ASTM D5877-95(2000)
(Guide)Standard Guide for Displaying Results of Chemical Analyses of Ground Water for Major Ions and Trace Elements-Diagrams Based on Data Analytical Calculations
Standard Guide for Displaying Results of Chemical Analyses of Ground Water for Major Ions and Trace Elements-Diagrams Based on Data Analytical Calculations
SCOPE
1.1 This guide covers methods that graphically display chemical analyses of multiple ground-water samples, discrete values and also those reduced to comprehensive summaries or parameters. Details required by the investigator to fully use the methods are found in the listed references. The methods included in this guide are many of the graphical procedures that were not discussed in two previous guides, Guides D5738 and D5754.
Note 1--The graphic methods in this guide apply to both raw and transformed data, for example, unaltered medians, maximums, and minimums and transformed means, square-roots, frequency distributions, and so forth. The methods are often computational intensive, requiring the use of a digital computer. Some graphical methods illustrate the results of the statistical analysis of a sample data set. For example, box plots are graphical portrayals of the maximum, minimum, median, 25th percentile, and 75th percentile of one variable, such as the chloride ion from a group of chemical analyses.
Besides chemical components, other variables that may be plotted to show an interdependence with water chemistry include time, distance, and temperature.
1.2 This guide on diagrams based on data analytical calculations is the third of several documents to inform the hydrologists and geochemists about traditional graphical methods for displaying ground-water chemical data.
Note 2--The initial guide described the category of water-analysis diagrams that use two-dimensional trilinear graphs to display, on a single diagram, the common chemical components from two or more analyses of natural ground water.
1.2.1 The second guide described the category of water-analysis diagrams that use pattern and pictorial methods as a basis for displaying each of the individual chemical components determined from the analysis of a single sample of natural ground water.
1.3 This guide presents a compilation of diagrams that allows for transformation of numerical data into visual, usable forms. It is not a guide to selection or use. That choice is program or project specific.
1.4 Many graphic techniques have been developed by investigators to illustrate the results of the data analytical computations to assist in summarizing and interpreting related data sets. In this guide, selected graphical methods are illustrated using ground-water chemistry data.
1.5 The basic or original format of each of the graphical techniques given in this guide has been modified in several ways, largely depending upon the data analytical techniques used by the investigators. Several minor modifications are mentioned, some significant revisions are discussed in more detail.
1.6 Notations have been incorporated within many diagrams illustrated in this guide to assist the reader in understanding how the diagrams are constructed. These notations would not be required on a diagram designed for inclusion in a project document.
Note 3--Use of trade names in this guide is for identification purposes only and does not constitute endorsement by ASTM.
1.7This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
1.i This guide offers an organized collection of information or a series of options and does not recommend a specific course of action. This document cannot replace education or experience and should be used in conjunction with professional judgment. Not all aspects of this guide may be applicable in all circumstances. This ASTM standard is not intended to represent or replace the standard of care by which the adequacy of a given professional service must be judged, nor should this document be applied without consideration of a project's many unique aspects. The word "Standard" in the title of this document means only tha...
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Designation: D 5877 – 95 (Reapproved 2000)
Standard Guide for
Displaying Results of Chemical Analyses of Ground Water
for Major Ions and Trace Elements—Diagrams Based on
Data Analytical Calculations
This standard is issued under the fixed designation D5877; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 1.3 This guide presents a compilation of diagrams that
allows for transformation of numerical data into visual, usable
1.1 This guide covers methods that graphically display
forms. It is not a guide to selection or use. That choice is
chemical analyses of multiple ground-water samples, discrete
program or project specific.
values and also those reduced to comprehensive summaries or
1.4 Many graphic techniques have been developed by in-
parameters.Detailsrequiredbytheinvestigatortofullyusethe
vestigators to illustrate the results of the data analytical
methods are found in the listed references. The methods
computations to assist in summarizing and interpreting related
includedinthisguidearemanyofthegraphicalproceduresthat
data sets. In this guide, selected graphical methods are illus-
werenotdiscussedintwopreviousguides,GuidesD5738and
trated using ground-water chemistry data.
D5754.
