download-manuals-ground water-training-dwlrg-wdatahandling

World Bank & Government of The Netherlands funded

Training module # 1

Understanding Conventionaland DWLR Assisted Water

Level Monitoring

New Delhi, March 2000

CSMRS Building, 4th Floor, Olof Palme Marg, Hauz Khas,New Delhi – 11 00 16 IndiaTel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685E-Mail: [email protected]

DHV Consultants BV & DELFT HYDRAULICS

withHALCROW, 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 alogical sequence. The actual selection of the topics and the depth of training would, ofcourse, depend on the training needs of the participants, i.e. their knowledge level and skillsperformance upon the start of the course. This is an independent module.


2. Module profile

Title : Understanding Conventional and DWLR Assisted WaterLevel 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 toolsrequired

: OHS

Handouts : As provided in this module

Further readingand references

:


3. Session plan

No Activities Time Tools1 • Discuss the prevailing water level monitoring,

• Show the nature of the hydrograph emerging fromconventional 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 MonitoringConventionally the groundwater monitoring in India has been conducted on the followinglines:

• Water levels are usually monitored in privately owned open dug wells tapping the upperunconfined aquifers. These levels reveal the piezometric head/water table elevation ofthe semi-confined/unconfined aquifers. However, the necessary well-aquifer hydraulicconnection is not always beyond suspicion.

• The frequency of monitoring has generally been restricted to four times in a year. Thesetimes are rather arbitrarily selected during pre-monsoon, monsoon, post-monsoon andwinter seasons. It is presumed that these water levels represent the troughs and peaksof the water table hydrograph. However, many a time these data may be too sparse toyield reliable and credible water table hydrograph, as illustrated in figure 1. The figureshows the true hydrograph (derived from high frequency DWLR data) superposed overthe corresponding hydrograph based upon four annual observations.

Fig 1: True Hydrograph from phreatic aquifer (Granitic rock), in KattangurVillage, Nalgonda District Andhra Pradesh


• Limited monitoring of the piezometric head of the deeper confined/leaky confinedaquifers has been carried out by some agencies, usually by observing the water level inthe deep production tube wells. The tube wells, many a time may not be adequatelyisolated from (or worse, may even be tapping) the unconfined aquifer. Dedicatedpiezometers tapping only the deeper aquifers and duly isolated from the unconfinedaquifer are almost non-existent.

The historical monitoring programmes though quite extensive and commendable in manyways, have been deficit in several respects. The practising hydrogeologists have beenconducting the resource evaluations quite credibly in spite of these deficits. They have beencircumventing the problem by certain subjective practices based upon norms/pastexperience or intuitive reasoning. Nevertheless, this has restricted their practice in manyways. For example, no norms have been developed for estimating resource of the deeperaquifers. (This estimation is no doubt difficult due to uncertainties regarding the rechargezone, but lack of the piezometric head data has pre-empted its solution.) Similarly, since thepractitioners have never been able to view a true water table hydrograph, rechargeestimation 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 atnecessary frequency are usually not available.

2. High Frequency Monitoring

The Hydrology Project has enabled construction of a large number of scientifically designedpiezometers tapping unconfined and the deeper aquifers. These piezometers have thenecessary hydraulic connection with the targeted aquifers and are suitably isolated fromoverlying/underlying aquifers. Further, digital automatic water level recorders (DWLRs) areinstalled in these piezometers. This ensures measurement of undistorted piezometric headat the desired frequency, which may be much larger than the present frequency. In fact, thefrequency may be so high that the resulting piezometric hydrograph may almost becontinuous.

3. True Hydrograph – What to do with it?

With the high frequency and credible piezometric head data emanating from theDWLRs, the groundwater practitioners in India shall have an access to truepiezometric head hydrographs, possibly for the first time. This is bound to inspire thepractitioners to enhance the scientific/technical content of their prevailing practiceand also to incorporate in it many new analyses. Some of the possibilities shall bediscussed subsequently.


