River discharge from ungauged catchments by least-squares prediction

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1 River discharge from ungauged catchments by least-squares prediction Institute of Geodesy, University of Stuttgart, Germany Geodetic Week October 213, Essen, Germany

2 Problem Number of available stations with data (Tourian et al. 213) x The sum of mean annual streamflow of available data

3 Goal using legacy data to boost the database Number of available stations with data using models to boost the database Number of available stations with data using covariance information from models 8 using covariance information 4 from data of ever gauged stations

4 Methodology Least-squares prediction (Moritz 198) l: observation s: unknown ŝ: prediction H: prediction model e: prediction error Data partitioning δs= Hδl+e [ ] ltr s tr the error is minimized for H = C sl C 1 ll ˆ δs= Hδl l s Two approaches from signal ltr, s tr : long-term mean C ll = 1 T tr (l tr l tr ) T (l tr l tr ), C sl = 1 T tr (s tr s tr ) T (l tr l tr ) from residual ltr, s tr : seasonal mean C ll = 1 T tr (l tr l tr ) T (l tr l tr ), C sl = 1 T tr (s tr s tr ) T (l tr l tr )

5 Covariance information l tr and s tr in training period from Global Runoff Data Center (GRDC) GLDAS CLM GLDAS Mosaic GLDAS NOAH2 GLDAS VIC Merra land

6 Case study 25 catchments 45 W

7 Case study Cyclo-stationarity factor γ = 1 RMS(x x) RMS(x)

8 Contribution from other catchment, H GRDC - residual GRDC - signal Amazon Amazon GLDAS VIC - residual GLDAS VIC - signal Amazon 45 W Amazon 45 W 45 W

9 Contribution from other catchment, H GRDC - residual GRDC - signal Amazon Amazon GLDAS NOAH2 - residual GLDAS NOAH2 - signal Amazon Amazon 45 W

10 Results, Amazon catchment H from GRDC Runoff [mm/month] RMSE= 19.39, NSE=.63 RMSE= 16.6, NSE=.79 measured runoff predicted runoff from signal approach predicted runoff from residual approach error from signal approach error from residual approach Prediction method 4 (zero mean) AMAZONAS Duration of training period: 1 years H from GLDAS VIC 2 Runoff [mm/month] 1 RMSE= 81.2, NSE= 6.1 RMSE= 71.6, NSE=

11 Results, Amazon catchment H from GRDC Runoff [mm/month] RMSE= 19.39, NSE=.63 RMSE= 16.6, NSE=.79 measured runoff predicted runoff from signal approach predicted runoff from residual approach error from signal approach error from residual approach Prediction method 4 (zero mean) AMAZONAS Duration of training period: 1 years Nash-Sutcliffe efficiency (xo ˆx) 2 NSE = 1 (xo x o) H from GLDAS VIC 2 Runoff [mm/month] 1 RMSE= 81.2, NSE= 6.1 RMSE= 71.6, NSE=

12 Results, Amazon catchment H from GRDC Runoff [mm/month] RMSE= 19.39, NSE=.63 RMSE= 16.6, NSE=.79 measured runoff predicted runoff from signal approach predicted runoff from residual approach error from signal approach error from residual approach Prediction method 4 (zero mean) AMAZONAS Duration of training period: 1 years Nash-Sutcliffe efficiency (xo ˆx) 2 NSE = 1 (xo x o) H from GLDAS NOAH2 2 1 RMSE= 52.9, NSE= 2. RMSE= 43.5, NSE=

13 Results, Amazon catchment H from GRDC Runoff [mm/month] RMSE= 19.39, NSE=.63 RMSE= 16.6, NSE=.79 measured runoff predicted runoff from signal approach predicted runoff from residual approach error from signal approach error from residual approach Prediction method 4 (zero mean) AMAZONAS Duration of training period: 1 years H from GLDAS NOAH2 2 1 RMSE= 52.9, NSE= 2. RMSE= 43.5, NSE=

14 Results, spectral analysis Fraser catchment, H from GRDC Runoff [mm/month] Error [mm/month] Time 2 NSE=.89 NSE= measured runoff predicted runoff from signal approach predicted runoff from residual approach Frequency [cycle/year]

