{"id":202,"date":"2023-08-24T00:23:58","date_gmt":"2023-08-24T00:23:58","guid":{"rendered":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/?post_type=part&p=202"},"modified":"2024-01-14T22:54:54","modified_gmt":"2024-01-14T22:54:54","slug":"notations","status":"publish","type":"part","link":"https:\/\/books.gw-project.org\/stable-isotope-hydrology\/part\/notations\/","title":{"raw":"14 Notations","rendered":"14 Notations"},"content":{"raw":"
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\r\n

\u2030<\/p>\r\n<\/td>\r\n

\r\n

parts per thousand (permil)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

1,<\/em>2,3,...<\/em><\/p>\r\n<\/td>\r\n

\r\n

subscript for input streams<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

a,b,c<\/p>\r\n<\/td>\r\n

\r\n

fitting constants (K2<\/sup>, K, dimensionless, respectively)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03b1<\/p>\r\n<\/td>\r\n

\r\n

equilibrium fractionation factor for the reaction at a given temperature (dimensionless)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

X,Y<\/sub><\/p>\r\n<\/td>\r\n

\r\n

fractionation factor for transition from X to Y (dimensionless)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

c<\/em><\/p>\r\n<\/td>\r\n

\r\n

y-intercept (dimensions of y-axis values)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

d<\/p>\r\n<\/td>\r\n

\r\n

deuterium excess (D-excess)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03b4<\/p>\r\n<\/td>\r\n

\r\n

deviation of stable isotope composition from a standard<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

\u03b5<\/em><\/p>\r\n<\/td>\r\n

\r\n

enrichment factor<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

f<\/em><\/p>\r\n<\/td>\r\n

\r\n

fraction (1 to 0) of water that remains (dimensionless)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

f<\/em><\/p>\r\n<\/td>\r\n

\r\n

subscript for output stream<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

g<\/em><\/p>\r\n<\/td>\r\n

\r\n

subscript indicating groundwater<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

m<\/em><\/p>\r\n<\/td>\r\n

\r\n

gradient, i.e., slope of the line (dimensions of y-axis values over dimensions of x-axis values)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

m<\/em>RMW<\/em><\/sub><\/p>\r\n<\/td>\r\n

\r\n

gradient, i.e., slope of the Reduced Major Axis Regression (dimensions of y-axis values over dimensions of x-axis values)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

p<\/em><\/p>\r\n<\/td>\r\n

\r\n

subscript indicating precipitation<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

Q<\/em><\/p>\r\n<\/td>\r\n

\r\n

flow rate (MT-<\/sup>1<\/sup>)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

R<\/em><\/p>\r\n<\/td>\r\n

\r\n

isotope ratio such as 2<\/sup>H\/1<\/sup>H (dimensionless)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

r<\/em>final<\/em><\/sub><\/p>\r\n<\/td>\r\n

\r\n

isotope composition of the pool of water with fraction f<\/em> remaining (dimensionless)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

r<\/em>initial<\/em><\/sub><\/p>\r\n<\/td>\r\n

\r\n

original isotope composition of the pool (dimensionless)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

s<\/em><\/p>\r\n<\/td>\r\n

\r\n

subscript indicating resultant total stream flow<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

SP<\/em>xy<\/em><\/sub><\/p>\r\n<\/td>\r\n

\r\n

sum of product of deviations from the mean of x and deviations from mean of y (dimensions are product of x and y dimensions)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

SS<\/em>x<\/em><\/sub><\/p>\r\n<\/td>\r\n

\r\n

sum of the squared deviations from the mean of x (squared dimensions of the x variable)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

SS<\/em>y<\/em><\/sub><\/p>\r\n<\/td>\r\n

\r\n

sum of the squared deviations from the mean of y (squared dimensions of the y variable)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

T<\/em><\/p>\r\n<\/td>\r\n

\r\n

temperature (K)<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

X<\/em><\/p>\r\n<\/td>\r\n

\r\n

subscript indicating reactant compound or state<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

x, y<\/em><\/p>\r\n<\/td>\r\n

\r\n

regression variables<\/p>\r\n<\/td>\r\n<\/tr>\r\n

\r\n

Y<\/em><\/p>\r\n<\/td>\r\n

\r\n

subscript indicating product compound or state<\/p>\r\n<\/td>\r\n<\/tr>\r\n

<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

<\/p>\r\n\r\n<\/div>","rendered":"