5. Overhead/flipchart master


6. Handout


7. Additional handoutThese handouts are distributed during delivery and contain test questions, answers toquestions, special worksheets, optional information, and other matters you would not like tobe seen in the regular handouts.

It is a good practice to pre-punch these additional handouts, so the participants can easilyinsert them in the main handout folder.


Training module # 2

Role of DWLR data inGroundwater Resource

Estimation





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 contextWhile 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 alogical sequence. The actual selection of the topics and the depth of training would, ofcourse, depend on the training needs of the participants, i.e. their knowledge level and skillsperformance upon the start of the course.


2. Module profile

Title : Role of DWLR data in Groundwater Resource Estimation



Objectives : After the training the participants will be able to:• 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



: OHS



:


3. Session plan

No Activities Time Tools1 • 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 thegroundwater resource (mainly monsoon recharge) by a lumped water balance of theunconfined aquifer, in accordance with GEC-84/97 norms. The high frequency water tabledata from the DWLRs can assist a practitioner in conducting such estimations morerationally and credibly. A few possible applications of such data are described in thefollowing paragraphs.

1. Understanding the Recharge ProcessThe high frequency DWLR water table data can assist a groundwater practitioner inunderstanding the recharge process. Such an understanding can lead to quantification ofrecharge parameters, which may be useful in conducting the resource estimation.

The water infiltrated into the ground surface has to follow a circuitous path through theunsaturated zone extending from ground to the water table. As the water flows through theunsaturated zone, a part of it may be held back in soil storage and another part transpired bythe vegetation. The conductivity of dry soil is very low. Thus, at the beginning of a rainyseason (when the soil may be dry), most part of (or all of) the infiltrated water may be heldback in the soil and there may practically be no recharge. However, as the initial rainfallevents build up the soil moisture, the recharge process may be initiated. Thus, the rainfallhas 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 asrecharge at the water table, there would be an inevitable lag (Tg) between a rainfall eventand the consequent recharge. As discussed in the following section, recharge parametersRC and Tg need to be estimated for a proper resource assessmentThere are two ways of determining these recharge parameters. First is to simulate the flowof 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 therecharge derived from a rainfall event, on the water table. With the advent of the highfrequency water level data emanating from the DWLRs, it is literally possible to see thesignatures of a rainfall event upon the water table hydrograph and identify the abovementioned recharge parameters. This is accomplished in the following steps:

• Superpose the hyetographs of all the rainfall events of a rainy season over thecorresponding water table hydrograph.

• Study the water level response following each rainfall event, starting from the beginningof the rainy season.

• Identify the first rainfall event (say X) which is followed by a conspicuous water tablerise.

• 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 watertable rises. Determine an average time lag. This provides Tg.


For an illustration, refer to the figure 1 showing the rainfall events superposed over the highfrequency water table data observed at Yeldurthy from May 27 to Oct 12, 1999. It is clearthat the infiltration from all the rainfall events prior to Aug 1 does not lead to any recharge. Itapparently 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 clearlyvisible in the figure.

Fig 1 Hydrograph of high frequency water table data observed at Yeldurthy, Medakdistrict Andhra Pradesh with rainfall events superposed

2. Lumped Water BalanceThe current practice of recharge assessment typically is based upon water balance study ofthe unconfined aquifer. A water balance study involves an application of the continuityequation to the unconfined aquifer. The continuity equation in this context is a statement tothe 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 thesame 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 averagedwater table elevation in the chosen period. This equation can be used to estimate anyone ofthe recharge or discharge components, or storage parameter.

Typically, this approach is adopted for estimating the Specific yield and the recharge frommonsoon 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 thenon-monsoon period. Subsequently, the rainfall recharge is estimated by carrying out thewater balance study of the monsoon season, employing the pre-computed value of theSpecific yield.


