# A Global-Scale Analysis of Hydrologic Extremes using Hidden Climate Indices

Benjamin Renard, David Mcinerney, Seth Westra, Michael Leonard, Dmitri

Kavetski, Mark Thyer, Jean-Philippe Vidal

► To cite this version:

Benjamin Renard, David Mcinerney, Seth Westra, Michael Leonard, Dmitri Kavetski, et al. A Global-Scale Analysis of Hydrologic Extremes using Hidden Climate Indices. EGU General Assembly 2022, May 2022, Vienna, Austria. 10.5194/egusphere-egu22-7122. [https://doi.org/10.5194/egusphere-egu22-7122](https://doi.org/10.5194/egusphere-egu22-7122)

HAL Id: hal-03710318

https://hal.science/hal-03710318

Submitted on 30 Jun 2022

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Hydrologic Extremes at the Global Scale
100-year Analysis and 180-year Reconstruction

B. Renard<sup>1,2,3</sup> D. McInerney<sup>2</sup> S. Westra<sup>2</sup>
M. Leonard<sup>2</sup> D. Kavetski<sup>2</sup> M. Thyer<sup>2</sup> J.-P. Vidal<sup>1</sup>

<sup>1</sup>INRAE, RiverLy Research Unit, Lyon, France

<sup>2</sup>School of Civil, Environmental and Mining Engineering, University of Adelaide, Australia

<sup>3</sup>INRAE, RECOVER Research Unit, Aix-en-Provence, France

EGU General Assembly, 27 May 2022

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

THE UNIVERSITY
of ADELAIDE

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>
<figure><img src="image_7.png" /></figure>

" The frequency and intensity of heavy precipitation events have increased since the 1950s over most land area for which observational data are sufficient [...]"
<figure><img src="image_8.png" /></figure>

" The frequency and intensity of heavy precipitation events have increased since the 1950s over most land area for which observational data are sufficient [...] "

" Confidence about peak flow trends over past decades on the global scale is low [...] "
<figure><img src="image_9.png" /></figure>

" The frequency and intensity of heavy precipitation events have increased since the 1950s over most land area for which observational data are sufficient [...] "

" Confidence about peak flow trends over past decades on the global scale is low [...] "

Water Resources Research

COMMENTARY

10.1029/2018WR023749

If Precipitation Extremes Are Increasing, Why Aren't Floods?

Ashish Sharma¹, Conrad Wasko², and Dennis P. Lettenmaier³
<figure><img src="image_10.png" /></figure>

" The frequency and intensity of heavy precipitation events have increased since the 1950s over most land area for which observational data are sufficient [...] "

" Confidence about peak flow trends over past decades on the global scale is low [...] "

Water Resources Research

COMMENTARY

10.1029/2018WR023749

If Precipitation Extremes Are Increasing, Why Aren't Floods?

Ashish Sharma¹, Conrad Wasko², and Dennis P. Lettenmaier³

"*changes may be more*
*complex than simple trends*"

Water Resources Research

RESEARCH ARTICLE

10.1029/2019WR026575

Key Issue:

* A method from scan statistics is to

Detecting Flood-Rich and Flood-Poor Periods in Annual
Peak Discharges Across Europe

David Lui², Svenja Fischer², Alberto Viglione¹, and Günter Blöchl¹

<figure><img src="image_11.png" /></figure>
# Objectives

Better understand the temporal variability of heavy precipitation (P) and flood (Q) at the global scale by means of an innovative probabilistic model

## 100-year analysis

* Identify common (P+Q) vs. specific (P-only or Q-only) signals behind global extremes

* Look for trends and low-frequency variability in those signals

## 180-year reconstruction

Using 20CRv3, reconstruct probabilities of extreme P/Q since 1836
**P:** a selection from Hadex 2+3
Donat et al. (2013); Dunn et al. (2020)

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

**Q:** a selection from GSIM
Do et al. (2018); Gudmundsson et al. (2018)

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>
**P:** a selection from Hadex 2+3
Donat et al. (2013); Dunn et al. (2020)

