How To Get The Most Out Of Your Transducer Data

Transcription

1 How To Get The Most Out Of Your Transducer Data State-of-the-Art Techniques and Future Directions for Environmental Data Analysis By Dr. Farid Achour Tel: Mob:

2 Disclaimer 2016 Ramboll Environ Inc. The information contained in herein is not intended to constitute technical or legal advice and should not be relied on as such.

3 Dr. Achour published two book chapters in ) Solving Complex Environmental Problems Using Stochastic Data Analysis: Characterization of a Hydrothermal Aquifer Influenced by a Karst. 2) Anomaly Detection Methods for Hydrologists, Hydrogeologists and Environmental Engineers The two chapters were published in Practical Environmental Statistics and Data Analysis, ILM Publications (July 2011) Advanced/dp/ /ref=sr_1_fkmr3_2?ie=UTF8&qid= &sr=8-2-fkmr3

4 By Analyzing Transducer Data You Can: 1. Estimate the hydraulic parameters of an aquifer such as storage coefficient, effective porosity (volume), barometric efficiency (vulnerability), transmissivity and hydraulic conductivity, based solely on the natural fluctuations due to earth tides and barometric pressure. 2. Locate most productive areas within an aquifer 3. Locate most/least vulnerable areas within an aquifer 4. Assess the existence/absence of an overexploitation for a given aquifer and when it will occur (if exists) 5. Estimate safe yield for a given aquifer (kartic and porous) 6. Detect Hidden (Non declared) pumping wells 7. Determine the extent of a catchment area for springs (Bottled water) 8. Determine if a spring/well is impacted by nearby pumping wells 9. Detect early stage of clogging in water supply wells.

5 Why Switch From Time Domain to Frequency Domain? Heartbeat counts measurement is not as reliable as Electro cardiogram (ECG). A doctor will make a better diagnostic about a patient s heart problems when looking at the peaks as shown on an ECG. Using this analogy, we analyze environmental data (continuous water level, chemistry, temperature...) in the frequency domain instead of the temporal domain to locate the peaks corresponding to periodicities.

6 Spectral Analysis Applied to Environmental Time Series Joseph Fourier ( )

7 Recorded Transducer Data Can be Decrypted like a Rainbow A rainbow is an optical and meteorological phenomenon that causes a spectrum of light to appear in the sky when the Sun shines onto droplets of moisture in the Earth's atmosphere. They take the form of a multicolored arc, with red on the outer part of the arch and violet on the inner section of the arch.

8 Analogy Between Light Analysis and Spectral Analysis Light Chemical System prism Blue Green Yellow Red luminescence intensity Spectrum Spectrum = Signature of the system Rainfall Runoff Water level Electrical Conductivity Hydrological Hydrogeological System Spectral Analysis Var. 1 Var. 2 Var. 3 Variance Spectrum Temperature Noise...

9 Tools Water level fluctuations Time Domain Frequency Domain Simple Graph Spectral Density Function Cross Correlogram Wavelets Continuous MORLET Orthogonal Coherence Function Gain Function

10 Spectral Analysis Spectral Analysis represents the application of the Fourier transform to the signal (successive water level fluctuation records), it is a shift from the temporal to the frequencies domain. Spectral Analysis allows us to identify existing periodicities within the signal; these periodicities are represented by a peak on the spectral density function

11 The Simple Correlogram Simple correlation analysis quantifies linear dependency of successive values over time. The correlogram outlines the memory of the system. If an event has a long-term influence on the time series, the slope of the autocorrelation function decreases slowly.

12 Correlogram of Three wells Capturing the same Aquifer. Which one is the most productive?

13 The Cross-Correlogram Cross-correlation analysis is used to establish a link between the input time series X(t), and the output time series Y(t) If the input time series is random, the cross-correlation function r corresponds to the impulse response of the system. In other cases, the cross-correlation function provides information on the causal and non-causal relationships between the input and the output as well as the importance of these relationships.

