A quantitative probabilistic interpretation of SARCOF forecasts for agricultural production
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Transcript of A quantitative probabilistic interpretation of SARCOF forecasts for agricultural production
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A quantitative probabilistic
interpretation of SARCOF forecasts for agricultural
production USGS/FEWSNET, UCSB, SADC RRSU, SADC DMC
Presented by Tamuka Magadzire
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Outline Objective Background FACT – probability and rainfall
amounts Crop Water Requirements Example study for FMA 2003 Future work
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Objective
COF forecast p(crop success)
To generate a crop-specific interpretation of the COF forecasts
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Background Analysis based on two concepts
Analysis of the relationship between probability and rainfall amounts
Enabled by the FEWSNET AgroClimatology Toolkit (FACT)
Crop water requirements, and their relationship with yield
Derived from Water Requirements Satisfaction Index (WRSI) analysis
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Probability Distribution Function
Bar chart gives indication of frequency of events
Can be used to construct derive probabilities Increasing
quantity
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Probability Distribution Function
Area under the curve equals probability of an event falling within a range of values
Normal Distribution-2 0 2
0.0
0.1
0.2
0.3
0.4
We can model the rainfall distribution using a pdf with appropriate parameters. This pdf can be used to completely describe the rainfall distribution, and the probability of rainfall of different amounts.
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Probability Distribution Function
Has been shown to perform well for rainfall
Never less than zero Can be very flexible in form Described by only 2
parameters – shape and scale
We use Gamma Distribution rather than normal distribution because:
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Probability-Accumulation Relationship
Fitting a probability distribution to rainfall events at a location allows for the querying of the likelihood of a particular event
Similarly, the amount of rainfall corresponding to a particular likelihood can be derived
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Finding Probability Use x-axis to locate
the rainfall accumulation of interest
Trace up until it meets the curve
Trace left to find the probability of being less than the amount
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Finding Rainfall Use the y-axis to
find the likelihood of interest
Trace right to the curve
Trace down to find the accumulation associated with the likelihood
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Obstacle How can a
relationship between historical data and forecast probabilities be made?
Is it possible to make a meaningful connection between forecasts and accumulations?
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Drawing From Terciles Hypothetical forecast
for the region calls for 45/35/20
Draw user-defined number of samples randomly from theoretical terciles in proportion to forecast
New distribution parameters calculated
33% 33% 33%
DRY MID WET 20 35 45
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Old v New Distribution Old shape: 2.59 Old scale: 13.64 New shape: 3.12 New scale: 13.04 New distribution
reflects lower probability of dryness and increased wetness 5 30 55 80 105 130 155 180
0.000
0.005
0.010
0.015
0.020
Old Theoretical DistNew Theoretical Dist
Old and New Theoretical Distributions
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A Practical Example
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Water Requirements
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Gro
wth
-cha
nge
in
size
; W
ater
Req
uire
men
t
Growth and Development of a Maize crop
2
15-25 25-40 15-25 35-40 10-15
Est Veg Tass Silk Yld Rip
Days
15-2540-65
55-85
100-145
90-130
1
2
34
Development –change in phenological stage
Most critical
stages of maize
Water Requirements
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Crop Water Balance
WHC
PPTi ETi
Surplus
SWi = SWi-1 + PPTi - ETi
Drainage
Runoff
ET = WR (Water Requirement)
ET < WR
SWi
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Water requirements satisfaction index
Based on water balance model. WRSI correlates well to yield in water-limited areas.
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Examples
Climatological probability of exceedence of 80% of Water Requirements for (a) 120-day maize and (b) 90-day sorghum in JFM
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A study for FMA 2003
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A study for FMA 2003
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A study for FMA 2003
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A study for FMA 2003
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Future work Incorporating cropping areas into forecast Producing a single crop forecast for most
major cereal crops Interpreting the SARCOF-7 forecast, and
future COF forecasts in similar manner