USGS

EMR Method for Estimating Recharge*

*Please note that due to the recent government shutdown this web page has yet to be updated to refelct changes presented in the new publication: Nimmo, J.R. and Perkins, K.S., 2018, Episodic Master Recession Evaluation of Groundwater and Streamflow Hydrographs for Water-Resource Estimation, Vadose Zone Journal 2018 17:180050 ( PDF)

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Introduction

The Episodic Master Recession (EMR) method identifies and quantifies recharge episodes, along with their associated infiltration-related inputs, by a consistent, systematic procedure. It is based on the water-table fluctuation (WTF) method of recharge estimation, adapted such that the necessary system-characterizing parameter values, once established, are applied consistently through the entire data set. The EMR algorithm partitions a time series of water table elevations E(t) into discrete recharge episodes and intervals of no episodic recharge. It correlates each recharge episode with a specific interval of rainfall, so that a precise amount of storm input or infiltration, and its time-varying intensity, can be associated with the amount of recharge that results. When storms occur closely spaced in time, as commonly occurs in humid climates, the algorithm evaluates the separability of events, so that those whose recharge cannot be associated with a single storm can be appropriately lumped together.

The site-specific characteristics that must be established at the start are:

  • Parameters specifying the Master Recession Curve dE/dt vs. E
  • Specific yield, for calculations of recharge rate
  • Lag time, the characteristic travel time of water through the UZ, surface to water table
  • Fluctuation tolerance, the maximum dE/dt value allowable as system noise rather than response to incoming water flux

The master recession curve parameters, typically specified as the intercept and slope of a line fitted to calculated values of dE/dt vs. E, must be previously determined using the MRCfit program or other methods. Specific yield also must be estimated by other methods. The lag time and fluctuation tolerance are typically determined by trial and error, running the program with the data set of interest.

Though the determination of these parameter values requires hydrologic judgment, they can be established once for each given site, and thus do not allow subjective influences to affect episode-to-episode comparisons. By centralizing the elements requiring judgment, this method keeps the most subjective elements openly apparent, making it easy to maintain consistency. If applied to a data set with diverse recharge episodes, with broadly differing characteristics, the method serves in evaluating how storm characteristics and antecedent conditions affect recharge, with application to climate change and other important issues.

The MRC and EMR programs are written in the R programming language and run using R studio, an open-source platform available at www.rstudio.com. The downloadable versions of these codes have been set up with filenames and parameter values for a sample data set, which must be changed for the user’s data.

Downloadable Resources

Primary publication describing the method:

Nimmo, J.R., Horowitz, C., and Mitchell, L., 2015, Discrete-storm water-table fluctuation method to estimate episodic recharge: Groundwater, v.53, no. 2, doi: 10.1111/gwat.12177. ( PDF)

EMR Program information ( PDF)

Reference for the water table fluctuation method:

Heppner, C.S., and Nimmo, J.R., 2005, A computer program for predicting recharge with a master recession curve: U.S. Geological Survey Scientific Investigations Report 2005-5172. ( PDF)

MRC program file

EMR Main program file

EMR Modifiable start file

Example EMR input file

Required form of input data

Create an input file: this comma delimited (.csv) file created by the user contains 3 columns of data. It can be created in excel and saved in comma-delimited format. The first column is time, referenced from t=0 at any starting time that is relevant to the data set as a whole (usually at or before the earliest time in the data). Time must be specified on a continuous scale with consistent units such as h or d. Formats such as month/day/year must be converted to a continuous, single-unit scale. The second column is elevation of the water table, given as height above sea level, or depth below land surface (in which case the numbers will be negative), or any other convenient reference level. If it is known what elevation the recession asymptotically approaches as recession continues indefinitely without episodic input, this elevation may be a convenient reference level. The third column is cumulative precipitation from a chosen reference time. Water level and precipitation can be in any desired units.

Column headings should be chosen with care as their text will appear in output labels. It is usually a convenience to parenthetically specify units.

example data file

Using the MRC Program

MRCfit.v2.0.r: This program estimates values of the adjustable parameters needed to specify the fit to the master recession curve as required for the EMR program. Below is a screen shot of the MRCfit code on the R Studio interface. Lines that require changes are 13, 14, 17, 19, 22, 25, 30, 34, 37, 40, 44, 48, and 51. The # symbol indicates a comment in the program.

R Studio Interface

Many of these parameters will depend on site-specific data and will require some judgments based on water table behavior in response to precipitation. It is also good to start with a best guess and adjust parameters based on examination of the output graphs.