14 Cross-Correlogram configurations No relation between input and output Non-causal relation between input and output Input and Output are both the result the same cause The input should be the output and vice versa Causal Relation exits between Input and Output

15 Coherence Function The coherence function, C xy(f), expresses the linearity of the input-output relationship and depends on the simple and cross-spectral density functions A system is linear, C xy(f) 1, when a change in the input function creates a proportional change of the output function. Non-linearity means that other factors must be taken into account in the definition of the system.

16 Case Study 1: Optimizing Sampling Frequency For the purpose of this exercise, we used analysed groundwater elevations collected by the United States Geological Survey at three nested wells. Groundwater levels were collected every 15 minutes, between 2007 and Approximately 200,000 data for each well.

17 Feet Groundwater Level Fluctuations at MW-902 (USGS Well) Hours

18 Spectral Density Function The sampling Frequency should be one record per 4 hours instead of 15 minutes.

19 Flow rates (m3/s) Flow rates (m 3 /s) Log of Spectrum Case Study 2: Removing Noise from Spring Discharge Data Dates Log of Frequencies

20 Filtered Groundwater Level (m) Groundwater Level (m) Case Study 3: Removing the Effect of a Nearby Pumping Well on a Monitoring Well Hours Hours

21 Case Study 4: Removing the Combined Effect of the Ocean Tide and identify nearby pumping well (remediation) GW fluctuations due to pumping (1.9 cm) GW fluctuations due to Ocean tides (12 cm) GW fluctuations due to natural causes such as infiltration, boundary conditions, evaporation..(1.4 cm)

22 Case Study 4: Estimating Hydraulic Parameters without Extracting Water

23 Groundwater is Affected by Earth Tides (Newton s Gravitational Law)

24 Facts About Earth Tides It is known that the gravitational influences of the sun and moon cause sea level to rise slightly at some locations and to fall at other locations, depending on the geometric relation of each location with the astronomic bodies and the mass of the earth. These vary periodically with the changing positions of the sun and moon and are referred to as ocean tides. The solid earth also responds to these forces, producing an oscillatory pumping/injection sequence referred to as Earth Tides. There are 386 tides but only tides with high amplitude have a measurable impact on the aquifers. Melchior (1978) indicated that five larger tides are responsible for 95% of the water level fluctuations observed in wells.

25 Major Earth Tides

26 Barometric Pressure The other major class of natural stresses acting on subsurface formations, including aquifers, are the pressure loading and unloading caused by changes in atmospheric pressure. These changes are linked to both the periodic (diurnal and semidiurnal) changes in atmospheric pressure and to longer-term movements of masses of air of higher and lower pressure across the surface of the earth.

27 Hydrographs at Different Piezometers DTW Below TOC (feet) Time (Feb 22 to March 12) :00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 18:00 6:00 MW-57 MW-52 MW-54 TW-6 TW-8 TW-9

28 Spectral Analysis on Detrended Data The existence of the signature of the earth tide at 12 hours and the barometric pressure at 24 hours indicate that the aquifer is confined at locations where the amplitude of the peaks in more important.

29 Spectral Density Function

30 Morlet Wavelets: Scalogram Morlet Wavelet is a mathematical tool that was developed in the 80 s by Morlet et al. This tool allows the decomposition of a signal (successive water level fluctuation records) into different scales. It allows the identification of any periodicity (if it exists) by investigating each identified scale level.

31 Extraction of the 12 Hours (Semi Diurnal) Signal

32 Estimation of the Storage Coefficient We used Bredehoeft-Jacob model to derive the Specific storage coefficient: Ss = E/ h Ss: Specific Storage Coefficient E: Cubic dilatation of tide M2 ( kg/m 3 ) h: variation of water elevation due to tide M2 The storage coefficient was calculated by multiplying the specific storage coefficient by the thickness of the saturated aquifer

33 Gain Function The gain function, g xy(f), expresses an amplification (>1) or an attenuation (<1) of the output signal in comparison with the input signal. In this case (see figure), this phenomenon can be related to the change in velocity due to the change of aquifer characteristics.