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

\u2030<\/p>\n<\/td>\n

\n

parts per thousand (permil)<\/p>\n<\/td>\n<\/tr>\n

\n

1,<\/em>2,3,…<\/em><\/p>\n<\/td>\n

\n

subscript for input streams<\/p>\n<\/td>\n<\/tr>\n

\n

a,b,c<\/p>\n<\/td>\n

\n

fitting constants (K2<\/sup>, K, dimensionless, respectively)<\/p>\n<\/td>\n<\/tr>\n

\n

\u03b1<\/p>\n<\/td>\n

\n

equilibrium fractionation factor for the reaction at a given temperature (dimensionless)<\/p>\n<\/td>\n<\/tr>\n

\n

X,Y<\/sub><\/p>\n<\/td>\n

\n

fractionation factor for transition from X to Y (dimensionless)<\/p>\n<\/td>\n<\/tr>\n

\n

c<\/em><\/p>\n<\/td>\n

\n

y-intercept (dimensions of y-axis values)<\/p>\n<\/td>\n<\/tr>\n

\n

d<\/p>\n<\/td>\n

\n

deuterium excess (D-excess)<\/p>\n<\/td>\n<\/tr>\n

\n

\u03b4<\/p>\n<\/td>\n

\n

deviation of stable isotope composition from a standard<\/p>\n<\/td>\n<\/tr>\n

\n

\u03b5<\/em><\/p>\n<\/td>\n

\n

enrichment factor<\/p>\n<\/td>\n<\/tr>\n

\n

f<\/em><\/p>\n<\/td>\n

\n

fraction (1 to 0) of water that remains (dimensionless)<\/p>\n<\/td>\n<\/tr>\n

\n

f<\/em><\/p>\n<\/td>\n

\n

subscript for output stream<\/p>\n<\/td>\n<\/tr>\n

\n

g<\/em><\/p>\n<\/td>\n

\n

subscript indicating groundwater<\/p>\n<\/td>\n<\/tr>\n

\n

m<\/em><\/p>\n<\/td>\n

\n

gradient, i.e., slope of the line (dimensions of y-axis values over dimensions of x-axis values)<\/p>\n<\/td>\n<\/tr>\n

\n

m<\/em>RMW<\/em><\/sub><\/p>\n<\/td>\n

\n

gradient, i.e., slope of the Reduced Major Axis Regression (dimensions of y-axis values over dimensions of x-axis values)<\/p>\n<\/td>\n<\/tr>\n

\n

p<\/em><\/p>\n<\/td>\n

\n

subscript indicating precipitation<\/p>\n<\/td>\n<\/tr>\n

\n

Q<\/em><\/p>\n<\/td>\n

\n

flow rate (MT–<\/sup>1<\/sup>)<\/p>\n<\/td>\n<\/tr>\n

\n

R<\/em><\/p>\n<\/td>\n

\n

isotope ratio such as 2<\/sup>H\/1<\/sup>H (dimensionless)<\/p>\n<\/td>\n<\/tr>\n

\n

r<\/em>final<\/em><\/sub><\/p>\n<\/td>\n

\n

isotope composition of the pool of water with fraction f<\/em> remaining (dimensionless)<\/p>\n<\/td>\n<\/tr>\n

\n

r<\/em>initial<\/em><\/sub><\/p>\n<\/td>\n

\n

original isotope composition of the pool (dimensionless)<\/p>\n<\/td>\n<\/tr>\n

\n

s<\/em><\/p>\n<\/td>\n

\n

subscript indicating resultant total stream flow<\/p>\n<\/td>\n<\/tr>\n

\n

SP<\/em>xy<\/em><\/sub><\/p>\n<\/td>\n

\n

sum of product of deviations from the mean of x and deviations from mean of y (dimensions are product of x and y dimensions)<\/p>\n<\/td>\n<\/tr>\n

\n

SS<\/em>x<\/em><\/sub><\/p>\n<\/td>\n

\n

sum of the squared deviations from the mean of x (squared dimensions of the x variable)<\/p>\n<\/td>\n<\/tr>\n

\n

SS<\/em>y<\/em><\/sub><\/p>\n<\/td>\n

\n

sum of the squared deviations from the mean of y (squared dimensions of the y variable)<\/p>\n<\/td>\n<\/tr>\n

\n

T<\/em><\/p>\n<\/td>\n

\n

temperature (K)<\/p>\n<\/td>\n<\/tr>\n

\n

X<\/em><\/p>\n<\/td>\n

\n

subscript indicating reactant compound or state<\/p>\n<\/td>\n<\/tr>\n

\n

x, y<\/em><\/p>\n<\/td>\n

\n

regression variables<\/p>\n<\/td>\n<\/tr>\n

\n

Y<\/em><\/p>\n<\/td>\n

\n

subscript indicating product compound or state<\/p>\n<\/td>\n<\/tr>\n

<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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