Download-manuals-ground water-training-dwlrg-wdatahandling

World Bank & Government of The Netherlands funded
Training module # 1
Understanding Conventional
and DWLR Assisted Water
Level Monitoring
New Delhi, March 2000
CSMRS Building, 4th Floor, Olof Palme Marg, Hauz Khas,
New Delhi – 11 00 16 India
Tel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685
E-Mail: dhvdelft@del2.vsnl.net.in
DHV Consultants BV & DELFT HYDRAULICS
with
HALCROW, TAHAL, CES, ORG & JPS

HP Trng Module File: “ 1 Conventional and DWLR assisted water level monitoring.doc” Version 10/10/02 Page 1
Table of contents
Page
1. Module context 2
2. Module profile 3
3. Session plan 4
4. Main text 5
5. Overhead/flipchart master 6
6. Handout 7
7. Additional handout 8

1. Module context
While designing a training course, the relationship between this module and the others,
would be maintained by keeping them close together in the syllabus and place them in a
logical sequence. The actual selection of the topics and the depth of training would, of
course, depend on the training needs of the participants, i.e. their knowledge level and skills
performance upon the start of the course. This is an independent module.

2. Module profile
Title : Understanding Conventional and DWLR Assisted Water
Level Monitoring
Target group : Hydrogeologists, Asst-Hydrogeologists, Senior Technical Assistant
Duration : One Session of 30 minutes
Objectives : After the training the participants will be able to:
• Differentiate between conventional water level monitoring and
high frequency level monitoring.
Key concepts : • Prevalent water level monitoring
• High Frequency water level Monitoring
• True hydrographs
Training methods : Lecture
Training tools
required
: OHS
Handouts : As provided in this module
Further reading
and references
:

3. Session plan
No Activities Time Tools
1 • Discuss the prevailing water level monitoring,
• Show the nature of the hydrograph emerging from
conventional monitoring
• Discuss the nature of aquifers being monitored,
• List the deficiencies of the conventional monitoring,
• Describe the advantages of dedicated piezometers over
hand dug wells
• Explain the need for high frequency monitoring and role of
DWLR,
• Explain a true hydrograph
15 min OHS
2 • Illustration 5 min OHS
3 Feedback 5 min
4 Wrap up 5 min

4. Main text
Contents
1. Prevalent Monitoring 1
2. High Frequency Monitoring 2
3. True Hydrograph – What to do with it? 2

Understanding Conventional and DWLR Assisted Water Level Monitoring
1. Prevalent Monitoring
Conventionally the groundwater monitoring in India has been conducted on the following
lines:
• Water levels are usually monitored in privately owned open dug wells tapping the upper
unconfined aquifers. These levels reveal the piezometric head/water table elevation of
the semi-confined/unconfined aquifers. However, the necessary well-aquifer hydraulic
connection is not always beyond suspicion.
• The frequency of monitoring has generally been restricted to four times in a year. These
times are rather arbitrarily selected during pre-monsoon, monsoon, post-monsoon and
winter seasons. It is presumed that these water levels represent the troughs and peaks
of the water table hydrograph. However, many a time these data may be too sparse to
yield reliable and credible water table hydrograph, as illustrated in figure 1. The figure
shows the true hydrograph (derived from high frequency DWLR data) superposed over
the corresponding hydrograph based upon four annual observations.
Fig 1: True Hydrograph from phreatic aquifer (Granitic rock), in Kattangur
Village, Nalgonda District Andhra Pradesh

• Limited monitoring of the piezometric head of the deeper confined/leaky confined
aquifers has been carried out by some agencies, usually by observing the water level in
the deep production tube wells. The tube wells, many a time may not be adequately
isolated from (or worse, may even be tapping) the unconfined aquifer. Dedicated
piezometers tapping only the deeper aquifers and duly isolated from the unconfined
aquifer are almost non-existent.
The historical monitoring programmes though quite extensive and commendable in many
ways, have been deficit in several respects. The practising hydrogeologists have been
conducting the resource evaluations quite credibly in spite of these deficits. They have been
circumventing the problem by certain subjective practices based upon norms/past
experience or intuitive reasoning. Nevertheless, this has restricted their practice in many
ways. For example, no norms have been developed for estimating resource of the deeper
aquifers. (This estimation is no doubt difficult due to uncertainties regarding the recharge
zone, but lack of the piezometric head data has pre-empted its solution.) Similarly, since the
practitioners have never been able to view a true water table hydrograph, recharge
estimation by water balance of the unconfined aquifer gets uncertain in many ways. Further,
time series analysis of the water level data is not routinely done because the data at
necessary frequency are usually not available.
2. High Frequency Monitoring
The Hydrology Project has enabled construction of a large number of scientifically designed
piezometers tapping unconfined and the deeper aquifers. These piezometers have the
necessary hydraulic connection with the targeted aquifers and are suitably isolated from
overlying/underlying aquifers. Further, digital automatic water level recorders (DWLRs) are
installed in these piezometers. This ensures measurement of undistorted piezometric head
at the desired frequency, which may be much larger than the present frequency. In fact, the
frequency may be so high that the resulting piezometric hydrograph may almost be
continuous.
3. True Hydrograph – What to do with it?
With the high frequency and credible piezometric head data emanating from the
DWLRs, the groundwater practitioners in India shall have an access to true
piezometric head hydrographs, possibly for the first time. This is bound to inspire the
practitioners to enhance the scientific/technical content of their prevailing practice
and also to incorporate in it many new analyses. Some of the possibilities shall be
discussed subsequently.

