Statistical Modeling of Compound Events

Description

Tools for extracting occurrences, assessing potential driving factors, predicting occurrences, and quantifying impacts of compound events in hydrology and climatology.

Details

Examples of compound events in hydroclimatology include, but not limited to, compound dry-hot events and compound precipitation and surge (or sea level) events. Take the compound dry and hot event as an example. The function GetDH is used for extracting occurrences based on thresholds of dry and hot indicators. The function DriverLGR is used for assessing potential driving factors of compound events based on logistic regression model. The function PredLGR is used for predicting occurrences of compound events. The function ImpactMG is used for quantifying impacts of compound dry and hot events based on meta-Gaussian model.

Author(s)

Zengchao Hao

References

Hao, Z., et al.(2013). Changes in concurrent monthly precipitation and temperature extremes. Environ. Res. Lett. 8: 034014.

Hao, Z. et al. (2019). A monitoring and prediction system for compound dry and hot events. Environ. Res. Lett., 14:114034.

Hao, Z. et al. (2019). Statistical prediction of the severity of compound dry-hot events based on ENSO . J. Hydrol., 572: 243-250.

Feng, S. et al. (2019). Probabilistic evaluation of the impact of compound dry-hot events on global maize yields. Sci. Total. Environ., 689: 1228-1234.

Assess potential driving factors of compound dry-hot events.

Description

Use the logistic regression model to establish relationships between climate indices (e.g., ENSO) and occurrences of compound dry-hot events.

Usage

DriverLGR(Y,CI)

Arguments

Value

slope parameter and associated p-value

References

Hao, Z. et al. (2019). A monitoring and prediction system for compound dry and hot events. Environ. Res. Lett., 14:114034.

Examples

CI=c(-0.7,-1.2,1.3,0.7,-0.6,1.1,-0.5,0.8,0.5,-0.5,1.6,-1.8,-0.5,-1.4,-0.1,2.2,-0.7,-1.1, 0.6, -1.7)
Y=c(0,0,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0 )
res<-DriverLGR(Y,CI)

Univariate empirical probability

Description

Compute univariate empirical probability

Usage

Empdis1(mp)

Arguments

Value

The empirical probability

References

Hao, Z. et al., 2019a. Statistical prediction of the severity of compound dry-hot events based on El Ni??o-Southern Oscillation. J. Hydrol., 572, 243-250.

Examples

mp=matrix(rnorm(120,0,1),ncol=1)
nd<-Empdis1(mp)

Bivariate empirical probability

Description

Compute bivariate empirical probability

Usage

Empdis2(mp,mt)

Arguments

Value

The bivariate empirical probability

References

Hao, Z. et al., 2019a. Statistical prediction of the severity of compound dry-hot events based on El Ni??o-Southern Oscillation. J. Hydrol., 572, 243-250.

Examples

mp=matrix(rnorm(120,0,1),ncol=1)
mt=matrix(rnorm(120,0,1),ncol=1)
nd<-Empdis2(mp,mt)

Occurrence of compound dry-cold events

Description

Extract compound dry-cold occurrences based on thresholds of precipitation and temperature. The binary variable of the dry and cold (DC) event can be obtained.

Usage

GetDC(mp,mt,threp,thret)

Arguments

Value

The occurrence of compound wet-hot event (0-1 binary variable)

References

Hao, Z. et al (2013). Changes in concurrent monthly precipitation and temperature extremes. Environ. Res. Lett., 8(3): 034014.

Examples

mp=matrix(rnorm(120,0,1),ncol=1)
mt=matrix(rnorm(120,0,1),ncol=1)
threp=20
thret=20
DC<-GetDC(mp,mt,threp,thret)

Occurrence of compound dry-hot events

Description

Extract compound dry-hot (DH) occurrences based on thresholds of precipitation and temperature. The binary variable of the DH (or dry-warm) event can be obtained.

Usage

GetDH(mp,mt,threp,thret)

Arguments

Value

The occurrence of compound dry-hot events (0-1 binary variable)

References

Hao, Z. et al. (2018). A multivariate approach for statistical assessments of compound extremes. J. Hydrol., 565: 87-94.

Hao, Z. et al. (2019). A monitoring and prediction system for compound dry and hot events. Environ. Res. Lett., 14:114034.

Examples

mp=matrix(rnorm(20,0,1),ncol=1) # 20-year precipitation of a specific month (e.g., August)
mt=matrix(rnorm(20,0,1),ncol=1) # 20-year temperature of a specific month (e.g., August)
threp=20
thret=80
DH<-GetDH(mp,mt,threp,thret)

Occurrence of compound wet-hot events

Description

Extract compound wet-hot (WH) occurrences based on thresholds of precipitation and temperature.The binary variable of the WH (or wet-warm,WW) event can be obtained.

Usage

GetWH(mp,mt,threp,thret)

Arguments

Value

The occurrence of compound wet-hot events (0-1 binary variable)

References

Hao, Z. et al (2013). Changes in concurrent monthly precipitation and temperature extremes. Environ. Res. Lett., 8(3): 034014.

Examples

mp=matrix(rnorm(120,0,1),ncol=1)
mt=matrix(rnorm(120,0,1),ncol=1)
threp=80
thret=80
WH<-GetWH(mp,mt,threp,thret)

Impacts under droughts and hot extremes

Description

Use the meta-Gaussian model to construct conditional distributions of the impact variable (Y) given drought and hot conditions P(Y|PRC,TEM).

Usage

ImpactMG(PRC,TEM,Y,u0)

Arguments

Value

A vector of conditional mean and variance evaluated at u0

References

Feng, S. et al. (2019). Probabilistic evaluation of the impact of compound dry-hot events on global maize yields. Sci. Total. Environ., 689: 1228-1234.

Hao, Z. et al. (2018). A multivariate approach for statistical assessments of compound extremes. J. Hydrol., 565: 87-94.

Examples

PRC=matrix(rnorm(60,0,1),ncol=1)
TEM=matrix(rnorm(60,0,1),ncol=1)
Y=matrix(rnorm(60,0,1),ncol=1)
u0=c(-1.2,1.2) # Speficify the compound dry-hot condition
ImpactMG(PRC,TEM,Y,u0)

Likelihood multiplication factor (LMF) or probability multiplication factor (PMF) of compound dry-hot events

Description

Compute joint probabilities of compound dry-hot events and the independent case.

Usage

LMFDH(mp,mt,threp,thret)

Arguments

Value

Joint probability of DH divided by that of independent case

References

Zscheischler, J. and S. I. Seneviratne (2017). Dependence of drivers affects risks associated with compound events. Science Advances, 3(6): e1700263.

Examples

mp=matrix(rnorm(120,0,1),ncol=1)
mt=matrix(rnorm(120,0,1),ncol=1)
threp=20
thret=80
res<-LMFDH(mp,mt,threp,thret)

Prediction of compound event occurrences

Description

Fit the logistic regression model (LGR) based on occurrences of compound events (Y) and climate index (CI).The output is the predicted probability of compound event occurrence for the given climate index value CI0

Usage

PredLGR(Y,CI,CI0)

Arguments

Value

Probability of occurrences estimated at CI0

References

Hao, Z. et al. (2019). Statistical prediction of the severity of compound dry-hot events based on ENSO . J. Hydrol., 572: 243-250.

Examples

CI=c(-0.7,-1.2,1.3,0.7,-0.6,1.1,-0.5,0.8,0.5,-0.5,1.6,-1.8,-0.5,-1.4,-0.1,2.2,-0.7,-1.1, 0.6, -1.7)
Y=c(0,0,1,1,0,0,0,0,0,0,1,0,1,0,0,1,0,0,0,0 )
PredLGR(Y,CI,2)

Standardized Compound Event Indicator (SCEI)

Description

Compute SCEI based on monthly precipitation and temperature.

Usage

SCEI(mp,mt,ts)

Arguments

Value

The monthly SCEI series

References

Hao, Z. et al., 2019a. Statistical prediction of the severity of compound dry-hot events based on El Ni??o-Southern Oscillation. J. Hydrol., 572, 243-250.

Examples

mp=matrix(rnorm(120,0,1),ncol=1)
mt=matrix(rnorm(120,0,1),ncol=1)
ts=3; # ts<=12 otherwise you should revise line 98
nd<-SCEI(mp,mt,ts)
d=cbind(mp,mt,nd)
testd<-matrix(d, ncol=3,byrow=FALSE)