# Matching the scales: coupling local observational data to global hydrological model

Quentin Dassibat

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## To cite this version:

Quentin Dassibat. Matching the scales: coupling local observational data to global hydrological model. CIROQUO - Consortium industrie recherche pour l'optimisation et la quantification d'incertitude pour les données onéreuses, May 2024, Saint-Etienne (FR), France. hal-04735187

HAL Id: hal-04735187

https://hal.science/hal-04735187v1

Submitted on 14 Oct 2024

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# Matching the scales: coupling local observational data to Global Climate Model outputs.

A case study on the assessment of river integrity against the Planetary Boundaries framework in the Sud-Loire region, France

Quentin DASSIBAT¹,²,³,⁴, Natacha GONDRAN¹,², Fabrice BARDET¹,³

1. EVS - Environnement, Ville, Société - UMR CNRS 5600

2. Mines Saint-Étienne MSE - École des Mines de Saint-Étienne

3. ENTPE - École Nationale des Travaux Publics de l'État

4. EUL - Ecole Urbaine de Lyon - LabEx Institut Convergences

<figure><img src="image_3.png" /><figcaption>2023. Richardson et al. Earth Beyond Six of Nine Planetary Boundaries.</figcaption></figure>

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

## 2- How is done the environmental assessment of a sub-global system against the FW-PB?

* LCIA-based Method (Bjorn et al., 2015, 2020): coerce PB metrics to LCIA metrics

* PB-based Method (Ryberg et al., 2018, 2020): coerce LCIA metrics to PB metrics

<figure><img src="image_5.png" /><figcaption>Quantify carrying capacity</figcaption></figure>

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

→ **Key research questions**

* These models have not been calibrated for the studied region (Sud-Loire region, France): What are they worth?

* These models accounts for a limited set of anthropogenic pressures: How to enlarge this set?

* Uncertainty quantification is rarely made for it is highly difficult: What uncertainty in an Absolute Assessment of the FW-PB?

Where $I_S$ is the environmental impact of system S, EF is the $x^{th}$ elementary flow fulfilling the functional unit of S and CF is the characterization factor

## 1- What are Planetary Boundaries?

Keep the Earth system within a Holocene-like climate

Planetary Boundaries are a framework first published in the journal Nature in 2009 by lead author Johan Rockström. The aim of this framework is to identify thresholds on the key regulatory variables of the Earth System that define the Holocene climate era. These threshold make up a so-called Safe Operating Space (SOS) within which humanity can keep living well.

The Freshwater Planetary Boundary (FW-PB) aims at sustaining ecological functioning of rivers

In the 2023 revision of the framework, Rockström and his colleagues use the concept of Environmental Flow Requirement to set a threshold on human activities destabilizing flow regimes of rivers from their Holocene-like state (called pristine flow).

<figure><img src="image_7.png" /><figcaption>2010. Poff & Zimmerman, Ecological responses to altered flow regimes.</figcaption></figure>

River-dependant biosphere plummets beyond a 20-50% flow change

<figure><img src="image_8.png" /><figcaption>2011. Richter et al., A presumptive standard for environmental flow protection.</figcaption></figure>

20%-of-flow approach to preserve ecological functioning

<figure><img src="image_9.png" /><figcaption>At the global scale</figcaption></figure>

The global FW-PB is not overshot if $\Gamma = 0$

$\Gamma = \sum_{i,t} \gamma_{i,t}$ and

$\gamma_{i,t} = \begin{cases} 0 & \text{if } |QDIST_{i,t} - QPRIST_{i,t}| \le 1.2QPRIST_{i,t} \\ 1 & \text{else} \end{cases}$

## 3- Research Question

### How can point-like observational data from on-site gauging stations be coupled to pixel-like GCM's outputs?

#### 3.2.4 Numerical development of relio in Python³

<table><thead><tr><th>Modules</th><th>Total Run Time</th><th>Peak Memory Usage</th></tr></thead><tbody><tr><td>Hydrographic</td><td>aprox. 32'45</td><td>aprox. 25 Go</td></tr><tr><td>Convolution</td><td>aprox. 187'</td><td>aprox. 25 Go</td></tr><tr><td>Display</td><td>aprox. 445'</td><td>aprox. 25 Go</td></tr><tr><td>relio.py</td><td colspan="2">cross functions and utilities</td></tr></tbody></table>

Total Run Time for $1 \le t \le 12$, DIST model run, 3 watersheds out of aprox. 180 (i.e. $G_v$ for $1 \le v \le 3$)

## 4- Results

### 4.1 relio vs invdist resampling performances

Model performances were assessed through resampling a subset of gauging stations.

