Quantifying Rates of Soil Water Evaporation:
Implementing a Soil Water
Oxygen Isotope Model in Matlab
Erik Oerter
EPS 209
27 April 2011
Project Motivation:
Soil Water Oxygen Isotopes
Soil Water originates as meteoric water, preserving the
isotopic signature of precipitation
Hydrogen and Oxygen isotopes undergo Rayleigh
fractionation as water evaporates
 Enrichment in 18O relative to precipitation
The 18O/16O can be sampled:
Directly as soil water (contemporary water)
Indirectly as CaCO3 (ancient water)
Use 18O/16O to estimate evaporation rate  Climate Proxy
Evaporation Rate via Soil Water Oxygen Isotopes
Evap. Rate
18O/16O
of water
at “z” in soil profile
𝑹𝒘 𝒛 =
𝟏
Depth in soil profile
𝑬 𝒛−𝒛𝒆𝒇
−
𝑫
−𝒆
𝟏−
Diff coef. of
water in soil
𝑬 𝑳−𝒛𝒆𝒇
−
𝑫
𝒆
18O/16O
of
water at depth
𝑹𝒘,𝒓𝒆𝒔 − 𝑹𝒘,𝒆𝒇 + 𝑹𝒘,𝒆𝒇
18O/16O
Depth of evap. front
of water
at evap. front
L = Total depth of soil profile
(Barnes and Allison, 1988, J. of Hydrology)
Project Idea:
Fit modeled Oxygen isotope profile to observed
data and find the evaporation rate
Model 18O profile
Observed 18O profile
Data from Wang et al., 1996
Project Approach:
m-file Sequence of Events
1) Load in observed data as text file
2) Initialize variables
- Make an initial guess for evaporation rate
- Populate a vector with evap guesses (~100)
Specify the step between evap guesses
- Initialize a matrix for calculated 18O profiles
(# depth increments x # evap guesses)
3) Loop over all evap guesses, calculating 18O profiles
- Now have 100 18O profiles…
Project Approach:
m-file Sequence of Events
4) Compare the model 18O profiles to the observed
data using a Chi square measure:
2
𝑥 =
(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑−𝑚𝑜𝑑𝑒𝑙)2
𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 2
5) Plot 𝑥 2 vs Evap guesses
- Find the minimum
6) Display the best fit Evap guess
Some Results
Diffusion Coefficient of Water in Soil = 1.5*10-10 m2/sec
Starting Evap Rate Guess = 5x10-11 m/sec (0.15 cm/year)
E guess step = 1*10-12 m/sec
Best fit Evap rate = 1.02*10-10 m/sec (0.32 cm/year)
18O/16O
-9
-8
-7
-6
-5
-4
-3
0
0.1
0.2
0.3
Depth
0.4
0.5
0.6
0.7
0.8
Observed
0.9
Model
1
-2
Future Work
This interpretation of the Barnes and Allison Model:
- Single wet soil zone with the evaporating
front at the surface
Barnes and Allison envisioned a dry zone of soil overlying
the wet zone and evaporating front at some depth
 Implement the two zone scheme
- Allow for a migrating (+/- depth) evaporation front
 Allow for resetting of the 18O input value
(Allow it to rain on the soil)