Elisa Palazzi

STOCHASTIC RAINFALL DOWNSCALING FOR CLIMATE

MODELSTHE PROBLEM OF SCALES:

MISMATCH BETWEEN THE RESOLUTION OF CLIMATE MODELS AND THE SCALES NEEDED

FOR IMPACT STUDIES

Elisa Palazzi28/08/2012 Institute of the Atmospheric Sciences and Climate, CNR, Torino

Introduction & outline Precipitation is a key component of the hydrological cycle and one of the most

important parameters for a range of natural and socioeconomic systems. The study of consequences of global climate change on these systems requires scenarios of future precipitation change at the local scale as input to impact models.

Direct application of output from GCMs and RCMs is inadequate because of the coarse spatial resolution and limited representation of mesoscale atmospheric processes, topography, and land-sea distribution.

Of particular concern with precipitation, GCMs exhibit a much larger spatial scale than is usually needed in impact studies and this leads to inconsistencies in rainfall statistics, extremes and small-scale variability, particularly in the presence of complex terrain and heterogeneous orography.

Techniques have been developed to downscale information from GCMs (RCMs) to regional (local) scales. (Dynamical, statistical and stochastic downscaling)

In the absence of full deterministic modelling of small-scale rainfall, stochastic downscaling techniques generate ensembles of possible realizations of small scale rainfall fields starting from a smoother distribution on larger scale.

Small scale fields are consistent with the large scale features of the coarse field and the known statistical properties of the small-scale rainfall fields.

Stochastic downscaling is not a substitute for physically-based dynamical models, also used to better understand rainfall dynamics; it is a way to introduce variability at scales not resolved by physical models.

Introduction & outline

Modelling chain: bridging the gap

• Global Climate Models• Global Reanalyses

Regional Climate Models

High-resolution Climate Scenarios

Dynamical downscaling

Stochastic downscaling

Future projections of water availabilityFlood forecasting , etc.

Model-measurement comparison

Hydrological modelsRainfall-runoff models

few km

10-30 km

100-120 km

non-hydrostatic

hydrostatic

- The most advanced tools currently available for simulating the global climate system (physical processes in the atmosphere, ocean, cryosphere and land surface, and their interactions) and the response of the global climate system to anthropogenic and natural forcings.

- Spatial Resolution: 100-120 km

GCMs

- GCMs spatial resolution is too coarse to capture the local aspects (smooth topography)and it is limited by computational resources.

- The sub-grid physical processes have to be parameterized. Parameterization is a way of describing the aggregated effect of sub-grid processes over a larger scale.Parameterization is one source of uncertainty in simulations of current/future climate.

~ 500 km

~ 110 km

GCMs: EC-Earth, spatial res. 1.125°

An important field: Rainfall

convective cells

Synoptic scale

mesoscale structures

- Highly non-homogeneous phenomenon - Phenomenon organized in hierarchic structures (scaling property of rainfall)

• Convective scale (or microscale) 0-20 km

(convective cells characterized by high precipitation intensity and short duration) embedded within

• Mesoscale 20-200 km (clusters of lower precipitation intensity) embedded within

• Synoptic scale > 1000 km(scale of the general circulation)

- Highly intermittent in space and time (alternating between dry and rainy periods).

No interpolation (nearest neighbors, linear interpolation,

distance-weighted interpolation) is possible.

Need for downscaling

- Climate model simulations/predictions need to be generated at finer scales than those of GCMs if their results are to be of use

- The need is for regional climate scenarios but the most complete models are the coupled GCMs

1) One solution is to employ EMICs, developed to emphasize particular aspects of the climate system. 2) Another is to run the full GCM at a finer resolution (or enhanced resolution in the regions of interest). This would require a very powerful computer (such as the Earth Simulator in Japan) or a very short simulation period (time slice, e.g. 5 years)

Downscaling - generating locally relevant data from GCMs.

3) Another is to downscale climate data: a strategy for generating locally relevant data from GCMs. Downscaling can be done in several ways.

