Assessing Crop Insurance Risk Using An
Agricultural Weather Index
CAS Seminar on Reinsurance
June 6-7, 2005
S. Ming Lee
www.air-worldwide.com
Challenges in Agricultural Risk Assessment

Every risk assessment starts with evaluation of historic data, i.e. crop yields,
weather parameters, ….
Observed Corn Yields: Nemaha County
140
12
120
10
100
8
80
6
60
40
4
20
2
0
0
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
Yield
Observed Corn Yield Distribution
Nemaha County
Year
© 2005 AIR Worldwide Corporation
20
35
50
65
80
95
110
125
140
155
Yield
CONFIDENTIAL
Challenges in Agricultural Risk Assessment…

However, direct use of historical crop yield distributions is inadequate
for predicting future yields



Technological progress produces a trend in crop yield histories that must be
removed in order to develop appropriate crop yield distributions
Weather variability produces significant crop yield variability that masks the
technology trend, making its removal difficult
How to properly de-trend historical crop yield time series?
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Typical Detrending Approach
110
Technological Improvements
Weather Effect
10
100
5
90
0
80
-5
70
-10
60
50
-15
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Observed Yields
110
100
90
80
70
60
50
0
© 2005 AIR Worldwide Corporation
5
10
15
20
25
30
CONFIDENTIAL
Trend in Corn Yield in Nemaha County, Nebraska
Time Window: 1974-2001
Corn Yield [bushels/acre]
140
120
100
80
60
40
20
1974
1978
© 2005 AIR Worldwide Corporation
1982
1986
1990
1994
1998
2002
CONFIDENTIAL
Trend in Corn Yield in Nemaha County, Nebraska
Time Window: 1974-2003
Corn Yield [bushels/acre]
140
120
100
80
60
40
20
1974

1978
1982
1986
1990
1994
1998
2002
Low yields in 2002 due to a drought situation and lower yields in 2003
result in a less steep linear trend than for the time window 1974-2001
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Trend in Corn Yield in Nemaha County, Nebraska
Time Window: 1982-2003
Corn Yield [bushels/acre]
140
120
100
80
60
40
20
1974

1978
1982
1986
1990
1994
1998
2002
A shorter time window results in an almost horizontal slope
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Summary of Yield Trends Computed for Different
Time Windows, Corn Yield in Nemaha County, NE
Corn Yield [bushels/acre]
140
120
100
80
60
40
20
1974
1978
© 2005 AIR Worldwide Corporation
1982
1986
1990
1994
1998
2002
CONFIDENTIAL
Proposed Weather-based Detrending Method
110
Technological Improvements
Weather Effect
10
100
5
90
0
80
-5
70
-10
60
50
-15
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Observed Yields
110
100
90
80
70
60
50
0
© 2005 AIR Worldwide Corporation
5
10
15
20
25
30
CONFIDENTIAL
Proposed De-Trending Method
Yield(t) = c0 + m*t + c1*AWI(t) + e
c0, m and c1 ……… regression coefficients, m measures the
technology trend
t …………………… time (year)
AWI ………………. AIR Weather Index, weather indicator,
measures weather effects on yield
e ………………….. residual error
This equation is also called the AWI yield model
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Crop Growth Depends on the Integrated Effect of
Weather Over the Entire Growing Season


Weather data during a growing season should be partitioned into time
periods corresponding to plant growth stages
Data need to be analyzed by…

Crop





Corn
Soybeans
Wheat
…
Location


County
Farm
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Weather at Various Stages of Crop Development
Determines Yield
Phenological stages of corn growth
Source: University of Illinois Extension
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Introducing the AIR Agricultural Weather Index
(AWI)


Effects of weather during different plant growth stages are
indexed into a single AWI
AWI is a “score” for the overall quality of the growing season.
Accounts for

Weather variables


Weather-derived parameters


Growing degree days, evapotranspiration
Soil-related parameters


Accumulated precipitation; minimum, maximum and average
temperature
Plant-available water capacity, surface moisture, sub-surface
moisture, runoff, crop moisture
Crop-specific parameters

Water requirements, planting dates, crop phenological stages
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
AWI Computation - Overview
Temperature
Precipitation
Available Water Capacity (Soil)
Water Balance Model
Run Off [inches]
Evapotranspiration [inches]
Time Series of AWI
Surface Moisture %
AWI Model
Crop Specific Data
Soil Moisture Levels
+
Run-Off
Degree Days
Etc.
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Linear Detrending
Models based on just a linear trend

Yield(t) = c0 + m*t + e
Corn Yield Time Series - Nemaha County, NE
140
Historic
Linear
120
Bushels / Acre

R2=.22
100
80
60
40
20
1974
1978
© 2005 AIR Worldwide Corporation
1982
1986
1990
1994
1998
2002
CONFIDENTIAL
Detrending Using a Single Weather Variable
Models based on one or two weather variables