5. Overhead/flipchart master

6. Handout

7. Additional handout
These handouts are distributed during delivery and contain test questions, answers to
questions, special worksheets, optional information, and other matters you would not like to
be seen in the regular handouts.
It is a good practice to pre-punch these additional handouts, so the participants can easily
insert them in the main handout folder.

Training module # 2
Role of DWLR data in
Groundwater Resource
Estimation
Tel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685
with

HP Trng Module File: “ 2 Role of DWLR data in GW Resource Estimation.doc” Version 10/10/02 Page 1
Table of contents
Page
1. Module context 2
2. Module profile 3
3. Session plan 4
4. Main text 5
6. Handout 7

1. Module context
performance upon the start of the course.

2. Module profile
Title : Role of DWLR data in Groundwater Resource Estimation
• Appreciate the utility of high frequency DWLR water level
monitoring.
• Correlate the rainfall hyetograph to the corresponding water
level hydrograph.
• Appreciate the utility of high frequency ground water levels for
systematic assessment of ground water resources.
Key concepts : • Understanding the recharge process
• Lumped water balance
• Role of DWLR data
Training tools
required
: OHS
Further reading
and references
:

3. Session plan
1 • Discuss the prevailing Water balance computations for
unconfined aquifers
• Scope for improvement of water balance computations by
using DWLR data
• Methodology for selection of water balance periods
• Identification of effective rainfall events
• Estimation of evapotranspiration loss
30 min OHS
3 Feedback 15 min
4 Wrap up 5 min

4. Main text
Contents
1. Understanding the Recharge Process 1
2. Lumped Water Balance 2
3. Role of DWLR data 3

Role of DWLR data in Groundwater Resource Estimation
An important activity of many of groundwater practitioners in India is to estimate the
groundwater resource (mainly monsoon recharge) by a lumped water balance of the
unconfined aquifer, in accordance with GEC-84/97 norms. The high frequency water table
data from the DWLRs can assist a practitioner in conducting such estimations more
rationally and credibly. A few possible applications of such data are described in the
following paragraphs.
1. Understanding the Recharge Process
The high frequency DWLR water table data can assist a groundwater practitioner in
understanding the recharge process. Such an understanding can lead to quantification of
recharge parameters, which may be useful in conducting the resource estimation.
The water infiltrated into the ground surface has to follow a circuitous path through the
unsaturated zone extending from ground to the water table. As the water flows through the
unsaturated zone, a part of it may be held back in soil storage and another part transpired by
the vegetation. The conductivity of dry soil is very low. Thus, at the beginning of a rainy
season (when the soil may be dry), most part of (or all of) the infiltrated water may be held
back in the soil and there may practically be no recharge. However, as the initial rainfall
events build up the soil moisture, the recharge process may be initiated. Thus, the rainfall
has to accumulate to a certain level (RC), before a rainfall event starts producing recharge.
Further, since the water has to flow through the unsaturated zone before it appears as
recharge at the water table, there would be an inevitable lag (Tg) between a rainfall event
and the consequent recharge. As discussed in the following section, recharge parameters
RC and Tg need to be estimated for a proper resource assessment
There are two ways of determining these recharge parameters. First is to simulate the flow
of water through the unsaturated zone extending from the ground surface to the water table.
Unsaturated flow is a complex phenomenon and its simulation requires intensive data of soil,
which may not be available on a regional scale. The other way is to study the impact of the
recharge derived from a rainfall event, on the water table. With the advent of the high
frequency water level data emanating from the DWLRs, it is literally possible to see the
signatures of a rainfall event upon the water table hydrograph and identify the above
mentioned recharge parameters. This is accomplished in the following steps:
• Superpose the hyetographs of all the rainfall events of a rainy season over the
corresponding water table hydrograph.
• Study the water level response following each rainfall event, starting from the beginning
of the rainy season.
• Identify the first rainfall event (say X) which is followed by a conspicuous water table
rise.
• Compute the cumulative rainfall preceding the X rainfall event. This provides the RC
• Study the time lags between the rainfall events (starting from X) and the following water
table rises. Determine an average time lag. This provides Tg.

