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Modeling
5
Assaad Mrad
Groundwater irrigated agriculture: a predator-prey interaction
Assaad Mrad, Duke University
Posted
3 months ago
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This notebook contains the underlying computational analysis of a recent open-access publication in PNAS,
Peak grain forecasts for the US High Plains amid withering waters
. It is a representation of groundwater use–crop production dynamics across three High Plains states of Kansas, Nebraska, and Texas.
Crop statistics
Survey Data
Combining Northern and Southern High Plains data from the
USDA National Agricultural Statistics Service query tool
(Access January 2020)
I have downloaded data for 4 crops: cotton, corn, sorghum, and wheat. On the USDA NASS query tool, I chose to retrieve data for two Texas agricultural districts of interest: the northern and southern High Plains agricultural districts.
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Corn data only exists for after 1981 compared to the early 1970s for the other three crops. We will need to supplement the data for corn using separate data sources. This will be done below.
For which years does survey data exist for all four crops?
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(
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&
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;
Sum weights and areas per year
I
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[
]
:
=
c
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]
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|
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]
;
Add census data for all four crops in 1959, 1964, and corn irrigated acreage in 1974 and 1978
The USDA data we extracted above were survey data which apparently only started in the 1970s for a lot of the crops and only in the 1980s for corn, probably because corn wasn’t as popular back then (as we will see below). However, there are census data from even before. For example, if you play around the USDA website, you will be able to find census data containing harvested irrigated crop by county in Texas for 1964 and 1959 (
link
). This will be used to supplement data for all four crops considered here. We still need census data for corn in 1974 (
link
) and 1978 (
link
). The first unfortunate characteristic of these censuses is that they are in pdf in low quality. This means I had to manually go through each county and copy the data to an excel sheet to make it convenient to analyze here. Moreover, for 1974 and 1978, there are only data on the amount of acres of irrigated corn, not production. We will then need to estimate the yield of irrigated corn in the Texas northern and souther High Plains districts. Yield is expressed in Bushels (unit of weight) per Acre so by multiplying the acreage (data we have) by the yield, we obtain the production in Bushels.
Estimate Texas irrigated corn yields by agricultural district and obtain production estimates
Import Kansas irrigated corn yields from downloaded excel sheet
Irrigated
corn yield in Kansas (in Bushels/acre )
I
n
[
]
:
=
k
a
n
s
a
s
C
o
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S
t
a
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e
"
]
,
"
K
A
N
S
A
S
"
]
&
]
]
;
Import Texas irrigated corn yields from downloaded excel sheet for the two districts
Irrigated corn yield in Texas (in Bushels/acre )
I
n
[
]
:
=
t
e
x
a
s
C
o
r
n
Y
i
e
l
d
D
a
t
a
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t
=
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m
p
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t
[
"
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t
s
\
\
c
o
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n
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y
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"
,
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e
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1
]
;
Show Keys
I
n
[
]
:
=
N
o
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m
a
l
@
K
e
y
s
@
t
e
x
a
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〚
1
〛
O
u
t
[
]
=
{
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(
%
)
}
Show Ag Districts
I
n
[
]
:
=
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l
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}
Compare Texas northern and southern districts to Kansas irrigated corn yields
I
n
[
]
:
=
L
i
s
t
P
l
o
t
[
{
k
a
n
s
a
s
C
o
r
n
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t
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{
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}
]
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#
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"
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]
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,
{
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,
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a
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n
d
i
s
t
r
i
c
t
We need to estimate Texas irrigated corn yields prior to 1981 using the Kansas yields. We first compute the ratios of yields between Texas north and south High Plains agricultural districts to Kansas’ after 1980:
For the northern district
I
n
[
]
:
=
N
o
r
m
a
l
@
t
e
x
a
s
C
o
r
n
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t
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n
g
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t
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#
[
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g
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]
,
"
N
O
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R
N
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A
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N
S
"
]
&
]
,
"
V
a
l
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e
"
]
/
N
o
r
m
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l
@
k
a
n
s
a
s
C
o
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n
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i
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t
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t
[
S
e
l
e
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t
[
#
[
"
Y
e
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r
"
]
>
1
9
8
0
&
]
,
"
V
a
l
u
e
"
]
O
u
t
[
]
=
1
.
0
5
5
4
1
,
1
.
0
4
6
3
1
,
1
.
2
2
7
6
1
,
1
1
1
0
,
1
.
0
3
8
7
8
,
1
.
0
7
6
1
9
,
1
.
2
1
0
8
3
,
1
.
1
2
1
8
8
,
1
.
0
7
6
4
3
I
n
[
]
:
=
{
M
e
a
n
@
#
,
S
t
a
n
d
a
r
d
D
e
v
i
a
t
i
o
n
@
#
}
&
@
%
O
u
t
[
]
=
{
1
.
1
0
5
9
4
,
0
.
0
6
9
3
4
7
4
}
For the southern district
I
n
[
]
:
=
N
o
r
m
a
l
@
t
e
x
a
s
C
o
r
n
Y
i
e
l
d
D
a
t
a
s
e
t
[
S
e
l
e
c
t
[
S
t
r
i
n
g
M
a
t
c
h
Q
[
#
[
"
A
g
D
i
s
t
r
i
c
t
"
]
,
"
S
O
U
T
H
E
R
N
H
I
G
H
P
L
A
I
N
S
"
]
&
]
,
"
V
a
l
u
e
"
]
/
N
o
r
m
a
l
@
k
a
n
s
a
s
C
o
r
n
Y
i
e
l
d
D
a
t
a
s
e
t
[
S
e
l
e
c
t
[
#
[
"
Y
e
a
r
"
]
>
1
9
8
0
&
]
,
"
V
a
l
u
e
"
]
O
u
t
[
]
=
{
0
.
