LandCaRe 2020 Dynamical and Statistical Downscaling

Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008

LandCaRe 2020

Dynamical and Statistical Downscaling

Ralf Lindau


1 Validation of CLM Precipitation by ObservationsConsortial Runs (Downscaling Input 18 km) are tested for 1997 – 2000

2 Comparison of Surface Temperatures from CLM and TERRA-StandaloneDownscaling Input is compared to downscaling output

3 Two Statistical Downscaling Methods

3.1 Spline plus Red Noise

3.2 Kriging


Part 1Validation of CLM with Observations

For a 4-years period (1997 – 2000)observations from Precipitation stations of DWD are compared with CLM results

On average 3000 observations of daily precipitation are available in each 18 km x 18 km grid box.


Observations show precipitation of more than 1000 mm/a at the foothills of the Alps, in BlackForest and Bergian Land. Large areas of EastGermany receive on the other hand less than 600 mm/a.

The overall mean of all stations is 811 mm/a


In the model Middle Europe receives 1009 mm/a (left).

Taking into account only such model data where observations areavailable, the modelprecipation is increasedto 1156 mm/a (right).


On average the model overestimates the rain by 345 mm/a (44%) (left).

In northern Germany theoverestimation is small; inmany mountain regionsof southern Germany the overestimation is higher than 100%. (right)


Beside the absolute rain amount, the followingstatistical properties of the model are validated:

• PDF of rain intensity

• Spatial autocorrelations


+ Modell

0-9 Obse

In the model it rains too often.

Each rain class frequency is overestimated by a factor of100.2, i.e. about 50%.

No rain is observed at 49% ofthe days, in the model only21% of the days are rain-free.

And by the way...the overrepresentation of wholenumber reports is noticeable, whereas 7 and 9 tenth are seldom. In the model such priority numbers are of course unknown.


____ Modell

0-9 Obse

Frequencies of extremes arewell reproduced by model.

As shown on the previous slidethe model produces too much lightand moderate rain.

However, the frequency of extremerain amounts (20 to 100 mm/day)is in good agreement with the observations.


M Modell

O Obse o TheoObse

Spatial autocorrelation of rain

The autocorrelation of the model (M)is for all distances larger than thoseof the observations (O).

For zero-distance the obervationsshow a correlatin of 0.9.

The decrease compared to 1 is caused by the lack of representativityof point measurements for the 18-kmgrid box.

All other O-correlation are also reducedby this factor. TheoObs (o) are givingthe corrected values.


The frequency of extreme rain events is well modelled.

Also the autocorrelation is in good agreement with observations, if spurious effects of the different resolutions of model (18km) and observations(point measurements) are taken into account.

It simply rains too much in the model. The rain is overestimated by about 50%.

Summary of part 1:


Part 2

Downscaling of CLM runs (18 km) by a stand-alone version of the soil model Terra (2.8 km).

Comparison of the forcing model (CLM) with high resolved output (Terra) exemplary examined by the modelled surface temperature in the Uckermark during July 2020.


Modelled Surface Temperatureat 31 July 2020, 0:00.

CLM shows warm Baltic Sea, Bornholm isdetectable as cold nocturnal anomaly. The mean temperature of Uckermark is 286.5 K.

At this time the high-resolution Terra output iscolder (285 K).

CLM Ter

ra


CLM

Time series of the surface temperature, exemplary for the gridpoint Prenzlau

Midnights are marked by crosses.

Considerable difference betweenobviously cloudy days withoutdaily cycle and radiation days witha normal daily cycle of 15 – 20 K.


TERRA

Time series of surface temperature at Prenzlau

Smaller variations of daily cycles (10 K). The mean is at this location slightly smaller. No hot extremesabove 30°C.


Means and total variances in space and time

The temporal and spatial mean of the surface temperature over theentire July 2020 and the entire Uckermark is:

CLM: 289.14 KTerra: 289.90 K

Die total variance in Terra is larger compared to CLM,

CLM: 16.65 K2

Terra: 23.77 K2

But attention: The increased variance cannot be interpreted as addition of small-scale variance by Terra, because the temporalvariance dominates strongly:

Total variance within Terra 23.77 K2

spatial variance portion 0.58 K2

small-scall spatial variance (below 18 km) 0.21 K2


Structure function

Terra shows a decreased variance for the same scale.

This is unexpected, because:

Differences between temperatures of e.g. 18 kmdistance should be larger in Terra compared to CLM, because the difference canbe interpreted as difference of the coarse means plus the double variability within a grid box.

C CLM

T Terra


Summary Part 2

Terra modifies the original surface temperature of CLMconsiderably.

Variation of daily cycles is smaller.

Spatial variances of small scales (18 km) are reducedinstead of increased.


Downscaling by splinesOriginal 16 x 16 grid boxes

Averaged to 4 x 4 grid boxes

Is it possible to retrievethe original?


Splines / Idea

Obviously, variance has to be added at small scales.

But if variance is just added to the averaged field, nasty edges would remain visible

Thus, the averaged field has to be smoothed.

But simple smoothing reduces the variance.

Thus, smooth the field but conserve its variance,

i.e. conserve all 16 grid box averages while smoothing


Common TecniqueSplines fit a polynom f(x,y) to a small peace

of area.The boundary conditions are continuity and

differentiabilityIn this way a smooth 2-dim surface is

peacewise constructed The classic bicubic spline uses 16

coefficients

With 16 boundary conditions 0 1 2 3

0 1 x x2 x3

1 y x y x2 y x3 y

2 y2 x y2 x2 y2 x3 y2

3 y3 x y3 x2 y3 x3 y3

cornerstheofeachat

yx

f

y

f

x

ff

4

,,,2

3316

2315

3214

313

2212

311

310

29

28

37

265

24321),(

yxcyxcyxcyxcyxcxycycxycyxcxcycxycxcycxccyxf


Variance conserving technique

We use only 13 coefficients

with 13 boundary conditions

0 1 2 3

0 1 x x2 x3

1 y x y x2 y x3 y

2 y2 x y2 x2 y2 x3 y2

3 y3 x y3 x2 y3 x3 y3

cornerstheofeachaty

f

x

ff

4

,,

yxcyxcxycycxycyxcxcycxycxcycxccyxf

313

2212

311

310

29

28

37

265

24321),(

F

conservedbetovaluegriddxdyyxf ),(

12+1


Variance conserving spline

Original

Artificiallycoarsen

Splineretrieval


Adding Red Noise

+ =

Sp

line

Red

No

ise


Spline (last)Original

Coarsen

Spline

Noise

Result


KrigingKriging is a prediction by the

weighted average of surrounding data points.

Existing kriging methods suppose that any new data point must reduce the predicting error.

We state that an optimum selection of data points extists, which is reached if all possible new data points have negative weights.


Negative Kriging weights

231312

213

223

212

23131202132312012

12033

21

1

cccccc

cccccccccc

Kriging is solving this matrix:

Kriging error is:


Precipitation from 01.01.1996 to 07.01.1996

DWD Original Kriged Variance characteristics

DWD Original

Kriged

ObsError:0.037 mm2/d2

Constantvariancereductionby the ObsError


Summary

1. Attention, the rain of the Cortortial Runs might be overestimated by 50%.

2. Dynamical downscaling by TERRA results in less instead of more spatial variance.

3.1 Variance-conserving splines plus red noise are a promising tool for statistical downscaling.

3.2 The proposed kriging method subtracts exactly the observation error variance and conserves the shape of autocorrelation function.

Documents

LandCaRe 2020 Dynamical and Statistical Downscaling