For an illustration, refer to the figure 1 showing the rainfall events superposed over the high
frequency water table data observed at Yeldurthy from May 27 to Oct 12, 1999. It is clear
that the infiltration from all the rainfall events prior to Aug 1 does not lead to any recharge. It
apparently is used up in building the soil moisture and providing the evapotranspiration.
Thus RC may be estimated by adding up all the rainfall events preceding Aug 1. Similarly,
the time lag between a productive rainfall event and the consequent recharge is clearly
visible in the figure.
Fig 1 Hydrograph of high frequency water table data observed at Yeldurthy, Medak
district Andhra Pradesh with rainfall events superposed
2. Lumped Water Balance
The current practice of recharge assessment typically is based upon water balance study of
the unconfined aquifer. A water balance study involves an application of the continuity
equation to the unconfined aquifer. The continuity equation in this context is a statement to
the effect that the difference between the net recharge volume (I) and net discharge volume
(O) equals the change of groundwater storage ( S). I, O and S must be in respect of the
same aquifer area and the time period.
I - O = S
∆S = Sy.∆h
Where Sy is the Specific yield of the aquifer, and ∆h is the change in the spatially averaged
water table elevation in the chosen period. This equation can be used to estimate anyone of
the recharge or discharge components, or storage parameter.
Typically, this approach is adopted for estimating the Specific yield and the recharge from
monsoon rainfall. This involves first dividing a hydrologic year into the monsoon and non-
monsoon periods. The Specific yield is estimated by carrying out the water balance of the
non-monsoon period. Subsequently, the rainfall recharge is estimated by carrying out the
water balance study of the monsoon season, employing the pre-computed value of the
Specific yield.

3. Role of DWLR data
The above stated strategy of water balance studies can be improved upon by employing the
high frequency water table data emanating from DWLRs. These data shall permit a more
realistic water balance study and hence a more accurate assessment of recharge.
3.1 Periods of water balance
For estimation of a specific component of the water balance, it is necessary to select a
period during which the component is just fully generated. Any period less than that shall
lead to an underestimation of the component. A longer period shall attenuate the
predominance of the component and hence shall lead to a less reliable estimate of the
component. Thus for estimating the rainfall recharge by carrying out water balance study of
a rainy season, it shall be desirable to define a period during which the entire rainfall
recharge just occurs. This period could be different from the period of the monsoon rainfall
because of the inevitable time lag between the occurrence of the rainfall and the consequent
recharge. The period must span between the discrete times of the lowest and the highest
water table and not the start and end of the rainy season. Similarly while estimating the
specific yield by carrying out the water balance of the dry period, the duration of the water
balance should incorporate the maximum possible decline from the viewpoint of activation of
the specific yield. This implies that the duration should span between the discrete times of
the highest and the lowest water table.
Thus, for optimal identification of the specific yield it is necessary to carry out the water
balance study from the highest (peak) to the lowest (trough) water table. Similarly for optimal
estimation of rainfall recharge, it is necessary to carry out the water balance study from the
lowest (trough) to the highest (peak) water table. This calls for an identification of the peaks
and troughs and their times of occurrence.
The frequency of manual monitoring of water table is generally not adequate to estimate the
peaks and troughs accurately. The high frequency data from the DWLRs shall permit
identification of true hydrograph of water level. A true hydrograph can lead to estimation of
the pre-monsoon (troughs) and the post-monsoon water table elevations (peaks), and their
times of occurrences; with a far higher resolution. Thus, the identified peak may be higher
and the trough lower, than the corresponding estimates derived from the manually monitored
hydrographs. This is illustrated in figure 2. The figure shows two years’ six hourly DWLR
data, and manually monitored four-yearly data, from Nuthangal village in Nalgonda district of
Andhra Pradesh. The hydrograph of the manually monitored data underestimates the peak
by about a meter.

Fig 2. Hydrograph showing two years’ six hourly DWLR data, and manually
monitored four-yearly data, from Nuthangal village in Nalgonda district of Andhra
Pradesh
3.2 Selection of water balance years
As already discussed, the rainfall recharge during a rainy season starts occurring only after a
cumulative rainfall RC has occurred from the beginning of the season. Thus, if the total
rainfall in a rainy season is equal to or less than RC, there may not be any rainfall recharge.
As such, the years selected for estimation of recharge should have rainfall well above RC. As
already discussed, this parameter can be estimated from the DWLR-derived water table
hydrographs and the corresponding rainfall hyetographs.
3.3 Identification of effective rainfall events
Identification of unambiguous times of the peak and the trough leads to an explicit
determination of the time period of a water balance study. Thus, all other components of
recharge and discharge in the water balance equation must correspond to this period. In this
context, a special reference is called for in respect of the rainfall. Rainfall does not appear
explicitly in the water balance equation. However, it does appear implicitly as rainfall-
recharge. Thus, only such rainfall should be included in the water balance study, whose
recharge occurs within the identified period. This could mean inclusion of a rainfall event,
which occurred before the period, or exclusion of an event occurring towards the end of the
period. This can be accomplished knowing the lag parameter of recharge Tg. As already
discussed, this parameter can be estimated from the DWLR derived water table hydrographs
and the corresponding rainfall hyetographs Fig 3.

