Weather and climate variable prediction for management of weather and climate risk

• US 7,249,007 B1
• Filed: 01/15/2003
• Issued: 07/24/2007
• Est. Priority Date: 01/15/2002
• Status: Expired due to Fees

• Current Assignee: John A. Dutton
• Original Assignee: John A. Dutton
• Inventors: Dutton, John A.
• Primary Examiner(s): Rodriguez; Paul
• Assistant Examiner(s): Thangavelu; Kandasamy
• Application Number:
  US10/345,108
• Time in Patent Office: 1,651 Days
• Field of Search: 703/2, 702/3, 702/10, 702/186, 709/224, 705/37, 705/76, 706/15, 706/25, 367/19, 382/224, 455/414.3, 290/44
• US Class Current: 703/2
• CPC Class Codes: G01W 1/10 Devices for predicting weather conditions computers per se G06; display devices G09
• CPC Class Codes: G06Q 20/3821 Electronic credentials
• CPC Class Codes: G06Q 40/04 Trading; Exchange, e.g. stocks, commodities, derivatives or currency exchange

Abstract

A method for simulating the statistical behavior of atmospheric, meteorological, or other geophysical time series having the following steps: (a) assembling an ensemble of observed data; (b) removing any evident cycles; (c) calculating the eigensystem and expansion coefficient according to the Loève theorem; (d) determining the distribution of said coefficients; (e) generating a larger set of coefficients based on the statistical distribution determined in step (d); and (f) using this larger distribution to create an ensemble of simulated atmospheric, meteorological, or other geophysical time series. The procedure can be used to develop a wide variety of climate statistics, including probabilities of severe events such as cold snaps or heat waves covering specific geographic regions and lasting for various periods of time. It can also be used to provide an evolving conditional estimate of the probabilities of extensive climate deviations persisting until the end of a month, season, or other period. The method is particularly useful for generating an extensive sample of simulated time histories to serve as the meteorological or geophysical input to a nonlinear computer model of an application or activity. In all of these applications, the invention provides information for assessing, managing, and mitigating risk arising from weather, climate, or other geophysical phenomena or processes.

Claims

1. A computer implemented method for predicting future time series and conditional probability distributions based upon observed statistical behavior of atmospheric, meteorological, or other geophysical time series comprising:

a) assembling an ensemble of observed time series;

b) removing any evident cycles;

c) calculating Fourier expansion coefficients according to Loè

ve'"'"'s theorem;

d) determining a statistical distribution of said expansion coefficients;

e) generating a larger set of expansion coefficients based on the statistical distribution determined in step (d);

f) using the larger set of expansion coefficients to create an ensemble of simulated atmospheric, meteorological, or other geophysical time series for a period P comprising past and future components;

g) selecting from the ensemble of simulated time series a subset for which at least one statistical moment accumulated over a past component of P is confined to a specific numerical range, thereby providing for a future component of P a set of predicted atmospheric, meteorological, or other geophysical times series and probability distributions conditioned on events in the past component of P; and

h) storing the set of predicted atmospheric, meteorological, or other geophysical times series and probability distributions in files in the computer.

3. The method according to claim 1, wherein the observed times series consist of daily values for every day of a year.

4. The method according to claim 1, wherein the statistical distribution used to represent the said expansion coefficients is a normal distribution.

5. The method according to claim 1, additionally comprising testing the statistical distribution using standard statistical approaches.

6. The method according to claim 5, wherein a testing method is selected from chi-squared, Kolmogorov-Smimov, and Anderson-Darling methods.

7. The method according to claim 1, wherein creating an ensemble of simulated time series comprises:

i) determining a number M of simulated time series needed;

ii) using a random number generator and standard techniques for shaping distributions to generate a matrix {α

_k,n} of expansion coefficients for eigenorder k and simulated record n;

iii) ensuring that the ensembles of expansion coefficients in the columns of the matrix have a statistical distribution analogous to the statistical distribution of step (g);

iv) ensuring that the columns of the matrix are orthonormal; and

v) generating the M simulated time series with the equation

$f<br><br>\left(t\right)=\underset{k=1}{\overset{L}{\sum <br><br>}}<br><br>a_k<br><br>{\mathrm{\varphi <br><br>}}_k<br><br>\left(t\right)$

and using them as a simulated set of meteorological time series.

8. The method according to claim 7, wherein in step (v), the predicted set of meteorological time series is used as meteorological input to a linear or nonlinear model of an application or activity.

9. The method according to claim 1, wherein the predicted time series or probability distributions are used in a decision system.

18. The method according to claim 1, wherein the future component of P corresponds to a time to an end of a month or an end of a season.

