Stokastinen sadantamalli realististen 2D-sadekenttien luomiseen hydrologisen tutkimuksen tarpeisiin Tero Niemi Aalto-yliopisto Vesi- ja

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1 Stokastinen sadantamalli realististen 2D-sadekenttien luomiseen hydrologisen tutkimuksen tarpeisiin Tero Niemi Aalto-yliopisto Vesi- ja ympäristötekniikka

2 Why rainfall simulation model? Natural hazards Thunderstorms, floods, mudslides, etc. Urban areas Vulnerable Short lead times for warnings Rainfall as input in hydrology High spatiotemporal variability Often ignored or simplified Extreme events are important But also rare IS

3 Aalto Rain Simulator Timeseries for mean rainfall intensity Stochastic model for generating ensembles of realistic design storms Probabilistic simulations Describes the main processes of a storm event Mean rainfall intensity during the event Field spatial structure including anisotropy Field temporal development Field advection Generates rain fields as observed by weather radar But assumes they represent ground observations Decomposition according to spatial scale Advection Spatial structure Recomposition Temporal development 3

4 Design principles Modular structure Easy adaptation for various needs Simplicity as a design principle Simple should be preferred over complicated Simple parameterization Using minimum number of parameters easily estimated from available data Open source licensing Common data format Support for GIS tools NetCDF(?) 4

5 Mean areal rainfall time series Drives the model Distributed in space for each time step High autocorrelations for large lags are required E.g. multiplicative broken-line model (Seed et al. 2000) Obtained by multiplying N simple broken lines Simple broken-line is a linear interpolation of i.i.d. random variables Other options: e.g. AR(p)-model 5

6 Field spatial structure Correlated in space Scaling (multifractality) small features statistically resemble large features ~ defines the structure of the field the higher the more correlated field Power-law filtering N(0,1) noise in Fourier domain (e.g. Bell, 1987) 6

7 Anisotropic extension to field spatial description In simulations rain features are often assumed isotropic, i.e. roundish Real rain features often come as rainbands E.g. orographic forcing or thunderstorm squall lines Method of Niemi et al. (2014) is used to create anisotropic scaling fields Isotropic power-law filters are replaced with anisotropic filters i.e. blobs to rainbands 7

8 Field advection "Torus from rectangle" by Kieff - Own work. Licensed under Public Domain via Wikimedia Commons - Temporally varying advection vectors to x- and y- directions Velocity is assumed constant across the field Advection estimation using e.g. correlation matching between consecutive fields Utilizing Fourier folding ( wraparound ) property and toroidal fields (Pegram & Clothier 2001) Features (at large scale) appear to continue from one side of the field to another

9 Spatial decomposition Rain fields exhibit dynamic scaling Size and lifetime are related : ~ Decomposition according to spatial scale using multiplicative cascade model (Seed, 2003) Gaussian band pass filtering in Fourier domain 9

10 Lagrangian temporal development According to dynamic scaling large features have longer lifetimes, while small features are replaced by new features sooner Temporal development for each spatial scale is modelled separately ARMA(p,q)-model applied separately to each cascade level Problems Lagrangian means we have to move with the rain Correlations after lag-1 are difficult to estimate especially for small features 10

11 Miscellanious concerns Data requirements Highspatial and temporal resolution data is required for parameter estimation Radar data For temporal statistics long sequences of data are preferable Rainfall events are non-homogeneous and non-stationary Model treats them as homogeneous and stationary Aim for minimum number of easily accessible parameters In reality each submodel needs parameters ~25-30 in total Creating fields is easy compared to parameter estimation 11

12 Results Brisbane Simulation Simulation 12

13 Future Applications Input data for hydrological applications, esp. distributed rainfallrunoff modeling Urban environment Ensemble simulations probabilistic framework Future steps Nowcasting; e.g. flash flood warnings Downscaling Operational radar data to very high resolution data for urban environments Utilizing satellite data to create design storms for areas without dense hydrometric networks Extensions Storm arrival process allows for continuous simulations 3rd spatial dimension vertical profile of reflectivity Different advection vectors for individual cascade levels 13

14 Summary Need for a model that produces rain as we want it Scaling models are capable of reproducing observed spatio-temporal statistics Developed model consists of modules describing sub-processes contributing to storm event Numerous applications for the model bright future? 14

15 THANK YOU! Contact: Tero Niemi tero.niemi[at]aalto.fi 15

16 References Bell, T. L. (1987), A Space-Time Stochastic Model of Rainfall for Satellite Remote-Sensing Studies, J. Geophys. Res., 92(D8), PP , doi: /jd092id08p Niemi, T. J., T. Kokkonen, and A. W. Seed (2014), A simple and effective method for quantifying spatial anisotropy of time series of precipitation fields, Water Resour. Res., 50(7), , doi: /2013wr Pegram, G. G. S., and A. N. Clothier (2001), High resolution space time modelling of rainfall: the String of Beads model, J. Hydrol., 241(1 2), 26 41, doi: /s (00) Seed, A. W. (2003), A Dynamic and Spatial Scaling Approach to Advection Forecasting, J.Appl.Meteor., 42(3), , doi: / (2003)042<0381:adassa>2.0.co;2. Seed, A. W., C. Draper, R. Srikanthan, and M. Menabde (2000), A multiplicative broken-line model for time series of mean areal rainfall, Water Resour.Res., 36(8), , doi: /2000wr

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