Three categories: - Dynamical downscaling- Statistical downscaling- Stochastic downscaling

Dynamical DownscalingNesting a RCM into an existing GCM.

RCMs work by increasing the resolution of the GCM in a limited area (e.g., the size of western Europe, or southern Africa). They need the climate (temperature, wind etc.) calculated by the GCM as boundary conditions (large scale driving factors) for the regional simulation.

WRF, RAMS, ROMS, COSMO-CLM, PROTHEUS, RegCM, etc.

RCMs can represent the effects of mountains, coastlines, changing vegetation characteristics on the weather much better than GCMs. They can provide weather and climate information at resolutions as fine as 50 km to 20 km.

Predicted changes in winter precipitation over Europe between the present day and 2080. Large reductions over the Alps and Pyrenees are predicted by

the RCM (right), but not the GCM (left)

RCMs vs GCMs- simulate/predict climate/climate changes more realistically, with more detail and with regional differences- are much better at simulating and predicting changes to extremes of weather

Dynamical Downscaling

Statistical Downscaling

Use of statistical regressions. These techniques assume that the relationship between large scale climate variables (e.g. grid box rainfall and pressure) and the actual rainfall measured at one particular raingauge will always be the same. So, if that relationship is known for current climate, the GCM projections of future climate can be used to predict how the rainfall measured at that raingauge will change in the future.

Wilby et al, WRR 1998

Stochastic DownscalingGenerates stochastic ensembles of small-scale predictions from the output of atmospheric models or from a measured field with a coarse spatial or temporal resolution, using different approaches, e.g.:- Random distribution of rain cells- Multifractal cascades based on the theory of scaling in rainfall- Nonlinearly transformed spectral models(Ferraris et al., 2003 – comparison of the various methods and their skill)

Suitable for precipitationThe precipitation fields generated by stochastic procedures are consistent with the large-scale features imposed by meteorological forecast, as the total rainfall volume, and with the known statistical properties of precipitation at multiple scales.

Rainfall Filtered Auto Regressive Model (RainFARM) It belongs to the family of “Metagaussian models”, based on nonlinearly filtering the output of a linear autoregressive process, whose properties are derived from the information available at the large scales.

Extrapolates the large-scale spatio-temporal power spectrum of the meteorological predictions to the small, unresolved scales. The basic idea is to preserve amplitude and phases of the original field at the scales at which we are confident in the limited area meteorological model prediction and to reconstruct the Fourier spectrum at the smaller (unreliable, unresolved) scales.

It is able to reproduce the small-scale statistics of the precipitation – scaling properties of the main statistical moments, spatiotemporal correlation structure of the fields, etc. – and capture the temporal persistence of the observed precipitation at the scales smaller than the reliability scales.

RainFARM procedureRebora et al., J. Hydrometeorol., 2006

Input field (model output)

Fourier spectrum

-Space-time power spectrum (assume a power low form), and estimate or fix the spectral slopes a, b; ;

Fourier and power spectrum extrapolated at lower scales, with random phases (f)

g: gaussian field obtained by inverting

Synthetic precipitation field, obtained by a nonlinear tranformation of g

RainFARM procedure in detail

To force the output field r t be equal to P on scaled larger than the confidence scales, we coarse-grain the field

L0 , T0

Finally, we obtain the output of the downscaling procedure, r, with resolution l and t, by imposing:

r = P, aggregating on L0 , T0

The stochastic nature of the downscaled field, r, is associated with the choice of a set of random Fourier phases (different phases different realizations)

RainFARM procedure in detail

RainFARM - summary

P (input) = predicted or measured large-scale precipitation fieldL0, T0 = reliable spatial and temporal scales

r (output)= one stochastic realization of the smmal-scale precipitation fieldl, t = spatial and temporal scales (l << L0 , t << T0 )

Purpose- to generate a stochastic precipitation field, r

- starting from a larger-scale field, P, reliable at the scales L0 and T0 (the only free parameters of the

method)- such that aggregating r on L0 and T0 give a coarse-

grained field R; R=Pr is modelled in terms of a nonlinear (static) transformation of a linear autoregressive process

Test on RainFARM Coarse graining (degradation) of a high-resolution measured precipitation field, p

p obtained from radar measurements at San Pietro Capofiume, Emilia Romagna, Italy (ARPA-SIM data).