34 Gain Function (Input Barometric Pressure Output GW Fluctuation) Gain Function

35 Estimation of the Effective Porosity Jacob links the barometric efficiency to the storage coefficient S: S = (σ g Ф e)/ (Ew B) (1) With Ф equals to the effective porosity, e equals to the thickness of the aquifer, g equals to gravity, σ equals to water density, and Ew equals to the water elasticity module. The B parameter can vary between 0 and 1, but stays constant for a given well-aquifer system. Bredehoft also derived the equation h = (Өt e)/s (2) h: Maximal water level variation due to earth tide Өt: Dilatation of aquifer due to tide M2 e: thickness of saturated aquifer S: Storage Coefficient Combining equations 1 and 2, we deduce the effective porosity Ф: Ф = (Өt Ew B )/ (h σ g)

36 Estimation of Aquifer Transmissivity By using the model developed Paul Hsieh (USGS). It is possible to estimate aquifer transmissivity from Earth tide analysis.

37 Conclusion It is possible estimate the hydraulic parameters of an aquifer based solely on the natural fluctuations due to earth tides and barometric pressure. By using Morlet wavelets and Spectral Analysis along with Jacob and Bredehoft-Cooper and Hsieh models it is possible to estimate the specific storage coefficient, Storage coefficient, barometric efficiency, effective porosity, transmissivity and hydraulic conductivity. The advantages of this methodology is that it is environmentally friendly (no contaminated water extracted), cost effective, fast to perform and allows to estimate hydraulic parameters on all observation wells.

38 Overexploitation? A water agency claimed that a bottling water company was responsible for the overexploitation of the aquifer, as suggested by the statistical trend shown by spring discharge evolution versus time: Linear regression showing decrease in GW resources!

39 Different Components (Signals) within Environmental Time Series x Time Series Three Components: a. secular, b. seasonal, c. random. t m Var. total = Var.a + Var.b + Var.c Decomposition of the total variance in the frequency domain = Fourier Transform of the Correlogram of the time series

40 Case Study 5: Spectral Analysis on Discharge Data Indicate the Presence of a Trend High values in the long term (0,0) indicate the presence of a trend

41 Continuous Morlet Wavelets

42 Orthogonal Wavelets Allow the Decomposition of the Signal into Different Components at Different Scales

43 Orthogonal Wavelets Allows the Determination of the Trend The long terms wavelets indicate the presence of an increasing trend.

44 Exploitable Volumes Estimation (Karst) Volumes in 10 6 m 3 Total Volume Exploitable Volume Years

45 Exploitable Volume for Porous Aquifers Per Square Kilometer Years GW elevation in meters Well MW-8 Well MW-8 Millions of Cubic Meters/Km 2 Years

46 Conclusions By analyzing transducer data you can: Estimate hydraulic parameters such as storage coefficient, effective porosity, barometric efficiency, transmissivity and hydraulic conductivity, based solely on the natural fluctuations due to earth tides and barometric pressure. Determine optimal sampling frequency Locate most productive areas within an aquifer Locate most/least vulnerable areas within an aquifer Assess the existence/absence of an overexploitation for a given aquifer and when it will occur (if exists) Estimate safe yield for a given aquifer (karst and porous media) Determine river-aquifer interaction (presence/absence) Detect Hidden (Non declared) pumping wells Determine the extent of a catchment area for springs (Bottled water) Determine if a spring/well is impacted by nearby pumping wells Detect early stage of clogging in water supply wells.

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53 Thank you for attending! Contact information: Farid Achour, Ph.D, PG Senior Science Advisor D M FAchour@ramboll.com Ashley Steinbach Environmental Product Manager asteinbach@in-situ.com 30% Rental Discount: