Statistical downscaling of surface temperature field in the region - PowerPoint PPT Presentation

Statistical downscaling of surface temperature field in the region of La Manche Chavro A.I.*, Nogotkov I.V.*, Dmitriev E.V.*, Khomenko G.A.** * Institute of Numerical Mathematics, Russian Academy of Sciences, Russia ** Universit é du Littoral C ô te d’Opale, Laboratoire LPCA, France

Plan of the talk • Downscaling techniques • Statistical model reliability • Treatment of data gaps • Numerical experiments • Conclusions • Perspectives

Downscaling • The global climate models give only a large-scale values of the meteoparameters • The number of the regional extreme events increases because of the climate changes • Downscaling allows estimating the regional consequences of global climate changes

Types of downscaling • Statistical • Dynamical Dynamical or Simulations of global Retrieved small- statistical model model scale field Downscaling is the reconstruction of the small-scale variables from large-scale parameters. It is also the procedure of interpolation from the model grid to irregular greed of measurements.

Statistical downscaling Inverse problem = Al + ε g g - large-scale field - small-scale field l A - averaging operator ε - error of averaging Retreval techniques operator A is known Regularisation techniques Biased reduction Retreival of the problem in the sub-space ~ = + + − − * * l El C A ( AC A C ) ( g Eg ) εε Principal components analysis ll ll SVD analysis Unbiased reduction ~ − − − = Canonical correlation analysis * * l ( A C A ) A C g εε εε operator A is unknown Filtering of the elements that contains information Multiple regeression ~ − = + − Steapwise regression l El C C ( g Eg ) l g gg

Statistical downscaling The statistical model allows : Example: comparison of the statistical downscaling with a polinomial interpolation in Moscow - To retrive the optimal estimate of the small-scale parameters - To estimate a priori erreur of the solution; - To test the solution stability ; - To make an estimation of quanity of information in the input data Statistical dowscaling is signifially more quick than a dynamical dowscaling Downscaling relative error is 20% Chavro A.I., Nogotkov I.V., Dmitriev E.V. Statistical In general the statistical model for reconstruction of surface temperature downscaling is more exact than a extremes at meteorological stations in the Moscow polinomial interpolation region // Russian Meteorology and Hydrology . 2008. (In the press)

Prediction of the most significant errors for the statistical do wnscaling For the downscaling of mean monthly temperature Reliability of the model ∞ ∫ α = ( ) m Fiabilit é du mod è le L'erreur de downscaling ( g ) p ( t ) dt χ 2 2 − 1 / 2 C g gg hypothesis alternative ~ g ~ N ( 0 , C ) g ~ N ( a , C ), ˆ ≠ > a 0 , C C The parameter « reliabilite of the model » can be For the downscaling of mean dayly temperature used for the a priori detection of situations when the error of downscaling significantly overcomes the expected value. Dmitriev E.V. , Nogotkov I.V., Rogutov V.S., Khomenko G., Chavro A.I. Temporal error estimate for statistical downscaling regional meteorological models // Fisica de la Tierra. 2007 . V. 19. P. 219- 241.

Gaps in data Frequently the series of meteorological observations contain gaps. It leads to significant decrease of accuracy. It also results in the instability of inversion of covariance matrixes.

To fill or not to fill… Estimation ignoring gaps Simple example Converge to zero with increasing the number of samples Observations with gaps Eigenvalues 2.3 and - 0.1 Covariance matrix Increasing the number of samples does not improve the stability

What is going on with the regression operator in the case of ignoring gaps The second norm of the inverted covariance matrix of predictor Length of calibration period

Filling Gaps in the Measurement Records. • Nearest neighbor method • Polynomial interpolations • Fourier transform based method • Gandin method (regression based) • Cressman analysis

Downscaling of surface temperature: the problem statement We suggest the statistical model for solving the inverse problem of reconstructing of daily mean, minimum and maximum surface temperatures at the network of meteorological stations in the region of La Manche from large-scale fields of temperature predicted by global short-term forecast model .

Costal zone of Dunkirk .

Employed data - Reanalisis NCAR/NCEP data (2.5° × 2.5°) - Mesurements at 18 meteorological stations in the north of France (le r é seau de surveillance ATMO Nord - Pas de Calais )

Numerical experiments • The daily values of temperature fields was used (3195 measurements, 9 years) • We considered the anomalies of fields of temperature. ( deviation from the annual variation) • Initial ensemble was divided in two parts: calibration (90%) and validation (10%) • The Cressman analysis was utilized for gaps filling

Results of downscaling of surface temperature without gaps filling A-priori A-priori Tempera- absolute relative absolute relative ture error, °C error, % error, °C error, % 1.38 54 1.27 47 mean 1.62 62 1.47 57 min 1.92 61 1.93 61 max • 75% - 80% of changeability is retrieved

Reliability parameter absolute error, and Real and retrieved reliability parameter temperature anomaly (r ~ - 0.3)

Results of downscaling of surface temperature with Cressman gaps filling A-priori A-priori Tempera- absolute relative absolute relative ture error, °C error, % error, °C error, % mean 0.88 34 0.89 34 min 1.13 44 1.07 42 max 1.39 43 1.25 39 • the retrievals with gaps filling are 30% - 35% more exact

Results of downscaling of surface temperature with random sampling (summary table) A-priori A-priori absolute relative Filling gaps absolute relative error, °C error, % error, °C error, % Mean daily temperature - 1.30 50 1.33 51 + 0.88 33 0.87 33 Minimum daily temperature - 1.55 60 1.58 61 + 1.12 44 1.11 44 Maximum daily temperature - 1. 87 58 1.92 59 + 1.37 43 1.36 42

Conclusions • The proposed statistical technique allows retrieving 80% (1.3°C) of the natural variability for the field of mean daily temperature and about 75% of variability of maximum (1.5°C) and minimum (1.9°C) temperatures. • It is shown that the application of the procedures of gaps filling allows improving the stability of solution of the inverse problem and significantly increase (30-35%) the precision of the reconstruction of small-scale field . • The parameter “reliability of the model” can be used for the detection of the realizations when the solution of the inverse problem has a big error which significantly increases the a priori estimate. (correlation between the reliability and the error is about -0.3).

Perspectives • For the solution of the problem we plan to employ non-linear methods such as non- linear regression and neural networks • We are going to use the data of ARPEGE model with a resolution of 20 km as an input data.