Fig3. Water table hydrograph and the corresponding rainfall hyetograph from
Garedapally village, Nalgonda district, Andhra Pradesh
3.4 Estimation of evapotranspiration loss
Evapotranspiration from the unconfined aquifer forms a component of the net discharge from
the aquifer. This loss could be quite significant during rainy seasons. Its estimation
essentially requires identification of such periods during which the depth to water table falls
below a shallow critical depth – dependent upon the capillary rise/root zone depth.
Identifying such periods on the basis of just pre and post monsoon depths could be quite
subjective and could lead to distorted estimates. Some periods may be missed altogether;
others may be overestimated or underestimated. On the other hand, water table depth
hydrographs derived from the DWLR data shall have much higher resolution and thus, shall
permit a far more accurate identification of such periods.

6. Handout

Training module # 3
Other applications of DWLR
data
Tel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685
with

HP Trng. Module File: “ 3 Other applications of DWLR data.doc” Version 10/10/02 Page 1
Table of contents
Page
1. Module context 2
2. Module profile 3
3. Session plan 4
4. Main text 5
6. Handout 7

1. Module context
performance upon the start of the course. This module is related to module 2 and should be
referred during the discussions.

2. Module profile
Title : Other applications of DWLR data
• Appreciate the utility of high frequency DWLR water level
monitoring
• Enhance the professional practice beyond the primary task of
Ground water Resource Assessment
Key concepts : Conjunctive use planning
• Identification of over-exploited areas
• Scheduling of Pumpages
• Calibration of aquifer response models
• Identification of Cycles
Training tools
required
: OHS
Further reading
and references
:

3. Session plan
1 • Discuss the utility of high resolution water level data in
water logged areas, over-exploited areas, coastal areas.
• Discuss the utility of high resolution data for reliable and
credible model calibration.
30 min OHS
2 • Illustrations 10 min OHS
3 Feedback 15 min
4 Wrap up 5 min

4. Main text
Contents
1. Conjunctive use Planning 1
2. Identification of Over-Exploited areas 2
3. Scheduling of Pumpage 2
4. Calibration of Aquifiers Response Models 3
5. Identifications of Cycles 3

Other applications of DWLR data
The high frequency water level data from DWLRs, apart from permitting a more rational and
credible lumped water balance studies, can be useful in many other ways such as follows:
1. Conjunctive use Planning
Conjunctive use of the canal water and the groundwater in a canal command area is
essentially aimed at avoiding water logging of the land. A land is considered to be water
logged if the water table depth (below ground) is lower than a stipulated critical depth. Thus,
a check for water logged conditions essentially involves a study of the water table depth
hydrograph at a few key points with in the study area. The study leads to identification of
such periods (if any) during which the depth is found to be less than the critical value. The
manually monitored water table hydrographs are generally not of high enough resolution to
identify such periods of water logging. Some water logging periods may be missed
altogether; others may be overestimated or underestimated. On the other hand, water table
depth hydrographs derived from the DWLR data shall have much higher resolution and thus,
shall permit a far more accurate identification of water logging periods. This is illustrated in
figure 1. The figure shows a DWLR-derived water table hydrograph from a canal command
area. The water table rise coinciding with canal opening, and decline after its closure, and
the consequent waterlogged periods are quite visible in the hydrograph. Such an
identification of the waterlogged conditions can lead to much better planning of the
groundwater development in the command area.
Fig 1 shows the Water level hydrograph from canal command area

2. Identification of Over-Exploited areas
Over exploited areas are characterised by falling annual peaks and troughs (refer figure 2).
Thus, to identify such areas, it would be necessary to identify annual peaks and troughs of
successive years. As already mentioned, the hydrograph derived from manually monitored
water levels may miss either peak or trough or both. The high frequency data from the
DWLRs shall permit identification of true hydrograph of water level and hence the peaks and
troughs.
Fig 2 shows the Water level hydrograph from an over exploited area
3. Scheduling of Pumpage
The high frequency data from DWLRs may provide useful prompts regarding opportunity
times for pumpage. A few examples are as follows:
3.1 Coastal Aquifers
In coastal aquifers the times of daily peaks and troughs may to a large extent be governed

by the tidal cycle (refer figure 3). The DWLR data can permit its identification, which may
assist in designing daily pumping schedules.
3.2 Canal Commands
Seepage from canal may recharge the water table and may lead to its rise in the vicinity of
the canal. However, there would be a time lag between the beginning of the discharge in the
canal and the rise (refer figure 4). The rise may sustain for a while even after the closure of
the canal discharge. The DWLR data can assist in identifying such time lags and hence the
opportunity times for the pumpage.
Fig 4 shows recharge to the water table hydrograph showing recharge
contributions after canal openings
4. Calibration of Aquifiers Response Models
Aquifer response modelling is a powerful tool to check the feasibility of a given spatial and
temporal pattern of discharge and/or recharge. Thus, such models are being increasingly put
to use to plan various activities like groundwater development, artificial recharge, conjunctive
use etc. These models are very data intensive and require among others, spatially
distributed aquifer parameters. Such data are almost never available, and thus, have to be
derived by calibration. Calibration implies running the model in the historical period and
arriving at such distributions of the parameters which lead to the closest possible match
between the observed and the computed water level hydrographs/contours. It is evident that
the high frequency data from the DWLRs shall permit far more reliable and credible model
calibrations.
5. Identifications of Cycles
A water level hydrograph represents the resultant effect of a number of phenomenon
many of which may be periodic (that is, self repeating). Each periodic phenomenon
imparts a periodicity to the hydrograph. However, due to their superposition, all these

periodicities may not be visible. Usually the hydrograph derived from manually
monitored data, may comprise only an annual cycle displaying a relatively fast rise
from trough to peak, followed by a short fast recession and finally a prolonged slow
recession till the trough. (However, some exceptional phenomena like extreme
exploitation, artificial recharge, discontinuation of pumpage may modify this trend.)
On the other hand, a hydrograph derived from DWLR data shall comprise apart from
an annual cycle, many cycles of shorter durations like seasonal, barometric, daily,
tidal etc.
5.1 Harmonic Analysis
Harmonic analysis is essentially a numerical algorithm capable of breaking a time
series of a periodic attribute into these hidden periodicities (or say cycles). (The
analysis however, is applicable only to stationary time series i.e., to time series
devoid of any long-term trend.) The analysis reveals periodicities hidden in the time
series. This may ultimately facilitate identification of significant or dominant cycles. A
hydrograph is essentially a time series of water levels and cycles hidden in it may be
identified by Harmonic analysis. The details of Harmonic analysis shall be discussed
subsequently.

Hydrology Project Training Module File: “ 3 Other applications of DWLR data.doc” Version 10/10/02 Page 8
6. Handout

Hydrology Project Training Module File: “ 3 Other applications of DWLR data.doc” Version 10/10/02 Page 8

Training module # 4
How to identify the cycles using
Harmonic Analysis
Tel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685
with

HP Trng. Module File: “ 4 How to identify the cycles using Harmonic Analysis.doc” Version 10/10/02 Page 1
Table of contents
Page
1. Module context 2
2. Module profile 3
3. Session plan 4
4. Main text 5
6. Handout 2

1. Module context
performance upon the start of the course. This module is related to module 2 & 3 and should
be referred during the discussions.

2. Module profile
Title : How to identify the cycles using Harmonic Analysis
• Understand the concept of Harmonic analysis,
Key concepts : Components of a hydrologic time series
• The Harmonics
• Variance or power of a harmonic
• Perodogram
• Identifiable Cycles
• What to do with Cycles
• Analysis of hydrograph recession
• Estimation of tidal efficiency
• Estimation of barometric efficiency
Training tools
required
: OHS
Further reading
and references
:

3. Session plan
1 • Discuss the periodicities in time series.
• Describe the harmonics and periodogram
• Discuss the methodology of harmonic analysis, isolation of
dominant cycles.
• Describe the estimation of T&S by analysing the
hydrograph recession
• Describe the estimation of Tidal Efficiency and barometric
efficiency using the hydrograph
30 min OHS
3 Feedback 10 min

4. Main text
Contents
1. Components of a Hydrologic Time Series 1
2. The Harmonics 1
2.1 Identifiable Harmonics 2
3. Periodogram 2
4. An Illustration 2
5 What to do with cycles 5

How to identify the cycles using Harmonic Analysis
1. Components of a Hydrologic Time Series
A hydrologic time series (say of groundwater level) represents the resultant effect of a
number of phenomenon many of which may be periodic (that is, self repeating). Each
periodic phenomenon imparts a periodicity to the time series. However, due to their
superposition, all these periodicities may not be visible in the time series. Harmonic analysis
is essentially aimed at breaking up the time series into these hidden periodicities (or say
cycles). This reveals the hidden periodicities. This may ultimately facilitate identification of
significant or dominant cycles.
Each periodicity is represented by an independent time series of the form of a sinusoid wave
(also known as a harmonic) and having its own parameters. The parameters include
wavelength (time period), amplitude and starting point. Thus, first step of the analysis
involves computation of the parameters. The parameters are so computed that superposition
(summation) of the sinusoids leads to the original time series. Further sum of variances of
individual sinusoids equals the variance of the original time series. The computed
parameters permit an identification of the predominant cycles.
2. The Harmonics
Consider a time series comprising n attribute data (Yi, i varying from 0 to n-1) at a uniform
time interval (say ∆t). Thus, the total span of the time series is ∆t.(n-1). Spectral analysis
describes the departure of the attribute (Y) from its arithmetic mean [say, (a0/2)], as a sum of
(n-1)/2 harmonics [Hj, j varying from 1 to (n-1)/2]. Thus. Y at any time t since the beginning
of the series is given by the following equation:
∑
−
=
+=
2/)1(
12
1
)(
n
j
jo HatY
where:
∑
−
=
=
1
0
2 n
i
io Y
n
a
)()( θθ jSinbjCosaH jjj +=
where:
tn
t
∆
=
π
θ
2
∑
−
=