Event of 25 December 2001, starting at 0000 UTC. Data resolution: 1km, 15 min. Maximum scales:128 km, 16 hCoarse-graining 8km, 1h.

Generation of a smoother field, P, used as the input to the downscaling model. Generation of the downscaled field, r

Performance of the downscaling procedure verified by assessing whether the reconstructed fields r reproduce the correct rainfall pattern and the statistical properties of the true field p.

Test on RainFARMRainFARM ensemble (95%)Original

Time evolution of the instantaneous spatial average of the original field p and of an ensemble of 100 realizations of the stochastic field r(x, y, t) produced by RainFARM (for a midlatitude intense rainfall event).

RainFARM ens. mean

Rebora et al., 2006

Test on RainFARM

Spatial and temporal power spectra of the original field p(x, y, t) and an ensemble of 100 realizations of the stochastic field r(x, y, t) produced by RainFARM

Spatial power spectrum

Temporal power spectrum

Rebora et al., 2006

Test on RainFARMSt

atist

ical

mom

ents

Rebora et al., 2006

RainFARM applications

A. Spatio-temporal downscaling of intense rainfall events and operational applications (e.g., forecasting floods in small catchments) (Rebora et al., 2005,2006)

B. Stochastic downscaling as a method to quantitatively compare numerical forecasts and raingauge measurements and verify limited-area model prediction skills (e.g., Brussolo et al., 2008)

C. Climatic and climate change studies: downscaling of GCM and RCM outputs and generation of high-resolution precipitation fields for present and future conditions (Variant of RainFARM for purely spatial downscaling) examples of application to the PROTHEUS (case 1) and COSMO-CLM (case 2) regional models

B. Verification of rainfall forecast via stochastic downscaling

Usually, the verification of meteorological forecasts (e.g., for assessment of hydrological risk) is made through comparison with different observational sources (e.g., raingauge data), by

1- upscaling rain gauge data limited representativeness and large uncertainities2- downscaling the model output to the gauge positions underestimation of the local precipitation variability

Brussolo et al., 2008: RainFARM used to downscale numerical precipitation forecasts (COSMO-LAMI model): 50 high resolution (1h, 850 m) stochastic realizations for each model forecast and comparison with rain gauge data accumulated over 1-h period. One advantage is that ensembles of stochastic fields can be used to characterize the expected variability at each rain gauge position

B. Verification of rainfall forecast via stochastic downscaling

Brussolo et al., 2008

C. Climatic Application – case 1







ERA40

PROTHEUS

RainFarm

Model precipitation vs data from a rain gauge network in the Piedmont and Val d’Aosta regions, Italy

Aim

Is the precipitation produced by the PROTHEUS RCM and spatially downscaled stochastically with the RainFARM procedure able to reproduce the main statistical properties of precipitation observed by a network of rain gauges?

Approach

Before downscaling

After downscaling

1

2

3

PROTHEUS vs rain-gauge data averaged in the model pixels

PROTHEUS vs individual rain-gauge data

Downscaled PROTHEUS vs individual rain-gauge data

Analysis on annual and seasonal basis of:

- Time series of total precipitation- PDFs of total precipitation

- PDFs of precipitation intensity- PDFs of no-rain and rainy periods

- Number of days with no rain.

PROTHEUS Regional Climate Model

Atmosphere-ocean RCM for the Mediterranean basin utmea.enea.it/research/PROTHEUS/

Artale et al., Climate Research, 2012

ATMOSPHERIC MODEL30 km res.