2. A computer implemented method for predicting future time series and conditional probability distributions based upon observed statistical behavior of atmospheric, meteorological, or other geophysical time series at a single observation station comprising:

a) assembling a data set of N records of regular observations for one or more atmospheric, meteorological, or other geophysical time series at a single station;

b) removing any annual or other evident cycle, giving N records of variations about the annual or other evident cycle;

c) calculating a covariance matrix using an equation

K(t,s)=E{f(t)f(s)}

d) calculating eigenvalues λ

_n and eigenyectors φ

_n in an equation

${\int <br><br>}_0^Y<br><br>K<br><br>\left(t,s\right)<br><br>{\mathrm{\varphi <br><br>}}_n<br><br>\left(s\right)<br><br>d<br><br>s={\mathrm{\lambda <br><br>}}_n<br><br>{\mathrm{\varphi <br><br>}}_n<br><br>\left(t\right)$

e) calculating Fourier expansion coefficients α

_n with an equation

$a_n={\int <br><br>}_0^Y<br><br>f<br><br>\left(t\right)<br><br><br><br>{\mathrm{\varphi <br><br>}}_n<br><br>\left(t\right)<br><br>d<br><br>t$

to determine an approximate time series

$f<br><br>\left(t\right)=\underset{k=1}{\overset{L}{\sum <br><br>}}<br><br>a_k<br><br>{\mathrm{\varphi <br><br>}}_k<br><br>\left(t\right)$

for each record, thus obtaining an ensemble of expansion coefficients;

f) normalizing said expansion coefficients by dividing each coefficient by the square root of its associated eigenvalue resulting in each ensemble having mean equal to zero and variance equal to one;

g) determining a statistical distribution of said expansion coefficients;

h) generating new sets of expansion coefficients from the statistical distribution determined in step (g), to produce a new ensemble of expansion coefficients;

i) using this new ensemble of expansion coefficients to calculate an ensemble of simulated atmospheric, meteorological, or other geophysical time series for a period P comprising past and future components;

j) selecting from the ensemble of simulated time series a subset for which at least one statistical moment accumulated over a past component of P is confined to a specific numerical range, thereby providing for a future component of P a set of predicted atmospheric, meteorological, or other geophysical times series and probability distributions conditioned on events in the past component of P; and

k) storing the set of predicted atmospheric, meteorological, or other geophysical times series and probability distributions in files in the computer.

10. A computer implemented method for predicting future time series and conditional probability distributions based upon observed statistical behavior of regional, national or global atmospheric, meteorological, or other geophysical time series at multiple observation stations, said method comprising:

a) assembling a data set of N records of concurrent observations for one or more atmospheric, meteorological, or other geophysical time series at each of a set of K observation stations, thereby resulting in K sets of N records;

b) removing any annual or other evident cycle in each of the K sets of N records;

c) calculating a covariance matrix from the K sets of N records;

d) calculating eigenvalues λ

_n and eigenvectors φ

_n of the covariance matrix of the K sets of N records;

e) calculating Fourier expansion coefficients α

_k with an equation

$a_k<br><br>\left(t_i\right)={\int <br><br>}_X<br><br>f<br><br>\left(x,t_i\right)<br><br>{\mathrm{\varphi <br><br>}}_k<br><br>\left(x\right)<br><br><br><br>d<br><br>x$

to determine an approximate time series

$f<br><br>\left(x,t_i\right)=\underset{k=1}{\overset{L}{\sum <br><br>}}<br><br>a_k<br><br>\left(t_i\right)<br><br>{\mathrm{\varphi <br><br>}}_n<br><br>\left(x\right)$

for each observation station, thus creating an ensemble of expansion coefficients;

f) normalizing said expansion coefficients resulting in each ensemble of expansion coefficients having mean equal to zero and variance equal to one;

g) determining a statistical distribution of said expansion coefficients;

h) generating sets of expansion coefficients from the statistical distribution determined in step (g), the sets of coefficients making up a new ensemble of coefficients; and

i) using this new ensemble of expansion coefficients to calculate an ensemble of simulated atmospheric, meteorological, or other geophysical time series at multiple stations for a period P comprising past and future components;

j) selecting from the ensemble of simulated time series a subset for which at least one statistical moment accumulated over a past component of P is confined to a specific numerical range, thereby providing for a future component of P a set of predicted atmospheric, meteorological, or other geophysical times series and probability distributions conditioned on events in the past component of P; and

k) storing the set of predicted atmospheric, meteorological, or other geophysical times series and probability distributions in files in the computer.

11. The method according to claim 10, wherein the concurrent observations consist of daily values for every day of a year.

12. The method according to claim 10, wherein the statistical distribution used to represent said expansion coefficients is a normal distribution.

13. The method according to claim 10, additionally comprising testing the statistical distribution using standard statistical approaches.

14. The method according to claim 13, wherein a testing method is selected from chi-squared, Kolmogorov-Smimov, and Anderson-Darling methods.

15. The method according to claim 10, wherein the simulation step comprises:

i) determining a number M of simulated time series needed;

ii) using a random number generator and standard techniques for shaping distributions to generate a matrix {α

_k,n} of expansion coefficients for eigenorder k and simulated record n;

iii) ensuring that the ensembles of expansion coefficients in the columns of the matrix have a statistical distribution analogous to the statistical distribution of step (g);

iv) ensuring that the columns of the matrix are orthonormal; and

v) generating the M simulated time series with the equation

$f<br><br>\left(x,t_i\right)=\underset{k=1}{\overset{L}{\sum <br><br>}}<br><br>a_k<br><br>\left(t_i\right)<br><br>{\mathrm{\varphi <br><br>}}_n<br><br>\left(x\right)$

and using it as a simulated set of meteorological time series.

16. The method according to claim 15, wherein in step (v), the simulated set of meteorological time series is used as the meteorological input to a linear or nonlinear model of an application or activity.

17. The method according to claim 10, wherein the predicted time series or probability distributions are used in a decision system.