Lecture 5: Variability in water resources Flashcards
Define the following:
dirunal cycle synoptic variability inter-onthly variability seasonal cycle interannual variability decadal/inter decadal variability trends or long term changes
• 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
what are some examples of temporal variability?
seasonal cycle of precipitation
diurnal cycle of precipitation
interannual variability, decadal variability and long term trend
What are the controls and behaviour of variability
• 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
How to reduce variability and increase water availability
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?
What is statistical analysis of hydrological processes and water resources?
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
What is the time series in hydrology and water resources?
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
What are the time series analysis concept- Mean, Anomaly and Z-score?
- Original time series, with
mean (horizontal line) - 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
What are time series analysis concepts- exceedance values and flow duration curves?
- 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
What is the time series analysis concept: auto-correlation?
• 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
why are time series correlations useful?
• 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.
what are non-stationarity of water resources processes?
• 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
What can cause non-stationarity?
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)
How to detect non-stationarity?
- viual
- statistical tests
How do you overcome non-stationairity?
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
what are the large-scale climate variability and teleconnections?
• 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
What are some examples of large-scale climate variations?
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)
What are the most iportant climate variability phenomenon?
increasing time scale of variability
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
What is ENSO
• 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.
What is the ENSO mechanism?
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
Describe the ENSO time series
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)
Where does the ENSO teleconnection impact?
• 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.
What are some examples of ENSO impacts
- 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
What was the EL NINO monster
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.
What is the Madden-Julian Oscillation?
• 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).
What are the NAO and AO
• 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.
What are the NAO teleconnections?
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
What is an example of the NAO teleconnection with European streamflow?
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.
What is the NAO teleconnection with snow in the alps?
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
what is the pacific decadal variability?
• 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.
what are the PDV/ PDO teleconnections?
• 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).
What is the atlantic multi-decadal variability (AMV,AMO)
• 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.
what are the AMV/AMO teleconnections?
• 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).
what are the AMO and tropical cyclones?
diagram on bb
what is hydrological/ water reosurces forecasting?
• Forecasting availability of water or extreme events (droughts, floods) over
the next weeks, months or years
Why is the forecasting important?
Why is it important?
• Water resources management can be improved or optimized
• Flood warnings, drought early warning
what is the basis of forecasts?
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
what is the difference between deterministic and probablistic predictions?
- Deterministic process is exactly defined, e.g. a single forecast
- Probabilistic process captures the uncertainty
what are the types of hydrological forecasting?
• 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)
What are the different time scales of forecasts?
• 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
give some examples of how forecats can be used?
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
what is regression analysis in statsitical forecasting?
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
explain linear regression?
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.
what is simple linear regression?
• 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
What is linear regression and correlation?
• 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
what are dynamical/ physical model forecasts?
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;
How are weather/ climate models run?
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.
What are the limitations of predictions?
• 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
what are longer-term climate predictions?
• 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
what is predictability?
Lorenz (1969) defined
predictability as “a limit to
the accuracy with which
forecasting is possible”.
What are hydrological forecasts?
• 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
In hydrological forecasts where is the source of predictability?
• A large source of predictability is the inertia or persistence in the land initial
conditions - soil moisture, snow, groundwater
An Example of a Hydrological Forecast used in
Water Resources Management- diagram on bb
• 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
Example - Skill of Hydrological Forecasts over Africa
Seasonal forecast skill is modest and seasonally/regionally dependent with part of the skill
coming from persistence in initial land surface conditions.
Example Hydrological Forecast for
Drought of 2011 in Horn of Africa
• 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