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>

**Q:** a selection from GSIM
Do et al. (2018); Gudmundsson et al. (2018)

<figure><img src="image_18.png" /></figure>

* Extract seasonal maxima at each site (SON, DJF, MAM, JJA)
**P:** a selection from Hadex 2+3
Donat et al. (2013); Dunn et al. (2020)

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

**Q:** a selection from GSIM
Do et al. (2018); Gudmundsson et al. (2018)

<figure><img src="image_21.png" /></figure>

* Extract seasonal maxima at each site (SON, DJF, MAM, JJA)

* The rectangle dilemma...
**P:** a selection from Hadex 2+3
Donat et al. (2013); Dunn et al. (2020)

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

**Q:** a selection from GSIM
Do et al. (2018); Gudmundsson et al. (2018)

<figure><img src="image_24.png" /></figure>

* Extract seasonal maxima at each site (SON, DJF, MAM, JJA)

* The rectangle dilemma...
**P:** a selection from Hadex 2+3
Donat et al. (2013); Dunn et al. (2020)

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

**Q:** a selection from GSIM
Do et al. (2018); Gudmundsson et al. (2018)

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

* Extract seasonal maxima at each site (SON, DJF, MAM, JJA)

* The rectangle dilemma...

* In this work, we'll use all data available during 1916-2015
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = \\ \\ \mathbb{E}[Q(s, t)] = \end{cases} $$

**Legend:** varies in space and time
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) \\ \\ \mathbb{E}[Q(s, t)] = \underbrace{c_Q(s)}_{\text{constant (intercept)}} \end{cases} $$

Legend: varies in space and time ; varies in space
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) \\ \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) \end{cases} $$

Legend: varies in space and time ; varies in space ; varies in time
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) \\ \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \underbrace{\lambda_Q(s)\tau(t)}_{\text{the SAME covariate } \tau \text{ affects both P and Q}} \end{cases} $$

Legend: varies in space and time ; varies in space ; varies in time
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) + \pi(s)\delta(t) \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) + \theta(s)\omega(t) \end{cases} $$

Legend: varies in space and time ; varies in space ; varies in time
After suitable data transformation...

$$ \left\{ \begin{array}{l} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) + \underbrace{\pi(s)\delta(t)}_{\text{P-specific covariate and its effects}} \\ \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) + \underbrace{\theta(s)\omega(t)}_{\text{Q-specific covariate and its effects}} \end{array} \right. $$

Legend: varies in space and time ; varies in space ; varies in time
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) + \pi(s)\delta(t) \\ \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) + \theta(s)\omega(t) \end{cases} $$

Legend: varies in space and time ; varies in space ; varies in time

* All covariates are considered unknown and are estimated
  → *Hidden Climate Indices (HCI)*
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) + \pi(s)\delta(t) \\ \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) + \theta(s)\omega(t) \end{cases} $$

Legend: varies in space and time ; varies in space ; varies in time

* All covariates are considered unknown and are estimated
  → *Hidden Climate Indices* (HCI)

* $\tau(t) \sim \text{AR}(1) + \text{trend.}$
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) + \pi(s)\delta(t) \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) + \theta(s)\omega(t) \end{cases} $$

Legend: varies in space and time ; varies in space ; varies in time

* All covariates are considered unknown and are estimated
  → *Hidden Climate Indices* (HCI)

* $\tau(t) \sim \text{AR}(1) + \text{trend.}$ Same for $\delta(t)$ and $\omega(t)$
After suitable data transformation...

$$ \begin{cases} \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) + \pi(s)\delta(t) \\ \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) + \theta(s)\omega(t) \end{cases} $$

Legend: varies in space and time ; varies in space ; varies in time

* All covariates are considered unknown and are estimated
  → *Hidden Climate Indices* (HCI)

* $\tau(t) \sim \text{AR}(1) + \text{trend}$. Same for $\delta(t)$ and $\omega(t)$

* $\lambda(s) \sim \text{Spatial Gaussian Process}$. Same for others
After suitable data transformation...

