Section 5
E: Modifications of imputed values
F: Other point variables
Andreea Erciulescu
CSSM - NRI Project
February 28, 2012
Andreea Erciulescu (Survey)
February 28, 2012
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Part E : Modifications of imputed values
Previous steps:
• Imputation was complete
• Tabulations comparing imputed and observed erosion values were
constructed
• Comparisons were made against estimated GLS estimates (described
in section 15)
• An erosion table was computed for each state as part of the
diagnostics; the variables used are:
•
•
•
•
USLE on (non)cultivated cropland
USLE on all land requiring USLE
WEQ on (non)cultivated cropland
WEQ on all land requiring WEQ
• EGLS estimates were also calculated for the change in urban acres
and the change in some aquatic variables
Andreea Erciulescu (Survey)
February 28, 2012
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Point erosion variables
The Universal Soil Loss Equation (USLE) is a soil loss model designed to
predict long-term average rate of erosion on a field slope based on specific
factors:
U=RKLCP
where
• U is soil loss
• R is rainfall factor
• K is soil erodibility factor
• L is slope length-gradiant factor
• C is management factor
• P is practice factor
Andreea Erciulescu (Survey)
February 28, 2012
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Point erosion variables - cont.
The Wind erosion equation (WEQ) is an erosion model designed to
predict long-term average annual soil losses from a field having specific
characteristics.
It is a function of the following factors:
• K0 is knoll erodibility index
• If is soil erodibility index
• Cw is climate factor
• Ld is unsheltered distance
• Kr is soil ridge roughness
• V is vegetative cover
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February 28, 2012
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Method - option not used in 2007
• Enter multipliers for the C factor of USLE
• Enter multipliers for wind V factor (vegetative cover)
• Enter multipliers for urban changes
Why? These multipliers make it possible to adjust imputed values so that
the sum agrees with the EGLS estimates, if required1 .
1
The default value of the multipliers is 1
Andreea Erciulescu (Survey)
February 28, 2012
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USLE
Multipliers
• Mu,00 ,Mu,01 ,Mu,02 ,Mu,03 .
Table: The imputed USLE C factors are multiplied by
2000
P01
P02
P03
Mu,00
Mu,00
Mu,00
2001
Mu,01
Mu,01
Andreea Erciulescu (Survey)
2002
2003
Mu,02
Mu,03
Mu,03
2003 MidW, NPlains
South Central
1.04
1.04
2003
NE, SE, W
1.028
1.028
Mu,02
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WEQ
Multipliers
• Mw ,00 ,Mw ,01 ,Mw ,02 ,Mw ,03 .
Table: The imputed Q values (Q = 12 exp(−0.0014V ))
P01
P02
P03
2000
Mw ,00
Mw ,00
Mw ,00
2001
Mw ,01
Mw ,01
2002
Mw ,02
2003
Mw ,03
Mw ,03
Mw ,02
The modified Q is transformed to V and V is rounded to an acceptable
value.
Andreea Erciulescu (Survey)
February 28, 2012
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URBAN
Table: The changes from 1997 to 2000, 2001, 2002, 2003
1997 to
2000
2001
2002
2003
linear extrapolated
Core urban
1839
2198
2584
3047
P01
1850
2564
945
Yearly rate
613
359
386
463
463
The core ratio from 2001 to 2003 = 3047/2198 = 1.386 ⇒
the predicted value for 2003 is 1.386 ∗ 1850 = 2564.
The multiplier for the linearly extrapolated changes for P01, from 2001 to
2002 and from 2002 to 2003, is 2564500−1850400
= 7141
945600
9456 = 0.75518.
Andreea Erciulescu (Survey)
February 28, 2012
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URBAN
Table: The changes from 1997 to 2000, 2001, 2002, 2003
1997 to
2000
2001
2002
2003
linear extrapolated
Core urban
1839
2198
2584
3047
P02
1834
2162
2211
Yearly rate
613
359
386
463
463
The core ratio from 2002 to 2003 = 3047/2584 = 1.18 ⇒ the predicted
value for 2003 is 1.18 ∗ 1834 = 2162.
The multiplier for the extrapolated changes for P02, from 2002 to 2003,
328
is 2162−1834
2211−1834 = 377 = .87.
Andreea Erciulescu (Survey)
February 28, 2012
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URBAN - cont.