=
1
0
22 n
i
ij
n
ij
CosY
n
a
π
∑
−
=





π
=
1n
0i
ij
n
ij2
SinY
n
2
b

The jth
harmonic represents a phenomenon of a time period equal to (n-1). ∆t/j. Since j varies
from 1 to (n – 1)/2, the time period of the identifiable harmonics varies from (n-1) ∆t to 2∆t.
2.1 Identifiable Harmonics
Thus, the smallest identifiable cycle is of time period 2∆t, and time period of the longest
identifiable cycle is the time domain (that is, length) of the time series. However, in practice
only the cycles of time period lying in the range 4∆t to one fourth (or even one sixth) of the
time domain may be identified reliably.
For example, for correctly identifying an annual cycle the length of the time series must be at
least four years. Further, if a daily cycle is to be identified, the interval must be 6 hours or
less.
2.2 Variance or power of a harmonic
The variance (or power) of the jth
harmonic is given by the following expression:
22
jjj baA +=
As pointed out earlier, the variance of the time series equals sum of the variances of the
individual harmonics. Variance is a measure of the scatter of a time series around the mean.
Thus, it can be inferred that variance of a harmonic is a proportional to its relative dominance
in the original time series and therefore, may be viewed as a measure of the relative
significance of the associated phenomenon.
3. Periodogram
A plot of the variance versus the harmonic number (j) is known as periodogram of the time
series. Since this plot comprises discrete number of variance values, it is also known as
discrete power spectrum.
By a visual inspection of the periodogram, one can identify the dominant harmonic numbers,
i.e., serial numbers of the harmonics displaying conspicuously high variance. Knowing the
harmonic numbers, the corresponding time periods can be computed.
4. An Illustration
As an illustration, harmonic analysis is performed on six days’ 144 hourly data of water level
monitored at OUAT campus, Bhubaneswar, from Oct 22 to 28, 1999 (refer figure 1).
Subsequent data were not included in the analysis, since they are rendered non-stationary
by the infamous cyclone. (That is, perform the analysis only such part of the time series
which does not display a long term trend.) The outcome of the analyses revealed that the
time series comprises three dominant cycles of time periods 8, 12 and 24 hours (refer figure
2). The identified cycles are shown in figures 3. The possible composite daily cycle obtained
by superposing these three cycles is shown in figure 4.

Fig 1. DWLR Data monitored at OUAT campus, Bhubaneswar, Orissa
Fig;2 Periodogram showing the result of the harmonic analysis

Fig.3. Amplitude of fluctuations in different cycles
Fig.4 Cumulative fluctuation for 6hr, 8hr, 12hr and 24 hr cycle

5. What to do with cycles?
Harmonic analysis is essentially a mathematical tool facilitating isolation of dominant cycles
from a stationary time series. Such isolated cycles shall be free from the noise and thus,
could be viewed as intrinsic cycles. Being a mathematical tool, harmonic analysis does not
lead to the physics of the identified cycles. The physics has in fact to be identified by the
practitioner of the analysis. This essentially implies identification of phenomenon (such as,
daily pumping/recovery, tidal effects, seasonal rainfall/pumpage/irrigation recharge)
responsible for the identified cycles. The groundwater practitioners can infer the relative
influence of the cycles on the groundwater system and can prioritise the field-work for their
identification accordingly. This can be professionally very gratifying and could result in
improvement of existing practices or evolution of new practices. A few suggestions are as
follows:
5.1 Analysis of hydrograph recession
The recession of a hydrograph comprises its declining phase, that is, from peak to the
trough. The recession may result from processes like natural drainage to the hydraulically
connected streams, pumpage and evapotranspiration.
A recession predominantly resulting from the natural drainage is related to the aquifer
geometry and the diffusivity (T/S). Thus, an analysis of such a recession can provide a
preliminary estimate of the diffusivity, which in turn may lead to estimation of transmissivity
or the storage coefficient, knowing the other. The steps of the computation are as follows:
• Isolate the intrinsic annual cycle from the time series. Derive the corresponding annual
cycle of the driving head by shifting the datum to stage of the draining stream during the
period of the recession.
• Plot the recession curve (log of the driving head versus the time). The curve may reveal
two or more straight lines segments. The first one, usually steep and short, may
represent a fast recession. This is usually followed by a relatively flat and long segment,
representing a moderate/slow recession.
• Assuming a linear relation between log of the driving head and the time, carry out a
regression analysis of the dominant segment of the recession. Hence compute the
depletion time. The time for one log cycle (to the base ten) change in the driving head,
divided by 2.3, is termed as the depletion time.
• The depletion time in general can be expressed as (k.L2
.T/S); where L is the distance of
the sampled well from the draining stream along the flowline and k is a constant
depending upon the boundary conditions. It could vary from 0.405 (drainage on both
sides of the well) to 1.0 (drainage only on one side).
The analysis described above holds for the recession of the outflow hydrograph also. The
outflow may manifest as stream flow during dry season (when the entire stream flow may be
derived from groundwater drainage) or as spring flow. The flow time series if available, may
also be analysed in a similar way. This may provide a means of corroborating the estimate of
diffusivity arrived at by analysing the driving head time series.
5.2 Estimation of tidal efficiency
Tidal efficiency (TE) is defined as the ratio of the piezometric head fluctuation resulting
exclusively from tides, to the causative fluctuation of the tide level. It’s estimate can provide
a tentative value of specific storage (Ss) in accordance with the following equation:

)1/( TESs −= γθβ
Where γ is the specific weight of water, θ is the porosity of aquifer and β is the inverse of the
bulk modulus elasticity of water.
Tidal efficiency may be estimated by separating tidal cycles from the water level hydrograph
of a piezometer tapping a confined aquifer in coastal region. Knowing the tidal variations in
the sea in the vicinity, the tidal efficiency can be computed.
5.3 Estimation of barometric efficiency
Barometric efficiency (BE) is defined as the ratio of the piezometric head fluctuation resulting
exclusively from the atmospheric pressure fluctuations, to the causative fluctuation of the
atmospheric pressure expressed as head of water. It’s estimate can also provide a tentative
value of specific storage (Ss) in accordance with the following equation:
BESs /γθβ=
Barometric efficiency may be estimated by first identifying the time period of a barometric
cycle from the atmospheric pressure data and subsequently separating a cycle of the
identified period from the water level hydrograph of a piezometer tapping a confined aquifer
in that area.
5.4 Software
The technical consultants to the Hydrology Project have conceptualised an approach for
Harmonic analysis. The approach has been assimilated in a software, christened as DWLR-
ANALYST.

6. Handout

Training module # 5
Understanding the Concept of Optimal
Monitoring frequency of DWLR
Tel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685
with

HP Trng. Module File: “ 5 Concept of Optimal Monitoring frequency of DWLR.doc” Version 10/10/02 Page 1
Table of contents
Page
1. Module context 2
2. Module profile 3
3. Session plan 4
4. Main text 5
6. Handout 7

1. Module context
performance upon the start of the course. This module is related to module 2, 3 & 4 and
should be referred during the discussions.

2. Module profile
Title : Understanding the Concept of Optimal Monitoring frequency
of DWLR
• Arrive at optimal monitoring frequency for any given intended
use of the DWLR data.
Key concepts : • Credibility of derived attribute(s)
• Preserving the hydrograph shape
• Identification of Cycles
• Correlation
Training tools
required
: OHS
Further reading
and references
:

3. Session plan
1 • Describe the strategies to be adopted for arriving at optimal
monitoring frequency, ensuring the credibility of the
attributes, preserving the shape of hydrograph.
30 min
3 Feedback 10 min

4. Main text
Contents
1. Objective based Optimal Frequency 1
2. Optimizing Criteria 1
3. Optimizing Strategy 2
4. Correlation 3
5 Software 4

Understanding the Concept of Optimal Monitoring frequency of DWLR
1. Objective based Optimal Frequency
The high frequency data emanating from the DWLRs shall assist the hydrogeologists in
performing their professional activities more objectively and hence more credibly. The
requirement of the frequency can apparently not be uniquely defined and shall depend upon
the intended use of the high frequency data as well as upon the local hydrogeological and
hydrological characteristics. For example, an aquifer having low specific yield may display
faster water level variations and hence may need a higher frequency of monitoring. Similarly,
if the objective is to estimate only the peaks and troughs, a higher frequency may be
adopted around the beginning and the end of the rainy seasons and a lower frequency may
be adopted at other times. On the other hand if the objective is to arrive at a true
hydrograph, a uniformly high frequency may have to be adopted. A few strategies for arriving
at the optimal monitoring frequency are described in the following paragraphs:
2. Optimizing Criteria
It follows from the preceding paragraph that there does not exist any unique optimal
monitoring frequency. The optimal monitoring frequency would depend upon the expectation
from (or intended use/uses of) the hydrograph to be monitored. Some criteria could be as
follows:
2.1 Credibility of Derived Attribute(s)
There may normally be a few well-defined objectives of monitoring the water
table/piezometric head. The objectives may relate to deriving one or more of the
following attributes from the observed hydrograph.
• Peak of the hydrograph
• Trough of the hydrograph
• Range of water level fluctuation
• Time of shallow water level, i.e., time during which the water level rises above a
stipulated shallow critical level
• Time of deep water level, i.e., time during which the water level falls below a stipulated
deep critical level
Thus, the criteria would be to arrive at such monitoring frequency that the desired attribute(s)
as derived from the observed hydrograph is (are) close enough to the true values (i.e., the
values derived from the true hydrograph).
2.2 Preserving the Hydrograph Shape
This implies that the selected monitoring interval should be such that the monitored
hydrograph resembles closely with the true hydrograph. This is indeed the most stringent
and all-encompassing expectation requiring uniformly small monitoring intervals. The
intervals would depend upon the degree of the desired resemblance. As discussed
subsequently, correlation is an index of similarity between the shapes of two time series. It
shall be an index of resemblance if the two time series display the variation of the same
variable. Thus, the criteria could be to arrive at such an interval which ensures a high

