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STOCHASTIC RAINFALL DOWNSCALING FOR CLIMATE MODELS THE PROBLEM OF SCALES: MISMATCH BETWEEN THE RESOLUTION OF CLIMATE MODELS AND THE SCALES NEEDED FOR IMPACT STUDIES Elisa Palazzi 28/08/2012 Institute of the Atmospheric Sciences and Climate, CNR, Torino

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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.

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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

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Modelling chain: bridging the gap Global Climate Models Global Reanalyses Global Climate Models Global Reanalyses Regional Climate Models High-resolution Climate Scenarios Dynamical downscaling Stochastic downscaling Future projections of water availability Flood forecasting, etc. Model-measurement comparison Hydrological models Rainfall-runoff models Hydrological models Rainfall-runoff models few km 10-30 km 100-120 km non-hydrostatic hydrostatic

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- 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

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GCMs: EC-Earth, spatial res. 1.125

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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.

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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)

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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

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Dynamical Downscaling Nesting 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.

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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

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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

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Stochastic Downscaling Generates 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 precipitation The 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.

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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 procedure Rebora et al., J. Hydrometeorol., 2006

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Input field (model output) Fourier spectrum -Space-time power spectrum (assume a power low form), and estimate or fix the spectral slopes ; ; Fourier and power spectrum extrapolated at lower scales, with random phases ( g: gaussian field obtained by inverting Synthetic precipitation field, obtained by a nonlinear tranformation of g RainFARM procedure in detail

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To force the output field r t be equal to P on scaled larger than the confidence scales, we coarse-grain the field L 0, T 0 Finally, we obtain the output of the downscaling procedure, r, with resolution and , by imposing: r = P, aggregating on L 0, T 0 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

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RainFARM - summary P (input) = predicted or measured large-scale precipitation field L 0, T 0 = reliable spatial and temporal scales r (output)= one stochastic realization of the smmal- scale precipitation field = spatial and temporal scales ( 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.

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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?