47

What are the limitations of predictions?

Answer 47

• A fundamental problem lies in the chaotic nature of the atmosphere.
• We cannot solve the equations that represent the physics of the atmosphere
exactly, and small errors grow with time (doubling about every five days).
• Present understanding is that this chaotic behavior limits accurate forecasts to
about 14 days even with perfectly accurate input data and a flawless model.
• In addition, the models also have to represent (parameterize) solar radiation,
moist processes (clouds and precipitation), heat exchange, soil, vegetation,
surface water, and the effects of terrain – leading to more uncertainty
• Ensemble forecasts and ensembles of different models can be used to represent
the uncertainty in the observed data (initial conditions), the uncertainty in the
model and its parameterizations that represent the physics of the real world

Question 48

what are longer-term climate predictions?

Answer 48

• Prediction at time scales beyond weather depends on variability driven by slowprocesses
in the climate system, particularly the ocean.
• Successful seasonal forecasts are often related to a model’s ability to reproduce
and predict the slowly changing ocean state (e.g. associated with El Niño) and
how this interacts with the atmosphere.
• The hope is that these slowly-evolving processes can provide a signal amongst
the noise of the weather

Question 49

what is predictability?

Answer 49

Lorenz (1969) defined
predictability as “a limit to
the accuracy with which
forecasting is possible”.

Question 50

What are hydrological forecasts?

Answer 50

• Hydrological forecasts are forecasts of hydrological variables (e.g. runoff,
streamflow, ET, soil moisture) and their extremes (floods, droughts)
• These are often made by taking a climate forecast and using it to force a
hydrological model

Question 51

In hydrological forecasts where is the source of predictability?

Answer 51

• A large source of predictability is the inertia or persistence in the land initial
conditions - soil moisture, snow, groundwater

Question 52

An Example of a Hydrological Forecast used in

Water Resources Management- diagram on bb

Answer 52

• The forecasts in this example, do a good job of predicting the future inflows to the
reservoir, mainly because of persistence in the streamflow
• Note that there is uncertainty in the forecasts as represented by the ensemble of
forecasts - we do not know exactly what will happen in the future but we may a have a
good sense of the range in possibilities
• The uncertainty comes from uncertainty in the climate forecast, uncertainty in the
hydrological model, and uncertainty in the initial conditions of the model
• We would like to reduce the uncertainty by using better models and data, but can never
remove the uncertainty completely

Question 53

Example - Skill of Hydrological Forecasts over Africa

Answer 53

Seasonal forecast skill is modest and seasonally/regionally dependent with part of the skill
coming from persistence in initial land surface conditions.

Question 54

Example Hydrological Forecast for

Drought of 2011 in Horn of Africa

Answer 54

• This forecast was based on a seasonal forecast of precipitation and temperature from a
climate forecast model, that was used to force a hydrological model.
• This forecast was mainly successful because the drought was driven by a strong La Nina
event, and the teleconnection with east African precipitation was well represented by the
climate forecast model