1.5 The basic or original format of each of the graphical
NOTE 1—The graphic methods in this guide apply to both raw and
techniques given in this guide has been modified in several
transformed data, for example, unaltered medians, maximums, and
ways, largely depending upon the data analytical techniques
minimums and transformed means, square-roots, frequency distributions,
used by the investigators. Several minor modifications are
andsoforth.Themethodsareoftencomputationalintensive,requiringthe
mentioned, some significant revisions are discussed in more
use of a digital computer. Some graphical methods illustrate the results of
the statistical analysis of a sample data set. For example, box plots are detail.
graphical portrayals of the maximum, minimum, median, 25th percentile,
1.6 Notationshavebeenincorporatedwithinmanydiagrams
and 75th percentile of one variable, such as the chloride ion from a group
illustrated in this guide to assist the reader in understanding
of chemical analyses.
how the diagrams are constructed. These notations would not
Besides chemical components, other variables that may be plotted to
be required on a diagram designed for inclusion in a project
showaninterdependencewithwaterchemistryincludetime,distance,and
document.
temperature.
NOTE 3—Use of trade names in this guide is for identification purposes
1.2 This guide on diagrams based on data analytical calcu-
only and does not constitute endorsement by ASTM.
lationsisthethirdofseveraldocumentstoinformthehydrolo-
gists and geochemists about traditional graphical methods for 1.7 This standard does not purport to address all of the
displaying ground-water chemical data.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
NOTE 2—The initial guide described the category of water-analysis
priate safety and health practices and determine the applica-
diagrams that use two-dimensional trilinear graphs to display, on a single
bility of regulatory limitations prior to use.
diagram,thecommonchemicalcomponentsfromtwoormoreanalysesof
natural ground water. 1.8 This guide offers an organized collection of information
or a series of options and does not recommend a specific
1.2.1 The second guide described the category of water-
course of action. This document cannot replace education or
analysis diagrams that use pattern and pictorial methods as a
experienceandshouldbeusedinconjunctionwithprofessional
basis for displaying each of the individual chemical compo-
judgment.Notallaspectsofthisguidemaybeapplicableinall
nents determined from the analysis of a single sample of
circumstances. This ASTM standard is not intended to repre-
natural ground water.
sent or replace the standard of care by which the adequacy of
a given professional service must be judged, nor should this
This guide is under the jurisdiction of ASTM Committee D18 on Soil and documentbeappliedwithoutconsiderationofaproject’smany
Rockand is the direct responsibility of Subcommittee D18.21 on GroundWater and
unique aspects. The word “Standard” in the title of this
Vadose Zone Investigations.
Current edition approved Dec. 10, 1995. Published February 1996.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D 5877 – 95 (2000)
document means only that the document has been approved ~valencesolutecomponent!
~equivalentweightfactor! 5
~formulaweightsolutecomponent!
through the ASTM consensus process.
(1)
2. Referenced Documents
Then to determine the equivalent weight (meq/L) of the
2.1 ASTM Standards: solute component, multiply the mg/L value of the solute
D596 Practice for Reporting Results ofAnalysis of Water component times the equivalent weight factor, as follows;
D653 Terminology Relating to Soil, Rock, and Contained
~meq/Lsolutecomponent! 5 ~mg/Lsolutecomponent!
Fluids
3 ~equivalentweightfactor!
D1129 Terminology Relating to Water
(2)
D5738 Guide for Displaying the Results of Chemical
2+
For example, the formula weight of Ca is 40.10 and the
Analyses of Ground Water for Major Ions and Trace
ionic charge is 2 (as shown by the 2+), and for a value of 20
Elements—Diagrams for Single Analyses
mg/LCa,theequivalentweightvalueiscomputedtobe0.9975
D5754 Guide for Displaying the Results of Chemical
meq/L:
Analyses of Ground Water for Major Ions and Trace
~2!
Elements—TrilinearDiagramsforTwoorMoreAnalyses
~0.9975meq/LCa! 5 ~20mg/LCa! 3 (3)
~40.10!
