Merging Rain-Gauge and Radar Data

Transcription

1 Merging Rain-Gauge and Radar Data Dr Sharon Jewell, Obserations R&D, Met Office, FitzRoy Road, Exeter

2 Outline 1. Introduction The Gauge and radar network Interpolation techniques 2. Gauge-radar merging tests 3. Performance factors 4. Conclusions

3 1. Introduction

4 Background Rainfall accumulation Hydrological Model Flood Warnings Flood forecasting models use real-time rainfall accumulations to feed in to hydrology models. Success of the scheme relies on: Realtime (15 minute) data runs Accurate rainfall accumulation measurements Accurate flood models Joint project between the EA and Met Office to improve the quality of the rainfall accumulation data input into the model.

5 Measuring rainfall accumulation: Rain-gauges Radar Network of 1000 realtime gauges across the UK measure rainfall at fixed locations. Data must be quality controlled to check for blockages etc. Accurate rainfall measurement but low spatial coverage. 15 radar sites around the UK measure the rainfall rate (mm/hr) at 5 minute intervals. Accumulation calculated for the past 60 minutes. Good spatial coverage but poorer intensity information due to interference from clutter etc.

6 Radar and gauge data Comparing datasets from the same 60 minute accumulation period highlights the differences in the two measurement schemes. Rain-gauges Radar

7 The Merged product Combining the gauge and radar data creates a merged product with an accuracy which is better than either of the individual methods. Gauge radar merged product (60 minute accumulation) Radar Gauge

8 Gauge-Radar Merging and Hydrological Modelling The merged product is an input for flood forecasting hydrological models. The Flood Forecasting Centre (FFC) currently uses a multiquadric scheme to combine gauge and radar readings. The EA and MO are currently running a joint project to investigate alternative merging schemes with improved accuracy and stability. MultiQuadric : A mathematical field is generated based on the ratio of gauge:radar values and applied to the radar data.

9 Interpolating Data - Basics The UK is divided up into a regular 1km 2 grid which matches the radar grid. Grid squares containing a rain-gauge are identified. The gauge-radar merged data is calculated for each square individually. The interpolated value at an un-gauged pixel is a weighted sum of the nearest neighbour gauge accumulations.

10 Weighting Factors 1 km resolution grid (matches radar resolution) 1 For a basic interpolation scheme the weighting is dependent on 1/r where r is the distance of the gauge from the ungauged point. r 1 r 2 P r 4 r BUT.. Scheme is not ideal for convective rainfall conditions. = Ungauged pixel = Nearest neighbour gauge Multiple contributions from one area can be at the expense of other areas.

11 Semivariance How closely one gauge corresponds to another gauge in the neighbourhood is referred to as the semivariance. This effect is quantified using a variogram to describe the whole area. The variogram can be derived either: Parametrically from the separation of each unique pair of gauges and their values. Non-Parametrically from the Fourier-Transform of the radar image. Semivariance Semivariance Distance Distance The closer a pair of gauges, the smaller the semivariance.

12 Kriging Kriging is a geostatistical method for estimating values at unsampled locations from a limited set of sample data. P is a weighted sum of the nearest neighbour gauges. n P = λ 1 i= Semivariance of gauges (n x n) i G i (n = number of nearest gauges to P) Gauge weights (n x 1) Semivariance of gauges and P (n x 1) 1 r 1 r 2 P = Ungauged pixel = Nearest neighbour gauge Ordinary Kriging constraints: Semivariance is included. The sum of the weighting factors for P equals 1. r 4 r c ij λ c = 1 0 µ 1 1 Pi Sum of weights

13 Kriging with Radar Error (KRE): Kriging with External Drift (KED): Radar is Included in the Kriging scheme. cij R λ 1 µ 0 µ R = Radar values at gauge points R P = Radar value at point P Semivariance is either from a Parametric (KEDs) or non-parametric (KEDn) variogram. Kriging Gauge and Radar Data P P = Radar atp P 1 0 a b c = R 1 Pi P G R n P = λ 1 i= i G i 1 r 1 r 2 P = Ungauged pixel = Nearest neighbour gauge Ordinary Kriging constraints: Semivariance is included. The sum of the weighting factors for P equals 1. r 4 In addition for KED: Applying the weighting factors to the radar values at the points 1-4 must give the radar value measured at P. r

