Development of a Parametric Regional Multivariate Statistical Weather Generator for Risk Assessment Studies in Areas with Limited Data Availability
Abstract
:1. Introduction
2. Literature Review
3. Model Description
3.1. Precipitation States
3.2. Precipitation Amount
3.3. Maximum and Minimum Air Temperature
3.4. Wind Speed Magnitude
4. Model Implementation
4.1. Preprocessing: Parameter Estimation and Matrix Preparation
- 1)
- Assume , , and , in which ω is a non-positive-definite correlation matrix.
- 2)
- Let .
- 3)
- Find , and , such that .
- 4)
- Replace the negative eigenvalues of by a small positive value to construct .
- 5)
- Set and . Then, replace all diagonal elements with 1.
- 6)
- Test whether is a positive-defined matrix or not. If not, repeat the steps from two to six by making and .
- 1)
- Generate the standard normal random deviate set y; y ~ N (0,1).
- 2)
- Use y with Equations (1) and (2) to identify the dry and wet days.
- 3)
- Generate a standard normal random deviate set x; x ~ N (0,1).
- 4)
- Apply the AR(1) of arbitrary values between –1 and 1 (e.g., φ’z).
- 5)
- Obtain the anomalies z by standardizing x of Step 4.
- 6)
- Apply Equations (6) and (7) to obtain T’X.
- 7)
- Calculate the AR (1) of TX (e.g., φ’v) and plot versus the φ’z, then regress them.
- 8)
- Use the regression equation obtained in Step 7 with the observed value φv (e.g., 0.82) to determine φz. In this case, 0.88 (as shown in Figure 2b).
4.2. Postprocessing Stage: Variable Generation
- 1)
- Use Equation (13) with ωs to generate Y anomalies that denote S. The length of Y denotes the day number of the generated time series. In this case, the user can generate any length (independently of the historic observation length).
- 2)
- Use Equations (1) and (2) with the estimated FTMC parameters ( and ) to identify the dry and wet day occurrences.
- 3)
- Apply Equation (13) with ωv to generate Z anomalies that denote the variable values. Of course, the length of Z must be the same of Y.
- 4)
- Obtain P for the wet days using Equations (3) and (4) with the estimated parameters µp, σp, and ιp. This will make sure the generated P have similar observed statistics.
- 5)
- Apply the AR (1) with coefficients Фz for Tx, TN and the WS anomalies to consider the auto-correlation magnitude for the variables.
- 6)
- Re-standardize the anomalies for TX and TN, as follows:
- 7)
- Apply Zstd in Equations (6)–(9) with the estimated parameters µX0, µX1, µN0, µN1, σX0, σX1, σN0, and σN1 to calculate Tx and TN.
- 8)
- Convert the anomalies Z of the WS to be uniformly distributed between 0 and 1 ZU, as follows:
- 9)
- Apply ZU in Equations (11) and (12) with the estimated parameters α0, α1, β0, and β1 to calculate the WS. Steps 3 to 9 enable us to preserve the observation statistics of Tx, TN and the WS and the spatial, temporal, and cross correlations with consideration of the precipitation states effects through decomposing their distribution functions.
- 10)
- Repeat Steps 1 to 9 for all months m.
5. Case Study and Data
6. Results and Discussion
6.1. Model Performance Evaluation
6.2. Model Validation
6.3. Model Comparison
6.4. Simulation of the Future Forecasting Scenarios
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Waheed, S.Q.; Grigg, N.S.; Ramirez, J.A. Development of a Parametric Regional Multivariate Statistical Weather Generator for Risk Assessment Studies in Areas with Limited Data Availability. Climate 2020, 8, 93. https://doi.org/10.3390/cli8080093
Waheed SQ, Grigg NS, Ramirez JA. Development of a Parametric Regional Multivariate Statistical Weather Generator for Risk Assessment Studies in Areas with Limited Data Availability. Climate. 2020; 8(8):93. https://doi.org/10.3390/cli8080093
Chicago/Turabian StyleWaheed, Saddam Q., Neil S. Grigg, and Jorge A. Ramirez. 2020. "Development of a Parametric Regional Multivariate Statistical Weather Generator for Risk Assessment Studies in Areas with Limited Data Availability" Climate 8, no. 8: 93. https://doi.org/10.3390/cli8080093