3. Terminology
3.1.5.1 Discussion—Many general geochemistry publica-
3.1 Definitions—Except as listed as follows, all definitions tions and water encyclopedias have a complete table of8
equivalent weight factors’ for the ions found in natural ground
are in accordance with Terminology D653:
3.1.1 adjacent values (statistics)—values that fall between water (3, 4).
the quartile and one step beyond the quartile position, where 3.1.6 far-out values (statistics)—values that fall beyond the
the interquartile range is from the 25th to 75th percentile of a
two-step range (see outside values) (1, 2).
sample, and a step is equal to 1.5 times the interquartile range
3.1.7 hinge(statistics)—asusedbyTukey(2),theupperand
(1). The same definition applies to hinges (2).
lower values of a ranked sample that, along with the median,
3.1.2 anion—an ion that moves or would move toward an
dividethenumberofdatavaluesintofourequalparts.Thedata
anode; thus nearly always synonymous with negative ion.
at the hinge position includes interpolated values.
3.1.3 cation—an ion that moves or would move toward a
3.1.7.1 Discussion—Tukey(2)usedthehingesystemforhis
cathode; thus nearly always synonymous with positive ion.
box and whisker plots and for his hinge plot and related
3.1.4 equivalent per million (epm)—for water chemistry, an
summaries. The hinge method of division is similar to the use
equivalent weight unit expressed in English terms, also ex-
of quartiles.
pressed as milligram-equivalent per kilogram. When the con-
3.1.8 interquartile or hinge range (statistics)— the differ-
centration of an ion, expressed in ppm, is multiplied by the
ence between the values at the quartile or hinge extremes (2).
equivalent weight (combining weight) factor (see explanation
3.1.9 maximum or sample maximum (statistics)— the value
of equivalent weight factor) of that ion, the result is expressed
of the variable having the greatest value in a data set (sample).
in epm.
3.1.10 milliequivalent per litre (meq/L)—for water chemis-
3.1.4.1 Discussion—For a completely determined chemical
try, an equivalent weight unit expressed in metric terms, also
analysis of a water sample, the total epm value of the cations
expressed as milligram-equivalent per litre. When the concen-
will equal the total epm value of the anions (chemically
tration of an ion, expressed in mg/L, is multiplied by the
balanced). The plotted values on the water-analysis diagrams
equivalent weight factor (see explanation of equivalent weight
described in this guide can be expressed in percentages of the
factor) of that ion, the result is expressed in meq/L.
total epm (although all illustrations are in milliequivalent per
3.1.10.1 Discussion—For a completely determined chemi-
litre) of the cations and anions of each water analysis.
cal analysis of a water sample, the total value of the cations
Therefore, to use the diagrams, analyses must be converted
will equal the total value of the anions (chemically balanced).
from ppm to epm by multiplying each ion by its equivalent
Theplottedvaluesonthewater-analysisdiagramsdescribedin
weight factor and determining the percent of each ion of the
this guide are expressed in percentages of the total meq/L of
total cation or anion.
thecationsandanionsofeachwateranalysis.Therefore,touse
3.1.5 equivalent weight factor—the equivalent weight fac-
the diagrams, analyses must be converted from mg/Lto meq/L
tor or combining weight factor, also called the reaction
by multiplying each ion by its equivalent weight factor and
coefficient, is used for converting chemical constituents ex-
determiningthepercentofeachionofthetotalcationoranion.
pressed in ppm to epm and mg/Lto meq/L(see explanation of
3.1.11 milligrams per kilogram (mg/kg)—for water chemis-
epm and meq/L). To determine the equivalent weight factor,
try, a weight-per-weight unit expressed in metric terms. The
divide the formula weight of the solute component into the
numberofmilligramsofsolute(forexample,Na)perkilogram
valence of the solute component:
of solution (water). For example, a 10000-mg/kg solute is the
same as 1% solute in the total 100% solution. The mg/kg unit
is equivalent to ppm according to Matthess (5).
Annual Book of ASTM Standards, Vol 11.01.