* invdist: $(x_{j,t})$ takes one station for each flow percentile

* relio: $(x_{j,t})$ takes the biggest station by watershed

<figure><img src="image_10.png" /></figure>

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

* invdist overestimates discharges

* relio has an improved residual peak density

* relio residuals are centered

* relio variance of residuals is smaller

<figure><img src="image_12.png" /><figcaption>Box 2. relio resampling technic: linear convolution</figcaption></figure>

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

### 3.1 Case study: resampling the 7500-m WBM model to a 30-m grid cell

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

## 4- Results

### 4.2 WBM resampling comparison of relio vs invdist

<figure><img src="image_15.png" /></figure>

* Resampled WBM model shows poor performances against observed discharges

* relio has an improved proportional residual peak density

* WBM model shows a inner calibration limitation for small watersheds, which resampling technics cannot overcome

* relio can still be used to assess water discharge at any given point in space, which is convenient for MAUP problem in spatial LCIA.

### 3.2 A mixture resampling technic

#### 3.2.1 Physical resampling technics in the field of Earth System Modelling

Global Climate Models can be “resampled” to Local Climate Models with the same physical equations but over a smaller sized region (no more than 12x smaller), which allows for higher resolution input datasets to be used. Since the studied region is a subset of a closed system it is an open system, which represents the modelling challenge of setting the Boundary Conditions Zone.

#### 3.2.2 Statistical resampling technics in the field of GIS applications

These are deterministic technics that lay on the principle of a distance-weighted relationship between known and unknown quantities: the further an unknown point is from a known point, the less probable the value of the unknown is to be close to that of the known point.

$$ \text{invdist} \qquad y_{i,t} = \sum_i \lambda_i \cdot \hat{x}_{j,t} \qquad \lambda_i = \frac{(d_{ij}^p)^{-1}}{\sum_j (d_{ij}^p)^{-1}} $$

($\hat{x}_{j,t}$) $1 \le j \le m, 1 \le t \le 12$ is the set of known points in domain $D_{source}$ of m pixels.

($\hat{x}_{j,t}$) are estimated from the set $(x_{j,t})$ of pixels, through a centroid pixel-to-point conversion.

($y_{i,t}$) $1 \le i \le n, 1 \le t \le 12$ is the set of unknown points in domain $D_{dest}$ of n pixels.

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

#### 3.2.3 Proposal for a mixture resampling technic

The idea of a distance-weighted relationship in GIS statistical technics is kept but the domain is acknowledged to be partly continuous only along the channel network, and is not independent of contiguous domains (i.e. boundary conditions). Hence it is a physically-coerced statistical resampling.

$$ y_{i,t} = q(\rho_i, \hat{x}_{j,t} : \alpha_a, \alpha_b, \beta_p, \delta) = \begin{cases} \emptyset & \text{if } i \notin G_w \\ \rho_i \cdot \max_{j \in G_w} \{\hat{x}_{j,t}\} & \text{if } i \in G_w \end{cases} \qquad \rho_i = \frac{a_i}{\max_{i \in G_w} \{a_i\}} $$

$\hat{x}_{j,t} = (x_{j,t})_{i \in \Omega_j}$ where $\Omega_j$ is the set of outflow outlets in pixel $j \in D_{source}$. Likewise $\Phi_j$ is the set of transfer outlets in pixel $j$.

$$ \forall i \in \Omega_j, \quad x_{i,t} = x_{j,t} \cdot \omega_j \cdot \frac{a_i}{\sum_{i \in \Omega_j} a_i} \quad \text{where } \omega_j = \frac{\sum_{i \in \Omega_j} a_i}{\sum_{i \in \Phi_j} a_i} $$

$$ \forall j \in D_{source}, \quad x_{j,t} = x_{j,t} \cdot (\omega_j \cdot \phi_j) \quad \text{where } \phi_j = \frac{\sum_{i \in \Phi_j} a_i}{\sum_{i \in \Omega_j} \sum_{i \in \Phi_j} a_i} $$

<figure><img src="image_17.png" /><figcaption>$\alpha_a$ : flow accumulation threshold</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>$\beta_p$ : vector of boundary conditions (inflows)</figcaption></figure>

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Environnement,
Ville, Société
UMR 5600

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ÉCOLE URBAINE
DE LYON
Université de Lyon

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SIS
SCIENCES
INGÉNIERIE SANTÉ
UNIVERSITÉ DE LYON

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ÉCOLE
DOCTORALE
488