<figure><img src="image_29.png" /></figure>

Legend: varies in space and time ; varies in space ; varies in time

* All covariates are considered unknown and are estimated
  → *Hidden Climate Indices* (HCI)

* $\tau(t) \sim \text{AR}(1) + \text{trend}$. Same for $\delta(t)$ and $\omega(t)$

* $\lambda(s) \sim \text{Spatial Gaussian Process}$. Same for others

* One component not enough at the global scale → 5 used here
After suitable data transformation...

$$ \mathbb{E}[P(s, t)] = c_P(s) + \lambda_P(s)\tau(t) + \pi(s)\delta(t) + \text{more components...} \\ \mathbb{E}[Q(s, t)] = c_Q(s) + \lambda_Q(s)\tau(t) + \theta(s)\omega(t) + \text{more components...} $$

**Legend:** varies in space and time ; varies in space ; varies in time

* All covariates are considered unknown and are estimated
  → *Hidden Climate Indices* (HCI)

* $\tau(t) \sim \text{AR}(1) + \text{trend}$. Same for $\delta(t)$ and $\omega(t)$

* $\lambda(s) \sim \text{Spatial Gaussian Process}$. Same for others

* One component not enough at the global scale → 5 used here

* (Bayesian + MCMC) estimation
Ex.: SON season, 1st common HCl

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>
Ex.: SON season, 1st common HCl

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>
Ex.: SON season, 1st common HCl

<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /></figure>
<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /></figure>

<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /></figure>

<figure><img src="image_49.png" /></figure>
<figure><img src="image_50.png" /></figure>
Trends and autocorrelations

<figure><img src="image_51.png" /></figure>
# Trends and autocorrelations

<figure><img src="image_52.png" /></figure>
Trends and autocorrelations

<figure><img src="image_53.png" /></figure>
Trends and autocorrelations

<figure><img src="image_54.png" /></figure>
Trends and autocorrelations

<figure><img src="image_55.png" /></figure>

<figure><img src="image_56.png" /></figure>

<figure><img src="image_57.png" /></figure>
Hidden Climate Indices

<figure><img src="image_58.png" /></figure>

<figure><img src="image_59.png" /></figure>

<figure><img src="image_60.png" /></figure>
# 180-year reconstruction

Climate predictors

<figure><img src="image_61.png" /></figure>

Hidden Climate Indices

<figure><img src="image_62.png" /></figure>
<figure><img src="image_63.png" /></figure>

- Using 20CRv3, reconstruction of HCs from 1836

- Hydro-extreme probability maps from 1836
# 180-year reconstruction

<figure><img src="image_64.png" /></figure>

- Using 20CRv3, reconstruction of HCs from 1836

- Hydro-extreme probability maps from 1836
Renard & Thyer (2019). Revealing Hidden Climate Indices from the Occurrence of Hydrologic Extremes. *Water Resources Research*.

Renard et al. (2021). A Hidden Climate Indices Modeling Framework for Multi-Variable Space-Time Data. *Water Resources Research*.

<figure><img src="image_65.png" /></figure>

https://globxblog.inrae.fr/

<figure><img src="image_66.png" /></figure>

https://github.com/STooDs-tools

<figure><img src="image_67.png" /></figure>

This project has received funding from the
European Union's Horizon 2020 research and
innovation programme under the Marie
Skłodowska-Curie grant agreement No 835496
Non-exceedance probability (↔ return period) of the largest event of the season

**Example:** Maximum streamflow in December-January-February for 2 Australian stations

<figure><img src="image_68.png" /><figcaption>Clarke Brooke at Hillview Farm (WA)</figcaption></figure>

