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How to make regional climate projections

calibration and evaluation (cross-validation).

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Downscaling and practicalities

Motivation: Get reliable results

Robust: the results do not vary much with different ad hoc choices, e.g. which global climate model runs that are include in the ensemble, decadal regional variability.

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Met Norway Downscaling approach

Methods

Empirical statistical downscaling
Common empirical orthogonal functions (EOFs) and principal component analysis (PCA) provide a framework for regression analyses
Cross-validation

Data

Weather stations – e.g. daily rain gauge measurements
Gridded reanalysis – e.g. ERA5 (as pseudo-observations)
Global climate model simulations – e.g. CMIP5/6
Aggregated data, e.g. seasonal or annual scales

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The MET Norway downscaling approach has been developed based on a set of well known statistical and mathematical methods and concepts such as Empirical statistical downscaling, Principal component analysis or Empirical Orthogonal Function Analysis and cross-validation for evaluation purposes, and in order to implement our approach various data sets are required including Weather stations, Gridded reanalysis, and global and regional climate model simulations.

As the spatial interdependence in the meteorological fields implies that there is a lot of redundant information stored in the data, it can be compressed to just a few numbers of PCs or EOFs describing most of the variability embedded in the climate data.

The MET Norway approach has benefited from the complementary of these two methods in order to study the spatial modes of climate and how they change with time.

How the combination is made, this is what I am going to explain in the following slides.

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Timeline: 1998 - 2021

The strategy and methods have evolved.

Now mature for climate change adaptation.

Different to the rest of downscaling community.

Why this divergence?

Divergence

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Probabilities

Statistical properties

Predictable

Robust

Decision-making

wet-day frequency f_w

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Traditional Empirical-Statistical Downscaling?

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Response or Predictand

- Climate variable

@ weather station

Transfer function (statistical link)

Large scale

Geography (local features)

2m air temperature at Oslo, Norway

Oslo

Predictors

2m air temperature at large scale (10–100 km – ERA5- reanalysis)

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60 years

3 EOFs

3x60 time-series

3 Eigenvalue

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60 years

3 EOFs

3x60 time-series

3 Eigenvalue

Same information,

less space

& GCM evaluation possible

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Principal component analysis or Empirical Orthogonal Functions

Singular Value Decomposition

Space-time meteo. field

Weather Stations

or

Gridded meteo. field

(REA, GCMs)

Source: Figure adapted from Rashid et al.: Climate change projections of maximum temperature in the pre-monsoon season in Bangladesh. Adv. Sci. Res., 1, 1–16, 2021

While Empirical-statistical downscaling tries to connect the large scale climate fields to the local climate, Principal component analysis or EOFs tries to decompose those fields into a set of orthogonal empirical functions or spatial patterns (EOFs) along with a set of associated uncorrelated time series or principal components (PCs).

Both EOF and PCA analyses were used to represent the predictand and the predictor in the traditional empirical statistical downscaling framework. In the case of the predictand, the PCs are derived from the weather station network, however, in the case of the predictor, the EOFs are derived from gridded reanalyses or global climate models.

which is then decomposed into a set of common spatial patterns and eigenvalues along with a set of common principal components (PCs) associated with each pattern and representing the temporal variations.

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MET Norway approach (summary)

→Preserve spatial structures ←

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Predictand

Principal components from weather station

Predictors

Empirical orthogonal functions

of combined reanalyses and

global climate model

Large scale surface air temperature pattern (EOF#1)

Local scale temperature pattern

(eof#1)

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Principal component analysis or Empirical Orthogonal Functions

Singular Value Decomposition

Space-time meteo. field

Weather Stations

or

Gridded meteo. field

(REA, GCMs)

Source: Figure adapted from Rashid et al.: Climate change projections of maximum temperature in the pre-monsoon season in Bangladesh. Adv. Sci. Res., 1, 1–16, 2021

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Validation

e.g. 2m air temperature over Norway (training period)

Leave-one-out Cross-validation

→Very Good model performances

Trend in the principal components

For each principal component:

→Leave-5 years-out from the data

→Train the downscaling model on the remaining data set

→Test the model on the left-5yrs-out and compute the correlation between prediction and original data

→Repeat the procedure to cover the full time period

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MET Norway approach (summary)

→Preserve spatial structures ←

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Predictand

Principal components from weather station

Predictors

Empirical orthogonal functions

of combined reanalyses and

global climate model

Large scale surface air temperature pattern (EOF#1)

Local scale temperature pattern

(eof#1)

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“Robust” results: not sensitive to ad hoc choices

Large ensembles
Evaluation
Various emission scenarios
Several approaches

Different strengths & weaknesses
Different assumptions

10 RCM runs (4 RCMs, 4 GCMs)

Norway

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Another way of evaluation

Making use of available information (CMIP5)

MET Norway approach has been used to downscale 2m air temperature across Norway assuming CMIP5 RCP4.5 (ESD, orange)
Predictions are compared to dynamically downscaled results based on Bias-corrected (Euro)CORDEX simulations for a subset of GCMs (DD, blue curve)
Common GCM subsets have also been extracted for comparisons purposes (ESD, red curve).