OCEANIC MODEL

COUPLER

PROTHEUS Regional Climate Model

Large scale driver: ERA40

Domain used for this study: (5.5°E-11.5°E, 43°N-47.3°N)

Artale et al., Climate Research, 2012

Cumulated annual precipitation

Rain-gauge networkAverage station altitude [m]

122 rain gauges 1958-2001 Altitude max: 2526 m Altitude min: 127 m Daily resolution

Rain gauges not uniformly distributed in the 33 model pixels Mininum (maximum) number of stations per pixel = 1 (11)

PROTHEUS vs aggregated rain gauges

PROTHEUSRain gauges Monthly

correlation

r= 0.8

JJAMAM

SON

Time series1

The interannual variability of PROTHEUS reflects that of the forcing field (ERA40)


1

0.4 < c < 0.8

Spatial distribution of the correlation

coefficient

Related to the number of rain gauges per pixel

1

Average of total

precipitation

Average of precipitation

intensity

Number of “zeros” (dry

days)

p0 = 0.1 mm/day

Spatially averaged over all model pixels (also true for each pixel)

The model does not produce more rain than the observations, but rain in the model is more frequent.


1PROTHEUSRain gauges

N0_model = 47%N0_obs = 64%

P0= 0.1 mm/day

GOODLESS GOOD

PDFs of total precipitation


YEAR

PROTHEUS vs individual rain gauges

2

PROTHEUSRain gauges

YEAR

GOODLESS GOOD

PROTHEUS vs individual rain gauges

2

PROTHEUSRain gauges

YEAR

GOODLESS GOOD

NEED FOR DOWNSCALING!

RainFARM downscaling: example

30 km ~ 1 km

Precipitation field from PROTHEUS Stochastic realization of the PROTHEUS downscaled field, obtained with RainFARM

Example SON 1958

PROTHEUS downscaled vs individual rain gauges

3 PROTHEUSRain gauges

N0_model = 47% (70%)N0_obs = 72%

P0= 0.1 (2) mm/day

GOODLESS GOOD

YEAR

Number of zeros

Threshold for zero rain: p0=0.1 mm/day

Almost the same: the downscaling procedure is not able to correct the number of

zeros

“Upscaling”

“Downscaling”

P0 (model)= 2 mm/day improves the comparison 72 %(obs) vs 70% (mod)

Summary case 1 The average precipitation of PROTHEUS data has a high bias. There is a strong bias also

in the number of dry days which is lower for the model (47%) than for the obs. (64%), using a threshold of 0.1 mm/day. There is a strong correlation between the interannual variability of model data (reflecting that of the large scale driver) and observed data.

BEFORE DOWSCALING Comparison between PROTHEUS and the rain-gauge data AVERAGED in the model pixels:

The PDFs from model and the obs. agree well (except in winter). Comparison between PROTHEUS and data from individual rain gauges: the PDFs do not

agree well, rain-gauge data show much more extreme events, not captured by the model

AFTER DOWSCALING Comparison between PROTHEUS (downscaled with RainFARM) and data from individual

rain gauges: the PDF agreement improves (except in winter). The number of dry days remain very different in the model and the observations. Using a no-rain threshold of 2 mm/day for the model, the model captures very well the number of dry days.

The stochastic downscaling procedure cannot correct the model outputs at large scale, such as the disagreement in the frequency of precipitation events, particularly evident during the winter season

The high-resolution precipitation fields obtained by downscaling the PROTHEUS output reproduce well the seasonality and the amplitude distribution of the observed rain gauge precipitation during most of the year.