<figure><img src="image_69.png" /></figure>
Beta distribution reparameterized in terms of mean $\mu$ and precision $\gamma$

$$ egin{cases} P(s, t) \sim \text{Beta}(\mu_P(s, t), \gamma_P(s)); Q(s, t) \sim \text{Beta}(\mu_Q(s, t), \gamma_Q(s)) \\ \text{logit}(\mu_P(s, t)) = \lambda_{P,0}(s) + \sum_{k=1}^{K} \lambda_{P,k}(s)\tau_k(t) + \sum_{k=1}^{K} \pi_k(s)\delta_k(t) \\ \text{logit}(\mu_Q(s, t)) = \lambda_{Q,0}(s) + \sum_{k=1}^{K} \lambda_{Q,k}(s)\tau_k(t) + \sum_{k=1}^{K} \theta_k(s)\omega_k(t) \end{cases} $$

<figure><img src="image_70.png" /></figure>
P-specific HCs with large trends

SON

<figure><img src="image_71.png" /></figure>

<figure><img src="image_72.png" /></figure>

DJF

<figure><img src="image_73.png" /></figure>

<figure><img src="image_74.png" /></figure>

MAM

<figure><img src="image_75.png" /></figure>

<figure><img src="image_76.png" /></figure>

JJA

<figure><img src="image_77.png" /></figure>

<figure><img src="image_78.png" /></figure>
HCIs with notable autocorrelation

DJF

<figure><img src="image_79.png" /></figure>

<figure><img src="image_80.png" /></figure>

SON

<figure><img src="image_81.png" /></figure>

<figure><img src="image_82.png" /></figure>

MAM

<figure><img src="image_83.png" /></figure>

Effect on P

<figure><img src="image_84.png" /></figure>

Effect on Q
Method: inverted regression

Step 1: $w(s, t)$: climate field at time $t$ and location $s$
$\hat{\tau}_k(t)$: estimated HCI's (from previous analysis)

Goal: estimate $\psi_k(s)$'s in:

$$w(s, t) = \psi_0(s) + \psi_1(s)\hat{\tau}_1(t) + \dots + \psi_K(s)\hat{\tau}_K(t) + \varepsilon(s, t)$$

Step 2: $w(s, t^*)$: climate field at time $t^*$ and location $s$
$\hat{\psi}_k(s)$: estimated from previous step

Goal: estimate $\tau_k(t^*)$'s in:

$$w(s, t^*) = \psi_0(s) + \hat{\psi}_1(s)\tau_1(t^*) + \dots + \hat{\psi}_K(s)\tau_K(t^*) + \varepsilon(s, t^*)$$

Alternatives: LASSO, RIDGE and other form of penalised regression, but first attempts inconclusive
Reconstructions from 20CRv3 (1836-2015)

<figure><img src="image_85.png" /></figure>
Reconstructions from 20CRv3 (1836-2015)

<figure><img src="image_86.png" /></figure>

SON 1840

<figure><img src="image_87.png" /></figure>
Reconstructions from 20CRv3 (1836-2015)

<figure><img src="image_88.png" /></figure>

<figure><img src="image_89.png" /></figure>

SON 1840

<figure><img src="image_90.png" /></figure>
<figure><img src="image_91.png" /></figure>

SON 1840

<figure><img src="image_92.png" /></figure>

SON 1840

<figure><img src="image_93.png" /></figure>

SON 1867

<figure><img src="image_94.png" /></figure>
Reconstructions from 20CRv3 (1836-2015)

<figure><img src="image_95.png" /></figure>

SON 1840

<figure><img src="image_96.png" /></figure>

SON 1840

<figure><img src="image_97.png" /></figure>

SON 1867

<figure><img src="image_98.png" /></figure>

SON 1916

<figure><img src="image_99.png" /></figure>
Reconstructions from 20CRv3 (1836-2015)

<figure><img src="image_100.png" /></figure>

SON 1840

<figure><img src="image_101.png" /></figure>

SON 1840

<figure><img src="image_102.png" /></figure>

SON 1867

<figure><img src="image_103.png" /></figure>

SON 1916

<figure><img src="image_104.png" /></figure>

→ **Reliability**: good (cross-validation); **Sharpness**: poor (P) to good (Q)