15 Results, NSE GRDC, signal GRDC, residual GLDAS VIC, signal GLDAS VIC, residual

16 Results, NSE GRDC, signal GRDC, residual GLDAS CLM, signal GLDAS CLM, residual

17 Results, NSE GRDC, signal GRDC, residual MERRA Land, signal MERRA Land, residual

18 Results, relative RMSE GRDC GLDAS CLM GLDAS VIC 5% 5% 5% relative RMSE from resdiual approach 4% 3% 2% 1% relative RMSE from resdiual approach 4% 3% 2% 1% relative RMSE from resdiual approach 4% 3% 2% 1% % % 1% 2% 3% 4% 5% relative RMSE from signal approach % % 1% 2% 3% 4% 5% relative RMSE from signal approach % % 1% 2% 3% 4% 5% relative RMSE from signal approach MERRA Land 5% GLDAS Mosaic 5% GLDAS NOAH2 5% relative RMSE from resdiual approach 4% 3% 2% 1% relative RMSE from resdiual approach 4% 3% 2% 1% relative RMSE from resdiual approach 4% 3% 2% 1% % % 1% 2% 3% 4% 5% relative RMSE from signal approach % % 1% 2% 3% 4% 5% relative RMSE from signal approach % % 1% 2% 3% 4% 5% relative RMSE from signal approach

19 Results Is the predicted runoff better than seasonal mean? ÑSE = 1 { (xo ˆx) 2 predicted is better if ÑSE > (xo x o) 2 seasonal mean is better if ÑSE <

20 Results Is the predicted runoff better than seasonal mean? ÑSE = 1 { (xo ˆx) 2 predicted is better if ÑSE > (xo x o) 2 seasonal mean is better if ÑSE < ÑSE, signal approach residual approach

21 Results Is the predicted runoff better than seasonal mean? ÑSE = 1 { (xo ˆx) 2 predicted is better if ÑSE > (xo x o) 2 seasonal mean is better if ÑSE < NSE ÑSE 1 1 NSE from residual approach.5 ÑSE from residual approach NSE from signal approach ÑSE from signal approach

22 Results, length of legacy NSE with different length of training period (residual approach) 1 AMAZONAS FRASER RIVER SUSQUEHANNA RIVER TOMBIGBEE other catchments NSE length of legacy [years]

23 Summary Least-squares prediction: a simple and efficient tool for runoff prediction in ungauged basins with legacy data Covariance matrices created through 2 approaches (signal and residual) from available in situ data and models (GLDAS, MERRA) Better results from residual approach especially in capturing the seasonality (demonstrated by spectral analysis) Covariance from hydrological models lead to poor prediction performance High variability in prediction skill between models When covariance matrices are from in situ data, NSE>.4 for 9%, NSE>.75 for 5% of the 25 catchments For 5% of the catchments LS prediction outperform the seasonal mean The method does not work properly for predicting extreme events

24 Outlook Using a more complete catchment dataset (larger than 25) for prediction Performing the analysis over individual gauging stations Using water level time series from satellite altimetry to improve the prediction model toward capturing the extreme events

25 References Moritz H (198) Advanced physical geodesy. Karlsruhe: Wichmann ISBN Tourian MJ, Sneeuw N, Bárdossy A (213) A quantile function approach to discharge estimation from satellite altimetry (ENVISAT). Water Resources Research 49:113, DOI 1.12/wrcr.2348 Lorenz C, Devaraju B, Tourian MJ, Riegger J, Kunstmann H, Sneeuw N (213) Global scale runoff from landmasses: assessing the closure of the hydrological and atmospheric water balances using state-of-the-art data and models. Journal of Hydrometeorology, submitted Thank you sneeuw@gis.uni-stuttgart.de

Geli Wu Omid Elmi, Mohammad Tourian, Nico Sneeuw Institute of Geodesy University of Stuttgart

Geli Wu Omid Elmi, Mohammad Tourian, Nico Sneeuw Institute of Geodesy University of Stuttgart Geli Wu (geli.wu@gis.uni-stuttgart.de), Omid Elmi, Mohammad Tourian, Nico Sneeuw Institute of Geodesy University of Stuttgart Geodetic Week 2013 Essen Outline Introduction Data Sets Methodology Results