For example, June to August average temperature:
Yield(t) = c0 + m*t + c1*JJA(t) + e
Corn Yield Time Series - Nemaha County, NE
140
R2=.51
Historic
JJA (R2=0.51)
120
Bushels / Acre

100
80
60
40
20
1974
1978
© 2005 AIR Worldwide Corporation
1982
1986
1990
1994
1998
2002
CONFIDENTIAL
AWI Yield Model Detrending
Yield model based on an agricultural weather index

Yield(t) = c0 + m*t + c1*AWI(t) + e
Corn Yield Time Series - Nemaha County, NE
140
120
Bushels / Acre

R2=.77
Historic
AWI-based
100
80
60
40
20
1974
1978
© 2005 AIR Worldwide Corporation
1982
1986
1990
1994
1998
2002
CONFIDENTIAL
County by County Model Comparison: Corn
Linear Trend
JJA Average
Temperature
AWI Yield Model
Regression
Coefficient
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Estimating the Risk of Obtaining Yields Below a
Defined Coverage Level
Yield Distributions
Frequency
AWI
Same coverage level, e.g 65% of mean value, for
different distributions results in different probabilities
(areas under curves)
© 2005 AIR Worldwide Corporation
Log-linear
Linear
Yield (Bushels/Acre)
CONFIDENTIAL
… and Associated Risk (Exceedance Probabilities)
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
AWI Is a “Score” for the Overall Quality of the
Growing Season
Corn – Le Sueur County, Minnesota
15
2002
AIR Weather Index
10
1992
5
0
-5
-10
-15
1993
Current Year
-20
-25
-30
5/1/04
1988
6/1/04
© 2005 AIR Worldwide Corporation
7/2/04
8/2/04
9/2/04
10/3/04
CONFIDENTIAL
Extending AWI Real-time Monitoring with Climate
Forecasts
In addition to historical and
real time distributions,
improved risk management
comes from coupling AWI
analysis with climate forecasts
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Weather and Climate Modeling Resources at AIR

Multi-disciplinary team





Computational horsepower



Climate scientists &
meteorologists
Statisticians
Software engineers
Specialists in risk management
75-processor computer cluster
dedicated to data processing,
analysis, and modeling
Additional database servers and
computers for quality control and
data analysis
Advanced numerical weather
prediction (NWP) models
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
AIR Collects and Processes Over Ten Gigabytes of
Weather Data Daily for Modeling and Analysis
NOAA Port
National Center for
Environmental
Prediction
National
Climatic Data
Center
© 2005 AIR Worldwide Corporation
•
Weather observations
•
Radar observations
•
Severe weather reports
•
Short-term climate data
•
Long-term climate data
•
Numerical forecast
information
CONFIDENTIAL
The Data Are Also Quality Controlled
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
High Quality Weather Data Provide a Solid
Foundation For Agricultural Risk Analysis
Data quality control:
NOAA Port
National Center for
Environmental
Prediction
National
Climatic Data
Center
© 2005 AIR Worldwide Corporation
•
Weather observations
• Check for erroneous data
•
Radar observations
• Check for missing data
•
Severe weather reports
• Replace missing data
where possible
•
Short-term climate data
•
Long-term climate data
•
Numerical forecast
information
Numerical
weather
prediction
Climate
data
archive
Statistical
analysis &
modeling
CONFIDENTIAL
Detailed Soil Data Supplement Weather Data
High resolution (~1 km) soil-specific Available Water Capacity
inches
Source: STATSGO, USDA
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Recap and Applications

The concept of AWI has been proven to explain most of the yield variability due
to weather for corn and soybeans
 AWI de-trended yield distributions reflect more accurately the weather risk
related to growing corn and soybeans
 Besides de-trending yield time series, the AWI Yield Model has further potential
applications:
 AWI can be used as a real time monitoring tool to assess current crop
conditions
 AWI can be used as an estimate of potential yield at harvest, which is
available long before official NASS county yields are published
 AWI can be utilized to objectively determine APH yields for individual farms
and therefore can be included in a procedure to mitigate declining yields due
to successive low yields
 AWI de-trended yields can be utilized to build more accurate yield
distributions for applications in risk assessment
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
Opportunities in Agricultural Risk Management
Brokers
Private
Reinsurers
Producers
(Farmers)
>200 m acres
insured
Crop Insurers
$4 billion
premium
Risk Mgmt
Agency
• Reinsures
• Regulates
• Subsidizes
Agribusinesses
© 2005 AIR Worldwide Corporation
Commodities
Markets
CONFIDENTIAL
… Crop Insurers


Optimizing policy allocations to Standard Reinsurance Agreement risk
sharing funds
Better planning of reserve requirements and reinsurance needs
© 2005 AIR Worldwide Corporation
CONFIDENTIAL
… Reinsurers




More informed underwriting decisions
Better pricing decisions
Better geographical diversification and portfolio management
More effective hedging strategies using commodity futures contracts
© 2005 AIR Worldwide Corporation
CONFIDENTIAL