14 2. Gauge-Radar Merging Tests

15 Canned Data Sets Data from Oct Sept available in 15 and 60 minute accumulations quality controlled gauges available within the merging region (England and Wales) - one-third set aside as cross-validation gauges. Data from 4 different meteorological conditions used. KRE, KEDs and KEDn tested and compared to the original radar data values. Slow moving Fast moving 1 st 6 th October th 16 th January 2011 Stratiform Slow and erratically moving weather fronts. Widespread heavy rain across the country Widespread rain and heavy orographically enhanced rainfall. Front lingered in the south Spatially uncorrelated (Convective) 15 th 18 th July rd 8 th August 2011 Deep depression tracked across the country bringing heavy localised showers. Scattered showers and localised thunderstorms following a belt of rain.

16 Cross-Validation The merged value at the cross-validation gauge locations was compared to the true value measured at the sites. Radar data was also cross-validated at these locations. and the measured radar value at the same location. A number of statistics were used to assess performance. Data quality (RMSE, MAE etc.) RMSE ( G M ) Binary detection efficiency (POD, CSI etc. perfect score = 1) N i= 1 = i N i 2 Threshold Accumulation (mm/hr) Hit Miss False Alarm True Merged True Merged Merged True Total Hits POD = Hits+ Misses Total Hits CSI = Hits+ Misses + False Alarms

17 60 Minute Accumulations Continuous Statistics (Data Quality) Binary Statistics (Detection Efficiency) 12 th -16 th January 2011 (Fast moving stratiform conditions) 3 rd -8 th August 2011 (Convective showers)

18 60 Minute Accumulations During stratoform conditions the KEDn clearly outperforms the other scheme on all levels. During convective conditions the merging adds little to the quality of the data. BUT merging significantly improves the detetion efficiency over radar alone. The detection efficiency is largely independent of the meteorological conditions.

19 15 Minute Accumulations Continuous Statistics Binary Statistics 12 th -16 th January 2011 (Fast moving stratiform conditions) 3 rd -8 th August 2011 (Convective showers)

20 15 Minute Accumulations KEDn still outperforms the other schemes during stratiform conditions. During convective conditions the merging adds even less to the product quality compared to longer accumulations. Detection efficiency is improved but to a lesser extent than for 60 minute accumulation. Overall, merging 15 minute accumulations still gives an improved product.

21 3. Performance Factors

22 15 vs. 60 minutes Accumulation RMSE (Data quality) CSI (Detection efficiency) 60 minute accumulation periods tends to have lower errors/better detection efficiency than the equivalent 4x15 minute periods. KEDn is still the best performing overall at both accumulations. Merged 15 minute data is still better than radar only.

23 15 Minute Accumulation Merged Product 01/10/ :00 Radar KEDs KEDn The difference between the KEDn and KEDs images for a 15 minute accumulation are comparable. The only difference in the merging schemes is the production of the semivariogram. The use of the radar data over a relatively short period (15 minutes) to generate the variogram makes it more suceptable to noise.

24 Effect of a Gauge-Radar Timing Offset (KEDn) The merged product relies on the gauge and radar data being synchronised in time. An offset was simulated by merging radar data with gauge data from periods offset by fixed amounts. An offset of 15 minutes produces a measurable effect BUT the result is still superior to using radar alone. In extreme convective situations the offset is most critical and the merging fails completely when an offset is introduced.

25 Additional Factors Gauge Density Testing the schemes on reduced data-sets indicates that the KED scheme is the least sensitive to a random reduction in gauge density. In particular, KEDn is less sensitive then KEDs. Gauge Quality Control All of the schemes require the gauges to be passed through a QC check before usr in the merging schemes. A real-time QC check for spurious gauge readings is being developed in conjunction with this project. Merging Scheme Processing Time The QC checks and merging scheme must run within 15 minutes and be available within 30 minute of the end of the accumulation period.

26 Conclusions Kriging is an effective method for interpolating randomly distributed data whilst incorporating the correlation of the data. Merging gauge and radar data together creates a product of better quality and detection efficiency than the original products alone. The merging schemes (KRE, KEDn, KEDs) are suitable for 15 and 60 minuye rainfall accumulations. The scheme is sensitive to, but can accommodate synchronicity offsets between datasets in most situations. The schemes are suitable for the required 15 minute processing time.

27 Questions and answers

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29 2. Effect of Gauge Density Study performed using the dense gauge network over the London area. Gauges systematically removed to produce the greatest change in the median gauge separation. (100%) (20%) Decreasing density