  • Line 13: path to inputfiles
  • Line 14: path to output files
  • Line 17: input file name
  • Line 19: output file name
  • Line 22: desired degree of the fitted polynomial
  • Line 25: do you want to force the fit through the origin? This will almost always be set to false
  • Line 30: this is the time increment between data points. For example, if you have hourly data and the units of T are days, the value will be 1/24
  • Line 34: the value is the minimum duration of interval between significant precipitation and the start of the interval of acceptable recession data
  • Line 37: this is the minimum amount of precipitation that can be tolerated as negligible during an interval of acceptable recession data
  • Line 40: this is the duration used in each linear fit segment of recession, for instance if you have hourly data it might improve the fit to linearize over a period of half a day, so that a line segment fit to 12 data points will be used as the slope
  • Line 44: maximum allowable elevation-increase for linearized segments to be used. This allows for elimination of some high-amplitude (positive-slope) noise in the recession data. Setting to 0 eliminates all upticks during accepted recession intervals
  • Line 48: desired bin sizes used for averaging of dE/Dt vs. E points before fitting the recession slopes
  • Line 51: if set to “true” an extra graph of slope vs. time will be generated, usually set to “false”

Step by step instructions

  • Open the RStudio Software
  • Go to File -> Open -> MRCfit.v2.0.r file
  • Insert proper information on lines described above
  • file
  • Click on the "source" button to run the program (a shortcut useful for trial-and-error procedures is to check the “Source on Save” box)

Output files

  • Graph of the fit to the recession data with fit coefficients and input parameters
  • Graph of water level vs time with recession periods highlighted that were used in the fitting
  • Output file with coefficients (.csv format)

Using the EMR Program

The program requires four time series:

  • Time, T (as a numerical quantity, e.g. in days)
  • Water table level, E
  • Cumulative precipitation, P
  • Water table rate of change, dE/dT (calculated by the program)

The three time series to be supplied by the user are the same as those needed for MRCfit, so identical input files can be used for the two programs.

The user chooses the time units for use with T and the length units for use with E and P. The same chosen units are used throughout the calculations and output.

There are 3 necessary files: a start file, the main program file, and the input file containing columns of T, E, and P.

Start file: This file contains information that informs the main program such as the location of the main program file, the data file, and the adjustable parameter values. Below is a screen shot of an EMRstart code on the R Studio interface. Lines that require changes are 2, 5, 6, 9, 10, 13, 14, 15, 16, 17, 18, and 20. The # symbol indicates a comment in the program

R Studio Interface
  • Line 2: Path to the location of the main program file
  • Line 5: path to input files
  • Line 6: path to output files
  • Line 9: input data file name
  • Line 10: output data file name
  • Line 13: Site or well name to appear on graph output
  • Line 14: Date to appear on graph output
  • Line 15: Fluctuation tolerance (the maximum dE/dt value allowable as system noise without being considered as episodic recharge)
  • Line 16: Lag time (the typical time difference between the start of rainfall and the first significant change in water level)
  • Line 17: Specific yield
  • Line 18: Moving-average interval used to smooth data
  • Line 20: MRC coefficients (of the polynomial fit to the water level recession data)

Main program file (EMR_main_v34.8 or later): this is the main code that takes the input data and determines periods of recharge based on parameters and tolerances set in the start file..

Step by Step Instructions

  • Open the RStudio Software
  • Go to File -> Open -> Choose your start file
  • Insert proper information on lines as described above
  • Save the start file
  • Click on the "source" button just above the interface file to run the main program (a shortcut useful for trial-and-error procedures is to check the “Source on Save” box)

Output files

  • Graph of water levels vs time with recharge periods highlighted
  • Graph of water level derivative vs. time with tolerance band recharge periods highlighted
  • Output file (.csv format). Columns to note are A-M, some are self-explanatory
    • A. Episode- just the episode number
    • B. Start_time- start of the episode
    • C. Duration- length of the episode
    • D. Delta_measurand- total change in water level
    • E. Storage- this is the recharge amount in length
    • F. Causal_input- precip associated with the recharge event
    • H. start_precip_time
    • I. end_precip_time
    • J. end_precip
    • K. avg_precip_rate
    • L. max_precip_rate
    • M. end_time- end of the episode

Recharge to precipitation ratio (RPR) can be calculated for each episode by dividing column E by column F. Note that unit conversion may be necessary if E and P are specified using different units in the input file.


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Last modified: July 2016