3. Role of DWLR dataThe above stated strategy of water balance studies can be improved upon by employing thehigh frequency water table data emanating from DWLRs. These data shall permit a morerealistic 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 aperiod during which the component is just fully generated. Any period less than that shalllead to an underestimation of the component. A longer period shall attenuate thepredominance of the component and hence shall lead to a less reliable estimate of thecomponent. Thus for estimating the rainfall recharge by carrying out water balance study ofa rainy season, it shall be desirable to define a period during which the entire rainfallrecharge just occurs. This period could be different from the period of the monsoon rainfallbecause of the inevitable time lag between the occurrence of the rainfall and the consequentrecharge. The period must span between the discrete times of the lowest and the highestwater table and not the start and end of the rainy season. Similarly while estimating thespecific yield by carrying out the water balance of the dry period, the duration of the waterbalance should incorporate the maximum possible decline from the viewpoint of activation ofthe specific yield. This implies that the duration should span between the discrete times ofthe highest and the lowest water table.

Thus, for optimal identification of the specific yield it is necessary to carry out the waterbalance study from the highest (peak) to the lowest (trough) water table. Similarly for optimalestimation of rainfall recharge, it is necessary to carry out the water balance study from thelowest (trough) to the highest (peak) water table. This calls for an identification of the peaksand troughs and their times of occurrence.

The frequency of manual monitoring of water table is generally not adequate to estimate thepeaks and troughs accurately. The high frequency data from the DWLRs shall permitidentification of true hydrograph of water level. A true hydrograph can lead to estimation ofthe pre-monsoon (troughs) and the post-monsoon water table elevations (peaks), and theirtimes of occurrences; with a far higher resolution. Thus, the identified peak may be higherand the trough lower, than the corresponding estimates derived from the manually monitoredhydrographs. This is illustrated in figure 2. The figure shows two years’ six hourly DWLRdata, and manually monitored four-yearly data, from Nuthangal village in Nalgonda district ofAndhra Pradesh. The hydrograph of the manually monitored data underestimates the peakby about a meter.


Fig 2. Hydrograph showing two years’ six hourly DWLR data, and manuallymonitored 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 acumulative rainfall RC has occurred from the beginning of the season. Thus, if the totalrainfall 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. Asalready discussed, this parameter can be estimated from the DWLR-derived water tablehydrographs 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 explicitdetermination of the time period of a water balance study. Thus, all other components ofrecharge and discharge in the water balance equation must correspond to this period. In thiscontext, a special reference is called for in respect of the rainfall. Rainfall does not appearexplicitly 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, whoserecharge 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 theperiod. This can be accomplished knowing the lag parameter of recharge Tg. As alreadydiscussed, this parameter can be estimated from the DWLR derived water table hydrographsand the corresponding rainfall hyetographs Fig 3.


Fig3. Water table hydrograph and the corresponding rainfall hyetograph fromGaredapally village, Nalgonda district, Andhra Pradesh

3.4 Estimation of evapotranspiration loss

Evapotranspiration from the unconfined aquifer forms a component of the net discharge fromthe aquifer. This loss could be quite significant during rainy seasons. Its estimationessentially requires identification of such periods during which the depth to water table fallsbelow 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 quitesubjective and could lead to distorted estimates. Some periods may be missed altogether;others may be overestimated or underestimated. On the other hand, water table depthhydrographs derived from the DWLR data shall have much higher resolution and thus, shallpermit a far more accurate identification of such periods.


6. Handout


Training module # 3

Other applications of DWLRdata





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

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 alogical sequence. The actual selection of the topics and the depth of training would, ofcourse, depend on the training needs of the participants, i.e. their knowledge level and skillsperformance upon the start of the course. This module is related to module 2 and should bereferred during the discussions.


2. Module profile

Title : Other applications of DWLR data



Objectives : After the training the participants will be able to:• 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



: OHS



:


3. Session plan

No Activities Time Tools1 • 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 min4 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 andcredible lumped water balance studies, can be useful in many other ways such as follows:

1. Conjunctive use PlanningConjunctive use of the canal water and the groundwater in a canal command area isessentially aimed at avoiding water logging of the land. A land is considered to be waterlogged 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 depthhydrograph at a few key points with in the study area. The study leads to identification ofsuch periods (if any) during which the depth is found to be less than the critical value. Themanually monitored water table hydrographs are generally not of high enough resolution toidentify such periods of water logging. Some water logging periods may be missedaltogether; others may be overestimated or underestimated. On the other hand, water tabledepth 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 infigure 1. The figure shows a DWLR-derived water table hydrograph from a canal commandarea. The water table rise coinciding with canal opening, and decline after its closure, andthe consequent waterlogged periods are quite visible in the hydrograph. Such anidentification of the waterlogged conditions can lead to much better planning of thegroundwater development in the command area.

Fig 1 shows the Water level hydrograph from canal command area


2. Identification of Over-Exploited areasOver 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 ofsuccessive years. As already mentioned, the hydrograph derived from manually monitoredwater levels may miss either peak or trough or both. The high frequency data from theDWLRs shall permit identification of true hydrograph of water level and hence the peaks andtroughs.

Fig 2 shows the Water level hydrograph from an over exploited area

3. Scheduling of PumpageThe high frequency data from DWLRs may provide useful prompts regarding opportunitytimes 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 mayassist 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 ofthe canal. However, there would be a time lag between the beginning of the discharge in thecanal and the rise (refer figure 4). The rise may sustain for a while even after the closure ofthe canal discharge. The DWLR data can assist in identifying such time lags and hence theopportunity times for the pumpage.

Fig 4 shows recharge to the water table hydrograph showing rechargecontributions after canal openings

4. Calibration of Aquifiers Response ModelsAquifer response modelling is a powerful tool to check the feasibility of a given spatial andtemporal pattern of discharge and/or recharge. Thus, such models are being increasingly putto use to plan various activities like groundwater development, artificial recharge, conjunctiveuse etc. These models are very data intensive and require among others, spatiallydistributed aquifer parameters. Such data are almost never available, and thus, have to bederived by calibration. Calibration implies running the model in the historical period andarriving at such distributions of the parameters which lead to the closest possible matchbetween the observed and the computed water level hydrographs/contours. It is evident thatthe high frequency data from the DWLRs shall permit far more reliable and credible modelcalibrations.

5. Identifications of Cycles

A water level hydrograph represents the resultant effect of a number of phenomenonmany of which may be periodic (that is, self repeating). Each periodic phenomenonimparts a periodicity to the hydrograph. However, due to their superposition, all these


periodicities may not be visible. Usually the hydrograph derived from manuallymonitored data, may comprise only an annual cycle displaying a relatively fast risefrom trough to peak, followed by a short fast recession and finally a prolonged slowrecession till the trough. (However, some exceptional phenomena like extremeexploitation, artificial recharge, discontinuation of pumpage may modify this trend.)On the other hand, a hydrograph derived from DWLR data shall comprise apart froman 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 timeseries of a periodic attribute into these hidden periodicities (or say cycles). (Theanalysis however, is applicable only to stationary time series i.e., to time seriesdevoid of any long-term trend.) The analysis reveals periodicities hidden in the timeseries. This may ultimately facilitate identification of significant or dominant cycles. Ahydrograph is essentially a time series of water levels and cycles hidden in it may beidentified by Harmonic analysis. The details of Harmonic analysis shall be discussedsubsequently.

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 usingHarmonic Analysis


CSMRS Building, 4th Floor, Olof Palme Marg, Hauz Khas,New Delhi – 11 00 16 IndiaTel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685

E-Mail: [email protected]



mailto:[email protected]

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

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 alogical sequence. The actual selection of the topics and the depth of training would, ofcourse, depend on the training needs of the participants, i.e. their knowledge level and skillsperformance upon the start of the course. This module is related to module 2 & 3 and shouldbe referred during the discussions.


2. Module profile

Title : How to identify the cycles using Harmonic Analysis



Objectives : After the training the participants will be able to:• 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



: OHS



:


3. Session plan

No Activities Time Tools1 • 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 anumber of phenomenon many of which may be periodic (that is, self repeating). Eachperiodic phenomenon imparts a periodicity to the time series. However, due to theirsuperposition, all these periodicities may not be visible in the time series. Harmonic analysisis essentially aimed at breaking up the time series into these hidden periodicities (or saycycles). This reveals the hidden periodicities. This may ultimately facilitate identification ofsignificant 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 includewavelength (time period), amplitude and starting point. Thus, first step of the analysisinvolves 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 ofindividual sinusoids equals the variance of the original time series. The computedparameters 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 uniformtime interval (say ∆t). Thus, the total span of the time series is ∆t.(n-1). Spectral analysisdescribes 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 beginningof the series is given by the following equation:

∑−

=

+=2/)1(

12

1)(

n

jjo HatY

where:

∑−

=

=1

0

2 n

iio Y

na

)()( θθ jSinbjCosaH jjj +=

where:

tn

t

∆=

πθ 2

∑−

=

=

1

0

22 n

iij n

ijCosY

na

π

∑−

=

π=

1n

0iij n

ij2SinY

n

2b


The jth harmonic represents a phenomenon of a time period equal to (n-1). ∆t/j. Since j variesfrom 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 longestidentifiable cycle is the time domain (that is, length) of the time series. However, in practiceonly the cycles of time period lying in the range 4∆t to one fourth (or even one sixth) of thetime domain may be identified reliably.

For example, for correctly identifying an annual cycle the length of the time series must be atleast four years. Further, if a daily cycle is to be identified, the interval must be 6 hours orless.

2.2 Variance or power of a harmonic

The variance (or power) of the jth harmonic is given by the following expression:

22jjj baA +=

As pointed out earlier, the variance of the time series equals sum of the variances of theindividual 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 dominancein the original time series and therefore, may be viewed as a measure of the relativesignificance of the associated phenomenon.

3. PeriodogramA plot of the variance versus the harmonic number (j) is known as periodogram of the timeseries. Since this plot comprises discrete number of variance values, it is also known asdiscrete 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 theharmonic numbers, the corresponding time periods can be computed.

4. An IllustrationAs an illustration, harmonic analysis is performed on six days’ 144 hourly data of water levelmonitored 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-stationaryby the infamous cyclone. (That is, perform the analysis only such part of the time serieswhich does not display a long term trend.) The outcome of the analyses revealed that thetime series comprises three dominant cycles of time periods 8, 12 and 24 hours (refer figure2). The identified cycles are shown in figures 3. The possible composite daily cycle obtainedby 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 cyclesfrom 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 notlead to the physics of the identified cycles. The physics has in fact to be identified by thepractitioner 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 relativeinfluence of the cycles on the groundwater system and can prioritise the field-work for theiridentification accordingly. This can be professionally very gratifying and could result inimprovement of existing practices or evolution of new practices. A few suggestions are asfollows:

5.1 Analysis of hydrograph recession

The recession of a hydrograph comprises its declining phase, that is, from peak to thetrough. The recession may result from processes like natural drainage to the hydraulicallyconnected streams, pumpage and evapotranspiration.

A recession predominantly resulting from the natural drainage is related to the aquifergeometry and the diffusivity (T/S). Thus, an analysis of such a recession can provide apreliminary estimate of the diffusivity, which in turn may lead to estimation of transmissivityor 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 annualcycle of the driving head by shifting the datum to stage of the draining stream during theperiod of the recession.

• Plot the recession curve (log of the driving head versus the time). The curve may revealtwo or more straight lines segments. The first one, usually steep and short, mayrepresent 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 aregression analysis of the dominant segment of the recession. Hence compute thedepletion 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 ofthe sampled well from the draining stream along the flowline and k is a constantdepending upon the boundary conditions. It could vary from 0.405 (drainage on bothsides of the well) to 1.0 (drainage only on one side).

The analysis described above holds for the recession of the outflow hydrograph also. Theoutflow may manifest as stream flow during dry season (when the entire stream flow may bederived from groundwater drainage) or as spring flow. The flow time series if available, mayalso be analysed in a similar way. This may provide a means of corroborating the estimate ofdiffusivity 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 resultingexclusively from tides, to the causative fluctuation of the tide level. It’s estimate can providea 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 thebulk modulus elasticity of water.

Tidal efficiency may be estimated by separating tidal cycles from the water level hydrographof a piezometer tapping a confined aquifer in coastal region. Knowing the tidal variations inthe 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 resultingexclusively from the atmospheric pressure fluctuations, to the causative fluctuation of theatmospheric pressure expressed as head of water. It’s estimate can also provide a tentativevalue 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 barometriccycle from the atmospheric pressure data and subsequently separating a cycle of theidentified period from the water level hydrograph of a piezometer tapping a confined aquiferin that area.

5.4 Software

The technical consultants to the Hydrology Project have conceptualised an approach forHarmonic analysis. The approach has been assimilated in a software, christened as DWLR-ANALYST.


6. Handout


Training module # 5

Understanding the Concept of OptimalMonitoring frequency of DWLR


CSMRS Building, 4th Floor, Olof Palme Marg, Hauz Khas,New Delhi – 11 00 16 IndiaTel: 68 61 681 / 84 Fax: (+ 91 11) 68 61 685

E-Mail: [email protected]



mailto:[email protected]

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 contextWhile 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 alogical sequence. The actual selection of the topics and the depth of training would, ofcourse, depend on the training needs of the participants, i.e. their knowledge level and skillsperformance upon the start of the course. This module is related to module 2, 3 & 4 andshould be referred during the discussions.


2. Module profile

Title : Understanding the Concept of Optimal Monitoring frequencyof DWLR



Objectives : After the training the participants will be able to:• 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



: OHS



:


3. Session plan

No Activities Time Tools1 • Describe the strategies to be adopted for arriving at optimal

monitoring frequency, ensuring the credibility of theattributes, 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 inperforming their professional activities more objectively and hence more credibly. Therequirement of the frequency can apparently not be uniquely defined and shall depend uponthe intended use of the high frequency data as well as upon the local hydrogeological andhydrological characteristics. For example, an aquifer having low specific yield may displayfaster 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 beadopted around the beginning and the end of the rainy seasons and a lower frequency maybe adopted at other times. On the other hand if the objective is to arrive at a truehydrograph, a uniformly high frequency may have to be adopted. A few strategies for arrivingat the optimal monitoring frequency are described in the following paragraphs:

2. Optimizing CriteriaIt follows from the preceding paragraph that there does not exist any unique optimalmonitoring frequency. The optimal monitoring frequency would depend upon the expectationfrom (or intended use/uses of) the hydrograph to be monitored. Some criteria could be asfollows:

2.1 Credibility of Derived Attribute(s)

There may normally be a few well-defined objectives of monitoring the watertable/piezometric head. The objectives may relate to deriving one or more of thefollowing 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 astipulated shallow critical level

• Time of deep water level, i.e., time during which the water level falls below a stipulateddeep 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., thevalues derived from the true hydrograph).

2.2 Preserving the Hydrograph Shape

This implies that the selected monitoring interval should be such that the monitoredhydrograph resembles closely with the true hydrograph. This is indeed the most stringentand all-encompassing expectation requiring uniformly small monitoring intervals. Theintervals would depend upon the degree of the desired resemblance. As discussedsubsequently, correlation is an index of similarity between the shapes of two time series. Itshall be an index of resemblance if the two time series display the variation of the samevariable. 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) bythe Spectral analysis is 4∆t, where ∆t is the interval between two successive water leveldata. Thus, the monitoring interval has to be at lone fourth of the time period of the smallestcycle intended to be identified.

3. Optimizing StrategyIt follows from the above discussion that for optimising the monitoring frequency, we shallrequire the true hydrograph. The hydrograph of smallest feasible interval (say hourly) couldbe deemed as the true hydrograph. Therefore, it is necessary to first procure a time series ofwater level with small enough monitoring interval. Subsequently under-sampled hydrographsof increasing monitoring intervals, are simulated as follows:

• Knock off the intermittent data from the true hydrograph to simulate the under-sampledseries of the chosen larger interval.

• Simulate the under-sampled hydrograph by estimating the knocked off data by linearinterpolation.

The simulated under-sampled hydrographs may be analysed to arrive at the optimalmonitoring frequency as follows:

3.1 Credible Attribute Estimation

Compute the desired attribute from the true hydrograph and from each of the simulatedunder-sampled hydrographs. Terming the attribute value as computed from the truehydrograph as X and the values computed from ith simulated under-sampled hydrograph asAi, compute the loss array [Li = ABS(X - Ai)/S]. Here, S is a relevant quantity for normalizingthe error. Thus the array represents the loss of information (expressed as a fraction of thechosen S) on account of increasing the time interval from the minimum feasible to the oneincorporated in ith simulated under-sampled hydrograph. This array could be interpreted forspecific attributes as follows:

Peak, Trough and Range: (Over-estimation of depth to peak, under-estimation of depth totrough, and consequent under-estimation of the range) Selecting S as the true range (thatis, vertical distance from trough to peak in the true hydrograph), the array shall represent theloss 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 theloss 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 intervalof monitoring.

3.2 Preservation of Hydrograph Shape

The simulated under-sampled hydrographs of increasing time interval may be successivelycompared visually with the true hydrograph. This may lead to a threshold interval beyondwhich the two series may cease to resemble each other. Alternatively, this could be donemore objectively in the following steps:

• Compute the correlation (described in the following section) between the truehydrograph 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 thetwo hydrographs.

•

3.3 Identification of Cycles

The longest permissible interval for identifying a cycle of any time period, by Harmonicanalysis is half the time period. For a more reliable identification of the cycle, it may bedesirable to further restrict the longest permissible interval say to one fourth of the timeperiod. Thus, for identifying a daily cycle, it may be desirable to have an interval no biggerthan 6 hours.

4. CorrelationThis statistic determines the degree of linear interrelation (that is, scaled similarity) betweentwo time series.

A direct linear relation (that is, as one series rises, the other also rises and vice versa) istermed as positive correlation. An inverse linear relation (that is, as one series rises, theother declines and vice versa) is termed as negative correlation. If the rise of one series hasapparently 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. Acorrelation between two series falling in different time spans can be computed by analysingthe overlapping period only, that is, by curtailing one or both the series. If there is nooverlapping period, the correlation can not be estimated. If the two series comprise data atdifferent frequencies, it is necessary to manipulate one of the two series to ensurefrequency-compatibility. Thus, either the series of higher frequency (say series of DWLRdata) may be pruned, or the missing data in the series of low frequency (say series ofmanual data) may be interpolated.

This correlation is essentially a normalised covariance between the pivotal and the derivedseries. 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

xx

i

n

i∑==

n

yy

i

n

i∑== 1

Sx = 2

1

)( xxin

i

−∑=

; Sx = 2

1

)( yyin

i

−∑=

;


Two positively correlated time series shall have a correlation greater than zero and it may goup to +1. A correlation of +1 indicates a perfect positive correlation, that is, a directproportionality of the fluctuations in the two series and hence a perfect linearity with positivegradient between the two variables. Similarly, two negatively correlated time series shallhave a correlation less than zero and it may go up to –1. A correlation of –1 indicates aperfect negative correlation, that is, an inverse proportionality and hence a perfect linearitywith negative slope. Two uncorrelated series shall have a zero correlation.

5 SoftwareThe above stated approach for optimising the monitoring frequency was conceptualised bytechnical consultants to the Hydrology Project. The approach has been assimilated in asoftware, christened as DWLR-ANALYST.


6. Handout

download-manuals-ground water-training-dwlrg-wdatahandling

Technology

conventional monitoring

frequency of monitoring

water levels

training module

prevalent monitoring

high frequency monitoring

limited monitoring

groundwater monitoring