landcare 2020 dynamical and statistical downscaling
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LandCaRe 2020 Dynamical and Statistical Downscaling. Ralf Lindau. Validation of CLM Precipitation by Observations Consortial Runs (Downscaling Input 18 km) are tested for 1997 – 2000 Comparison of Surface Temperatures from CLM and TERRA-Standalone - PowerPoint PPT PresentationTRANSCRIPT
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
LandCaRe 2020
Dynamical and Statistical Downscaling
Ralf Lindau
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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).
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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)
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
Beside the absolute rain amount, the followingstatistical properties of the model are validated:
• PDF of rain intensity
• Spatial autocorrelations
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
+ 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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
____ 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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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:
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
Downscaling by splinesOriginal 16 x 16 grid boxes
Averaged to 4 x 4 grid boxes
Is it possible to retrievethe original?
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
Variance conserving spline
Original
Artificiallycoarsen
Splineretrieval
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
Adding Red Noise
+ =
Sp
line
Red
No
ise
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
Spline (last)Original
Coarsen
Spline
Noise
Result
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
Negative Kriging weights
231312
213
223
212
23131202132312012
12033
21
1
cccccc
cccccccccc
Kriging is solving this matrix:
Kriging error is:
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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
Diplomanden-Doktoranden-Seminar Bonn – 23 June 2008
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.