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 **Université du Littoral Côte 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

Simulations of global model Dynamical or statistical model Retrieved small- scale field

Downscaling is the reconstruction

• f 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
• Dynamical

Regularisation techniques Principal components analysis SVD analysis Canonical correlation analysis Steapwise regression Retreival of the problem in the sub-space Filtering of the elements that contains information Biased reduction

• perator A is known

) ( ) ( ~

* *

Eg g C A AC A C El l

ll ll

− + + =

− εε

g C A A C A l

− − −

=

εε εε * *

) ( ~

Unbiased reduction

Retreval techniques

ε + = Al g g l

• small-scale field
• large-scale field
• averaging operator
• error of averaging

ε A

Inverse problem

) ( ~ Eg g C C El l

gg g l

− + =

−

• perator A is unknown

Multiple regeression

Statistical downscaling

Statistical downscaling

Example: comparison of the statistical downscaling with a polinomial interpolation in Moscow

Chavro A.I., Nogotkov I.V., Dmitriev E.V. Statistical model for reconstruction of surface temperature extremes at meteorological stations in the Moscow region // Russian Meteorology and Hydrology.

• 2008. (In the press)

The statistical model allows :

• 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

In general the statistical downscaling is more exact than a polinomial interpolation Statistical dowscaling is signifially more quick than a dynamical dowscaling

Downscaling relative error is 20%

hypothesis alternative

) , ( ~ C N g C C a C a N g > ≠ ˆ , ), ~ , ( ~

∫

∞

−

=

2 2 / 1 2

) ( ) (

) ( g C m

gg

dt t p g

χ

α

Reliability of the model

Prediction of the most significant errors for the statistical downscaling

Fiabilité du modèle L'erreur de downscaling

For the downscaling of mean monthly temperature The parameter « reliabilite of the model » can be 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. For the downscaling of mean dayly temperature

Gaps in data

Frequently the series of meteorological

• bservations 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

Increasing the number of samples does not improve the stability

Eigenvalues 2.3 and - 0.1

Simple example

Observations with gaps Covariance matrix Converge to zero with increasing the number of samples

What is going on with the regression

• perator 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

• f France (le réseau

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

Tempera- ture A-priori absolute error, °C A-priori relative error, % absolute error, °C relative error, % mean

1.38 54 1.27 47

min

1.62 62 1.47 57

max

1.92 61 1.93 61

• 75% - 80% of changeability is retrieved

Reliability parameter

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

Results of downscaling of surface temperature with Cressman gaps filling

Tempera- ture A-priori absolute error, °C A-priori relative error, % absolute error, °C relative 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)

Filling gaps Mean daily temperature

• +

Minimum daily temperature

• +

Maximum daily temperature

• +

A-priori absolute error, °C A-priori relative error, % absolute error, °C relative error, % 1.30 50 1.33 51 0.88 33 0.87 33 1.55 60 1.58 61 1.12 44 1.11 44

• 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.