Summary case 1

C. Climatic Application – case 2







CMCC-MED80 km

COSMO-CLM8 km

RainFarm

Model precipitation vs data from individual rain gauges in Africa (CLUVA project)

WEST Domain18°W-15.17°E3.3 °N-16.8°N465x190 grid points

EAST Domains -34.4°E-42.9°E 6.1°N-12.5°N 120x90 grid points

- 34.5°E-41.3°E 11.8°S-2.1°S 95 x 135 grid points

St.Louis (16.5 W, 16.03 N) Ougadougou (1.55 W, 12.37 N)Douala (9.71 E, 4.045 N)

Addis Abeba (38.75 E, 9.02 N)Dar es Salaam (39.27 E, 6.82 S)1950-

2050

Comparison between COSMO-CLM and ground rainfall data

Dar es Salaam and DoualaRainfall annual cycle

Dar es Salaam Douala

RainFARM downscaling: example

Precipitation field from COSMO-CLM Stochastic realization of the COSMO-CLM downscaled field, obtained with RainFARM

Example MAM, area of Doula

Comparison between downscaled COSMO-CLM and ground rainfall data

WHOLE YEAR PDFs

Dar es Salaam Douala

Summary- case 1

Annual rainfall cycle and rainfall PDFs at Dar es Salaam and Douala are only marginally reproduced by COSMO-CLM

Stochastic downscaling of the 8-km COSMO-CLM fields does not improve the agreement with the data

Open questions

Open questionsAt small scales, strong (on-off) intermittency changes the power spectrum and PDF shape and functional law.

PDF

Power Spectrum

Donatella D’Onofrio Jost von HardenbergAntonello Provenzale ISAC-CNR

Vincenzo ArtaleSandro Calmanti ENEA-UTMEA

and to all of you for your attention!

Thanks to

Last slide

Additional

Cluster models & Multifractal cascades

MULTIFRACTAL CASCADES

- Rainfall is assumed to be a multifractal process characterised by spatial discontinuities and variability. -Rainfall variability can be explained as a random cascade process - As multiplicative cascades are themselves random models, they can explain such spatial distributions quite well.

CLUSTER BASED MODELS

- stochastic continuous models for hourly rainfall based on the concept that each rainfall event (storm) is made up of a sequence of clustered rainfall cells, each representing the passage of a convective structure over a given site.

BARTLETT-LEWIS & NYMANN-SCOTT models: both based on Poisson processes

Which the reliable scales are? Due to numerical diffusion a model is not reliable at scales lower than six to four times its resolution

RainFARM procedure

a) Reliable scalesb) Unreliable scales:

the scales resolved by the model, but unreliable due to numerical issues or to the lack of assimilation procedures on these scales

c) Unresolved scales: not resolved by the model and where one needs to know a possible rainfall projection for hydrological purposes

RainFARM

αSlope derived from P and propagated to smaller scales

RainFARM uses simple statistical properties of large-scale rainfall field (e.g., from meteorological predictions), such as the shape of the power spectrum and generates small-scale rainfall fields propagating this information to smaller scales (unreliable and unresolved scales), provided that the input field shows a (approximate) scaling behaviour

SPATIAL Power spectrum of rainfall field

P(X, Y, T), input field, reliability scales L0, T0

PROTHEUS vs ERA40

# st

atio

n/m

odel

pi

xel

ERA40

PROTHEUS

r = 0.8r =0.5

7

33

PDFs of the duration of non-rain periods

3P0=0.1 mm/dayP0=0.1 mm/day (obs)

P0=2 mm/day (mod)

PROTHEUSRain gauges

PROTHEUSRain gauges

PDFs of the duration of rainy periods

3P0=0.1 mm/dayP0=0.1 mm/day (obs)

P0=2 mm/day (mod)

PROTHEUSRain gauges

PROTHEUSRain gauges

Additional: large scale biasWinter Summer

Composite 500hPa isobars during intense rainfall events at the weather station of Torino Caselle: ERA40 (blue) and PROTHEUS (red). Intense rainfall is defined as daily rainfall (observed) > 20mm.

The black boxes represent the PROTHEUS domain. The area between the inner and outer box is where PROTHEUS is nudged to the lateral boundary conditions.

Open question

Stochastic downscaling has been devised to work on space scales between about 30 km and 1 km, and on time scales between about 3 hr and 10 minutes: WHAT HAPPENS ON LARGER OR

SMALLER SCALES?

Elisa Palazzi

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