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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 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% 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

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A Practical Example

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Water Requirements

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Growth-change in size; Water Requirement Growth and Development of a Maize crop 2 15-2525-4015-2535-4010-15 EstVegTassSilkYldRip Days 15-25 40-65 55-85 100-145 90-130 1 2 3 4 Development –change in phenological stage Most critical stages of maize Water Requirements

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Crop Water Balance WHC PPT i ET i Surplus SW i = SW i-1 + PPT i - ET i Drainage Runoff ET = WR (Water Requirement) ET < WR SW i

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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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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

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Chapter 8 Confidence Intervals Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.

Chapter 8 Confidence Intervals Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.

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