enough correlation between the true and the monitored hydrographs.
2.3 Identification of Cycles
As already stated, the cycle of smallest time period that can be identified (or separated) by
the Spectral analysis is 4∆t, where ∆t is the interval between two successive water level
data. Thus, the monitoring interval has to be at lone fourth of the time period of the smallest
cycle intended to be identified.
3. Optimizing Strategy
It follows from the above discussion that for optimising the monitoring frequency, we shall
require the true hydrograph. The hydrograph of smallest feasible interval (say hourly) could
be deemed as the true hydrograph. Therefore, it is necessary to first procure a time series of
water level with small enough monitoring interval. Subsequently under-sampled hydrographs
of increasing monitoring intervals, are simulated as follows:
• Knock off the intermittent data from the true hydrograph to simulate the under-sampled
series of the chosen larger interval.
• Simulate the under-sampled hydrograph by estimating the knocked off data by linear
interpolation.
The simulated under-sampled hydrographs may be analysed to arrive at the optimal
monitoring frequency as follows:
3.1 Credible Attribute Estimation
Compute the desired attribute from the true hydrograph and from each of the simulated
under-sampled hydrographs. Terming the attribute value as computed from the true
hydrograph as X and the values computed from ith
simulated under-sampled hydrograph as
Ai, compute the loss array [Li = ABS(X - Ai)/S]. Here, S is a relevant quantity for normalizing
the error. Thus the array represents the loss of information (expressed as a fraction of the
chosen S) on account of increasing the time interval from the minimum feasible to the one
incorporated in ith
simulated under-sampled hydrograph. This array could be interpreted for
specific attributes as follows:
Peak, Trough and Range: (Over-estimation of depth to peak, under-estimation of depth to
trough, and consequent under-estimation of the range) Selecting S as the true range (that
is, vertical distance from trough to peak in the true hydrograph), the array shall represent the
loss of information expressed as a fraction of the true range.
Time of shallow/deep water level: Selecting S as true period, the array shall represent the
loss expressed as a fraction of the true time.
Plot the computed array [Li ] versus the corresponding intervals of the simulated under-
sampled hydrographs. Assigning an acceptable level of the loss, pick up the optimal interval
of monitoring.
3.2 Preservation of Hydrograph Shape
The simulated under-sampled hydrographs of increasing time interval may be successively
compared visually with the true hydrograph. This may lead to a threshold interval beyond
which the two series may cease to resemble each other. Alternatively, this could be done
more objectively in the following steps:
• Compute the correlation (described in the following section) between the true
hydrograph and each of the simulated under-sampled hydrographs.

• Plot the computed correlations against the time interval.
• Pick up the optimal interval corresponding to the minimum desired similarity between the
two hydrographs.
•
3.3 Identification of Cycles
The longest permissible interval for identifying a cycle of any time period, by Harmonic
analysis is half the time period. For a more reliable identification of the cycle, it may be
desirable to further restrict the longest permissible interval say to one fourth of the time
period. Thus, for identifying a daily cycle, it may be desirable to have an interval no bigger
than 6 hours.
4. Correlation
This statistic determines the degree of linear interrelation (that is, scaled similarity) between
two time series.
A direct linear relation (that is, as one series rises, the other also rises and vice versa) is
termed as positive correlation. An inverse linear relation (that is, as one series rises, the
other declines and vice versa) is termed as negative correlation. If the rise of one series has
apparently no effect on the other, the two series are known to be uncorrelated.
The two series must have the same data frequency and an adequately long overlap. A
correlation between two series falling in different time spans can be computed by analysing
the overlapping period only, that is, by curtailing one or both the series. If there is no
overlapping period, the correlation can not be estimated. If the two series comprise data at
different frequencies, it is necessary to manipulate one of the two series to ensure
frequency-compatibility. Thus, either the series of higher frequency (say series of DWLR
data) may be pruned, or the missing data in the series of low frequency (say series of
manual data) may be interpolated.
This correlation is essentially a normalised covariance between the pivotal and the derived
series. Thus, the correlation ® between two series (xi, i = 1, 2, ……., n) and (yi, i = 1, 2,
………, n) shall be given by the following equation:
COR =
yx
ii
n
i
SS
yyxx
.
)).((
1
−−∑=
;1
n
x
x
i
n
i
∑=
=
n
y
y
i
n
i
∑=
= 1
Sx = 2
1
)( xxi
n
i
−∑=
; Sx = 2
1
)( yyi
n
i
−∑=
;

Two positively correlated time series shall have a correlation greater than zero and it may go
up to +1. A correlation of +1 indicates a perfect positive correlation, that is, a direct
proportionality of the fluctuations in the two series and hence a perfect linearity with positive
gradient between the two variables. Similarly, two negatively correlated time series shall
have a correlation less than zero and it may go up to –1. A correlation of –1 indicates a
perfect negative correlation, that is, an inverse proportionality and hence a perfect linearity
with negative slope. Two uncorrelated series shall have a zero correlation.
5 Software
The above stated approach for optimising the monitoring frequency was conceptualised by
technical consultants to the Hydrology Project. The approach has been assimilated in a
software, christened as DWLR-ANALYST.

6. Handout

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