Bernoulli-Gamma-Gaussian Distribution for Daily Precipitation Forecast Calibration
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Solution Overview
Problem
Daily precipitation data exhibits a complex skew and discrete-continuous mixed distribution, making it difficult to model and analyze using existing methods, as Gamma distribution has no definition at zero and cannot handle the presence of zero values, which are common in daily precipitation data.
Innovation Solution
A method utilizing a Bernoulli-Gamma-Gaussian distribution to calibrate daily precipitation forecasts by performing precipitation occurrence analysis with a Bernoulli distribution, precipitation amount analysis with a Gamma distribution, and normal transformation to construct a bivariate joint normal distribution, allowing for conditional probability distribution and calibrated forecast generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Gamma distribution is used to model monthly precipitation data, then the modeling is simple and effective, but it cannot be applied to daily precipitation data due to the presence of zero values
Solution Approach 1:
The precipitation data is segmented into two parts: a Bernoulli component that models the occurrence (zero or non-zero) and a Gamma component that models the amount when precipitation occurs. This segmentation allows each component to handle its appropriate portion of the data characteristics independently.
Solution Approach 2:
The patent creates a composite probability distribution by combining Bernoulli distribution and Gamma distribution. The Bernoulli-Gamma composite model integrates the discrete nature of precipitation occurrence with the continuous nature of precipitation amount, making it suitable for daily precipitation data with zero values.
2Ease of operation
If conventional Gamma distribution calibration is applied to daily precipitation forecast, then the process is straightforward, but the calibration accuracy is poor due to the discrete-continuous mixed distribution
Solution Approach 1:
The calibration process is segmented into two independent calibration steps: first calibrating the Bernoulli parameter (precipitation occurrence probability) and second calibrating the Gamma parameters (precipitation amount distribution). This segmentation improves accuracy by addressing the discrete-continuous mixed nature of the data.
Solution Approach 2:
The patent introduces an intermediate variable that represents the precipitation occurrence indicator. This intermediary allows the model to first determine whether precipitation occurs (Bernoulli) and then model the amount (Gamma), improving the overall calibration accuracy for daily precipitation data.
3Device complexity
If daily precipitation data is treated as continuous distribution like monthly data, then the analysis is simplified, but the zero values and discrete nature are ignored leading to modeling errors
Solution Approach 1:
The analysis is segmented into two stages: first analyzing the discrete occurrence component using Bernoulli distribution, then analyzing the continuous amount component using Gamma distribution. This segmentation maintains modeling reliability by properly accounting for the discrete-continuous mixed nature while keeping each stage's complexity manageable.
Data Source
AI summary
The present disclosure provides a method for calibrating daily precipitation forecast by using a Bernoulli-Gamma-Gaussian distribution, including the following steps: acquiring daily raw forecast data and observed data; using a Bernoulli distribution to perform precipitation occurrence analysis; using a Gamma distribution to perform precipitation amount analysis on the data that precipitation occurs; using a Gaussian distribution to perform normal transformation on the raw forecast data and the observed data according to the analysis results of the Bernoulli distribution and the Gamma distribution, and obtaining corresponding normalized variables; constructing a bivariate joint normal distribution; constructing a conditional probability distribution of a predictand; and determining whether a forecast to be calibrated is that a precipitation event occurs, determining a conditional probability distribution parameter of the predictand, then randomly sampling the conditional probability distribution of the predictand, and finally obtaining the calibrated forecast by means of inverse normal quantile transform.