3.1.12 milligrams per litre (mg/L)—for water chemistry, a
Annual Book of ASTM Standards, Vol 04.08.
weight-per-volume unit expressed in metric terms. The weight
The boldface numbers given in parentheses refer to a list of references at the
−3
end of the text. in milligrams (10 g) of the solute within the volume (litre)
D 5877 – 95 (2000)
solution. The weight can be also expressed in micrograms relationship between the change in standard deviation and the
−6
(10 g).Theuseofthemg/Lunitistheworldwidestandardfor deletedobservationisnonlinearorapproximatelyquadraticfor
the analysis and reporting of water chemistry. the total number of sample observations considerably larger
than the standardization variable squared (7). Values as de-
3.1.12.1 Discussion—The ppm and mg/L values of the
scribed by Sara (8) as unusually high, low, or otherwise
constituents in natural ground water are nearly equal (within
unexpected values within the sample.
anticipated analytical errors) until the concentration of the
3.1.15.1 Discussion—Outliers (8) can be attributed to a
dissolved solids reaches about 7000 mg/L. For highly miner-
number of conditions, including: extreme, but accurately
alized waters, a density correction should be used when
detected, conditions or environmental conditions; sampling
computing ppm from mg/L (3).
errors or field contamination; analytical errors or laboratory
3.1.13 minimum or sample minimum (statistics)—the value
contamination; recording or transcription errors; and faulty
ofthevariablehavingthesmallestvalueinadataset(sample).
(water) sample preparation or preservation, or shelf-life ex-
3.1.14 natural ground water—is water positioned under the
ceedance.
land’s surface, which consists of the basic elements, hydrogen
3.1.16 outside values (statistics)—values that fall between
and oxygen (H O), and numerous major dissolved chemical
one and two steps beyond the interquartile range (see adjacent
constituents, such as calcium (Ca), magnesium (Mg), sodium
values) (1, 2).
(Na), potassium (K), carbonate (CO ), bicarbonate (HCO ),
3 3
3.1.17 parts per million (ppm)—for water chemistry, a
chloride (Cl), and sulfate (SO ).
dimensionless ratio of unit-of-measurement per unit-of-
3.1.14.1 Discussion—Other major constituents, in special
measurement expressed in English terms. One part per million
cases, can include aluminum (Al), boron (B), fluoride (F), iron
is equivalent to one milligram of solute in one kilogram of
(Fe), nitrate (NO ), and phosphorus (PO ). Minor and trace
3 4
solution. For example, if the total weight of the solution (one
elements that can occur in natural ground water vary widely,
millionppm)has99%solventand1%solute,thisisthesame
but can include arsenic (As), copper (Cu), lead (Pb), mercury
as 990000 ppm solvent and 10000 ppm solute in the one
(Hg), radium (Ra), and zinc (Zn). In addition, natural ground
million parts of solution.
water may contain dissolved gases, such as hydrogen sulfide
3.1.18 polar smoothing (statistics)—this type of smooth, as
(H S), carbon dioxide (CO ), oxygen (O ), methane (CH ),
2 2 4
used on a scatterplot or Piper diagram, improves the visualiza-
ammonia(NH ),argon(Ar),helium(He),andradon(Rn).Also
tionofmultiplegroupsofdatasetsbyenclosingafixedpercent
maybe included are neutrally charged mineral species, such as
(50 or 75%) of each group with a mathematically determined
silicate (SiO ), naturally occurring organics, such as tannic
ellipse (1, 9, 10, 11, 12, 13).
acids, colloidal materials, and particulates, such as bacteria
3.1.19 population (statistics)—a well-defined set (either
viruses and naturally charged pollen spores.
finite or infinite) of elements (14).
3.1.14.2 Discussion—Most of the natural ground water is a
3.1.19.1 Discussion—For ground-water quality data the in-
part of the hydrologic cycle, that is the constant circulation of
finite population is actually the finite sampled population, as it
meteoric water as vapor in the atmosphere as a result of
would be impossible, and certainly impractical, to obtain and
evaporation from the earth’s surface (land and ocean), liquid
chemically analysis all of the ground water from an aquifer.
andsolid(ice)onandunderthelandasaresultofprecipitation
3.1.20 quantile (statistics)—the data point corresponding to
from the atmosphere, and as liquid returned to the ocean from
a given fraction of the data. Similar to percentile, which is the
theland.Asmallamountofthegroundwatermaybemagmatic
datapointcorrespondingtoagivenpercentageofthedata (15).
waterori
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