Figure: Downscaling of annual mean temperature anomalies over Norway assuming CMIP5 scenarios based on empirical-statistical and bias-corrected dynamical downscaling. The ensembles include the full set and subsets of CMIP5 global model simulations.

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Extension to the full Ensemble of predictions based on CMIP models

Projection of future temperatures over Norway

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CMIP6 ensemble

CMIP5 and CMIP6 ensembles

As the computations are cheap, we applied our downscaling approach to cover the full spectrum of the CMIP simulations to produce future temperature projections over Norway, as displayed in the figure. The y-axis corresponds to the annual mean temperature anomalies and the x-axis correspond to the years from 1950 to 2100. the different colors correspond to the CMIP6 SSPs ensemble, the dashed lines correspond to the ensemble mean and the envelope to 1 standard deviation. As you can see from the figure, Norway is expecting an increase by almost 1 deg towards the end of the 21st century when considering the most optimistic scenario and by almost 5 deg. considering SSP5-8.5 scenario. We have also compared those results with those obtained using CMIP5 scenarios as you can see in the figure to the left showing the ensemble means of both CMIP5 and CMIP6 possible story lines, an interesting feature from the plot is that the future increase in temperature assuming the RCP8.5 is quite similar to the one considering SSP3-7.0 suggesting that these two climate scenarios are equivalent when focusing on temperature.

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ESD-R package

Easy and simple climate downscaling and analyses tool developed in R programming language.
Github repository at https://github.com/metno/esd
Wiki pages at https://github.com/metno/esd/wiki
Docker image

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docker pull abdelkadermet/esd-docker:v_01

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Compressing and Storing the data as EOFs and PCs

Example in R programming environment

Raw data Compressed data

> library(esd)

# Read 2m-air temperature from NCEP reanalysis

> t2m <- t2m.NCEP(latest=TRUE) # Predefined function in esd R package

> class(t2m)

[1] "field" "month" "zoo"

> range(index(t2m))

[1] "1948-01-01" "2022-11-01"

> dim(t2m) # Get the dimensions

[1] 899 10512

>format(object.size(t2m),units = "Mb")

[1] "72.1 Mb"

> library(esd)

# Read 2m-air temperature from NCEP reanalysis

> t2m <- t2m.NCEP() # Predefined function

> class(t2m)

[1] "field" "month" "zoo"

# Convert to EOF object

> eof <- EOF(t2m) # Predefined function

> class(eof)

[1] "eof" "field" "month" "zoo"

> dim(eof) # Get the dimensions

[1] 899 20

> format(object.size(eof),units = "Mb")

[1] "1.8 Mb"

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Limitations

Observational data is mandatory to obtain good results
Tunings require a good expertise in the region of interest

Choice of the spatial domain to characterize the large scale
The choice of the climate variable to downscale may depend on the scientific question of interest

As both, the response and the explanatory variables have been subject to transformations using EOF and PCAs, the choice of the reduced dimensions (i.e. n. of eofs and pcs) characterising most of the spatial and temporal variabilities is often arbitrary

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Summary and Future work

MET Norway approach for downscaling has become more mature and more robust over the last 20+years

Make use of mathematical and statistical properties

Weather statistics as “Climate” variables
Empirical orthogonal functions and Principal components analysis
Common EOFs between reanalyses and global models

New levels of evaluation

Evaluating the transfer function (i.e. the connection between local climate response from observations and large scale from reanalysis.
Evaluating the representation of the large scale predictor in reanalysis and GCM through common EOF analysis,
Comparing the spread of the downscaled ensemble to the variability of the observations as more high resolution gridded products are becoming available.
Test the method against newly developed ML approaches

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Thank you for your attention

abdelkaderm@met.no

E-mail:

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Common-EOFs to represent the large scale X

Common EOF approach in downscaling is introduced to represent the large scale climate features better,
Set of experiments e.g. spatial domain size, number of eofs, etc.
Applied to one global climate model

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What do we downscale or what is the targeted variable?

Parameters of the Probability Density Function

Climate ≈ weather statistics
Statistical properties: more predictable & robust
Information for decision-making

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Common Empirical Orthogonal Functions

Source: Figure adapted from Rashid et al.: Climate change projections of maximum temperature in the pre-monsoon season in Bangladesh. Adv. Sci. Res., 1, 1–16, 2021

Singular Value Decomposition