Table: The changes from 1997 to 2000,01,02,03
1997 to
2000
2001
2002
2003
linear extrapolated
Core urban
1839
2198
2584
3047
P01
P02
1850
2564
945
1834
2162
2211
Yearly rate
613 *
359
386
463
463
Notes:
• The core estimated change from 1997 to 2000 is (1839/3047 =)
60.4% of the change from 1997 to 2003.
• In the interpolation for the 2003 panel, 60.4% of the total change was
allocated to the 1997 to 2000 period and 13.2% to each of the
changes 2000 to 2001, 2001 to 2002, and 2002 to 2003.
• These percentages were used as the probabilities in allocating small
changes to the individual periods.
Andreea Erciulescu (Survey)
February 28, 2012
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Part F: Other point variables
Overview
• Imputation of remaining point variables
• The variables are placed in groups of related variables (i.e.
”FOREST” or ”CONCERN”)
• Let the current inventory year be T , first year missing be S, and the
most recent inventory prior to and after S for which the data were
collected be A and B, respectively.
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February 28, 2012
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Part F: Other point variables
Steps
1
Find an appropriate donor D for the variable using the C-factor
criteria and ... details later
2
If no donor is find, four different cases are considered ... details later
3
Complete the imputation ... details later
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February 28, 2012
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Step 1.
• Let R denote the point to be imputed for a given group of variables.
• Find match for years A and B for all members of the groups - all
groups except WIND require an exact match for the members of the
group.
• Donor selection criteria for WIND group:
• if wind variables are missing in year A (or B), then, the donor should
not have wind variables for the year A (or B).
• if we have wind data for year A (or B), the match criteria are:
Knollt,R − 2 ≤ Knollt,D ≤ Knollt,R + 2
Kt,R − 0.1 ≤ Kt,D ≤ Knollt,R + 0.1
0.9Lt,R − 200 ≤ Lt,D ≤ 1.2Lt,R + 200
0.9Vt,R − 200 ≤ Vt,D ≤ 1.2Vt,R + 200
• Find an appropriate donor D for the variable using the C-factor
criteria.
• Can relax donor criteria as done in C-factor except can’t relax the
match in 1997 and year T .
• Use donor for all variables in the group for all years requiring
imputation from a single donor.
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February 28, 2012
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Step 2.
If no donor is found, then each variable is imputed using broaduse as
follows:
1. A year of change is determined for the point
• Determine first year of change in broaduse if change occurs.
• If no change in broaduse occurs, select a year of change (Ch ) at
random with probability
t−A
T −A ,
where t is the year to be imputed.
2. If the variables defined at time A and B, and if the broaduse is the
same for all years
Imputed value = Time A Value if t < Ch
Imputed value = Time B Value if t ≥ Ch
3. If a point has the same broaduse for all years requiring imputation
and for year B and the variable is observed only in year B, then the
year B value is used for years requiring imputation.
Andreea Erciulescu (Survey)
February 28, 2012
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Step 2. - cont.
4. If broaduse of the point is not the same for all years, then the missing
years are imputed on the basis of the broaduse sequence
• variable observed at A → the value from A is carried forward as the
imputed value until broaduse changes
• variable observed at B → the value from B is carried backward as the
imputed value until broaduse changes
Example
Year
97 00 01 02
Year
Broaduse
01 01 02 03 → Broaduse
Ownership 6
?
?
1
Ownership
Step 3 is required to complete the imputation.
Andreea Erciulescu (Survey)
97
01
6
00
01
6
01
02
?
02
03
1
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Step 3.
If imputation is not complete after the first two steps, then use default
values specific to each variable.
Example - cont.
Year
97 00 01 02
Broaduse
01 01 02 03
Ownership 6
6
?
1
Use Table 5.8. For Ownership, rule is to impute randomly the 2001 value
for ownership, choosing the 1997 value, 6, with probability 1/5 and the
2002 value, 1, with probability 4/5.
What if imputation is not required? Such situations are called ”Not
applicable” (see Table 5.8) and the variables ← −1.
Andreea Erciulescu (Survey)
February 28, 2012
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Step 3. - cont.
If imputation is not needed.
Example
Year
97
00
01
02
Coveruse
001 003 341 003
Forest
?
?
?
?
Forest Imputed -1
-1
99
-1
From Table 5.8, if land coveruse is not 341 or 3422 , then FOREST is NA
(code =-1), but if coveruse is 341 or 342, default value for FOREST is 99
(non-stocked).
2
341 - forest land grazed, 342- forest land, not grazed
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February 28, 2012
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End
Thank you!
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February 28, 2012
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