9
1
8
2
4
3
,
1
.
0
1
9
4
6
,
1
.
1
4
4
0
3
,
0
.
9
7
5
3
3
3
,
0
.
9
9
3
8
7
8
,
0
.
9
8
9
1
1
6
,
1
.
0
8
8
3
3
,
1
.
0
2
5
,
0
.
9
9
6
4
2
9
}
I
n
[
]
:
=
{
M
e
a
n
@
#
,
S
t
a
n
d
a
r
d
D
e
v
i
a
t
i
o
n
@
#
}
&
@
%
O
u
t
[
]
=
{
1
.
0
1
6
6
5
,
0
.
0
6
5
6
8
7
1
}
We notice that the standard deviations of the ratios is two order of magnitudes smaller that the mean of the ratios. Based on these results, multiply Kansas yields in 1974 and 1978 by 1.11 (11%) to estimate the Texas northern district irrigated corn yield and 1.02 (2%) for southern district.
Import corn irrigated acreage for Texas. These are to be multiplied by the estimated yields to obtain production values.
We import an excel sheet that I have manually created based on the pdf files of the census (find the online links above).
I
n
[
]
:
=
t
e
x
a
s
I
r
r
i
g
a
t
e
d
C
o
r
n
A
c
r
e
s
B
y
C
o
u
n
t
y
X
L
S
=
I
m
p
o
r
t
[
"
S
h
e
e
t
s
/
/
c
o
r
n
A
c
r
e
s
.
c
s
v
"
,
"
D
a
t
a
s
e
t
"
,
"
H
e
a
d
e
r
L
i
n
e
s
"
1
]
;
I
n
[
]
:
=
H
e
a
d
@
t
e
x
a
s
I
r
r
i
g
a
t
e
d
C
o
r
n
A
c
r
e
s
B
y
C
o
u
n
t
y
X
L
S
[
1
,
"
A
R
M
S
T
R
O
N
G
"
]
O
u
t
[
]
=
S
t
r
i
n
g
Missing data is denoted by an empty string (“”). We want to be able to refer to a certain data point using the year, so we make the YEAR column a set of keys as follows:
I
n
[
]
:
=
t
e
x
a
s
I
r
r
i
g
a
t
e
d
C
o
r
n
A
c
r
e
s
B
y
C
o
u
n
t
y
=
D
a
t
a
s
e
t
[
A
s
s
o
c
i
a
t
i
o
n
T
h
r
e
a
d
[
N
o
r
m
a
l
[
#
[
A
l
l
,
(
*
T
h
e
h
e
a
d
e
r
f
o
r
y
e
a
r
s
i
n
t
h
e
e
x
c
e
l
s
h
e
e
t
i
s
a
n
e
m
p
t
y
s
t
r
i
n
g
*
)
"
"
]
]
,
N
o
r
m
a
l
[
K
e
y
D
r
o
p
[
#
[
A
l
l
]
,
"
"
]
]
]
&
@
t
e
x
a
s
I
r
r
i
g
a
t
e
d
C
o
r
n
A
c
r
e
s
B
y
C
o
u
n
t
y
X
L
S
]
O
u
t
[
]
=
A
R
M
S
T
R
O
N
G
B
A
I
L
E
Y
B
R
I
S
C
O
E
C
A
R
S
O
N
C
A
S
T
R
O
C
O
C
H
R
A
N
C
R
O
S
B
Y
D
A
L
L
A
M
D
E
A
F
S
M
I
T
H
F
L
O
Y
D
2
0
1
8
8
5
0
0
0
2
0
1
7
2
5
2
0
3
0
1
3
2
3
1
3
2
3
8
0
1
0
7
7
2
3
7
2
3
3
6
2
9
3
9
3
9
7
4
2
2
0
1
6
4
5
0
0
3
2
0
0
0
1
0
3
0
0
0
3
8
5
0
0
2
3
7
0
0
2
0
1
5
8
5
0
0
0
4
3
0
0
0
2
0
1
2
1
1
7
4
1
4
3
6
3
5
6
9
6
4
9
6
1
5
8
2
4
1
2
4
7
4
7
4
2
0
1
1
2
0
1
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1
1
1
0
0
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4
2
5
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2
0
0
7
3
5
5
9
5
6
9
1
7
6
7
4
8
1
2
0
6
1
0
8
7
1
3
5
0
6
1
2
0
6
0
3
5
8
4
1
2
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2
3
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3
1
0
6
1
0
7
7
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4
6
9
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1
3
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1
3
6
1
8
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8
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6
1
9
9
7
9
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4
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6
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4
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6
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2
9
1
1
3
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8
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9
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6
0
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9
1
9
8
8
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2
9
0
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3
0
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5
7
1
0
0
3
8
1
0
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1
0
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1
2
2
0
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1
9
8
6
1
6
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3
1
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0
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4
2
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0
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1
9
8
5
1
9
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3
5
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5
6
3
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8
0
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9
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4
2
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7
0
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2
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1
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5
0
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4
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0
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9
0
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9
8
1
2
3
6
0
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1
4
0
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5
0
0
8
3
2
0
0
4
0
4
0
0
2
7
1
0
0
1
0
9
0
0
1
9
8
0
1
9
7
9
1
9
7
8
3
4
3
2
9
1
3
1
1
7
7
2
1
5
1
9
4
1
1
5
2
6
1
1
8
6
2
3
7
0
1
1
6
9
1
7
0
1
9
4
8
3
r
o
w
s
1
–
2
0
o
f
3
9
c
o
l
u
m
n
s
1
–
1
0
o
f
3
2
Obtain irrigated corn production estimates for the Texas High Plains in 1978
1978
I
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