A quantitative probabilistic interpretation of SARCOF forecasts for agricultural production

A quantitative probabilistic

interpretation of SARCOF forecasts for agricultural

production USGS/FEWSNET, UCSB, SADC RRSU, SADC DMC

Presented by Tamuka Magadzire

Outline Objective Background FACT – probability and rainfall

amounts Crop Water Requirements Example study for FMA 2003 Future work

Objective

COF forecast p(crop success)

To generate a crop-specific interpretation of the COF forecasts

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

Probability Distribution Function

Bar chart gives indication of frequency of events

Can be used to construct derive probabilities Increasing

quantity

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.

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:

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

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

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

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?

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

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

A Practical Example

Water Requirements

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

Crop Water Balance

WHC

PPTi ETi

Surplus

SWi = SWi-1 + PPTi - ETi

Drainage

Runoff

ET = WR (Water Requirement)

ET < WR

SWi

Water requirements satisfaction index

Based on water balance model. WRSI correlates well to yield in water-limited areas.

Examples

Climatological probability of exceedence of 80% of Water Requirements for (a) 120-day maize and (b) 90-day sorghum in JFM

A study for FMA 2003

A study for FMA 2003

A study for FMA 2003

A study for FMA 2003

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