an Ensemble Kalman Filter framework based on

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KIT – The Research University in the Helmholtz Association

INSTITUTE OF METEOROLOGY AND CLIMATE RESEARCH, ATMOSPHERIC ENVIRONMENTAL RESEARCH, IMK-IFU REGIONAL CLIMATE AND HYDROLOGY

www.imk-ifu.kit.edu

Basin-scale runoff prediction:

an Ensemble Kalman Filter framework based on global hydrometeorological datasets

1 Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Garmisch-Partenkirchen, Germany 2. University of Stuttgart, Institute of Geodesy, Stuttgart, Germany

3. University of Hannover, Institute of Geodesy, Hannover, Germany

4. University of Augsburg, Institute of Geography, Regional Climate and Hydrology, Augsburg, Germany

Christof Lorenz¹, Mohammad J. Tourian², Balaji Devaraju³, Nico Sneeuw², Harald Kunstmann^1,4

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Institute of Meteorology and Climate Research, IMK-IFU, Regional Climate and Hydrology

2 25.10.2016

gauged

ungauged dischargeless

Catchments with limited (< 5 yrs) runoff observations after 2002

• cover an area of more than 11,500,000 km²!

• freshwater discharge of more than 125,000 m³/s!

Dai & Trenberth (2002):

Annual runoff rate over unmonitored areas equals annual runoff rate over monitored areas!

Decrease in the number of in situ observations

Lorenz et al. (2014), JHM

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3 25.10.2016

Estimation through water budgets?

• Can be applied globally

• Does not require, e.g., in situ runoff

• Not restricted to the basin scale

• Anthropogenic changes do not matter!

• Biases might (!!!) cancel out

• Only as good as the „worst“ input

• Error propagation

• Temporal/spatial resolution

PROS: CONS:

Terrestrial

𝑅 = 𝑃 − 𝐸𝑇 − 𝑑𝑆 𝑑𝑡

Atmospheric-terrestrial

𝑅 = −𝛻𝑸 − 𝑑𝑆

𝑑𝑡

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Hydrometeorological datasets

Variable Dataset Version Resolution Time-period

Spatial Temporal

P GPCC 6.0 0.5° x 0.5° 1 month 1901 - 2010

GPCP 2.2 2.5° x 2.5° 1 month 1979 - present

CRU 3.22 0.5° x 0.5° 1 month 1901 - 2013

DEL 3.02 0.5° x 0.5° 1 month 1900 - 2010

CPC 1.0 0.25° x 0.25° 1 month 1979 – present*

ET ERA Interim - 0.75° x 0.75° 1 month, 1day, 6h 1979 - present

GLDAS NOAH 3.3 1.0° x 1.0° 1 month, 3h 1948 - present

GLEAM v1B 0.25° x 0.25° 1 day 1984 - 2008

MOD16 A2 0.5° x 0.5° 1 year, 1 month, 8 days 2000 - 2013

Fluxnet MTE - 0.5° x 0.5° 1 month 1980 - present

MERRA Land - 1/2° x 2/3°

dS/dt GRACE CSR R5 - 1 month 2002 – present*

GRACE GFZ R5 - 1 month 2002 – present*

MERRA Land 1.0 1/2° x 2/3° 1 month, 1 day, 1h 1980 - present

GLDAS NOAH 3.3 1.0° x 1.0° 1 month, 3h 1948 - present

WGHM NOUSE 0.5° x 0.5° 1 month 1960 - 2009

R_obs GRDC - - -

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Water budgets are not closed

P (GPCC) – ET (MODIS) – dS/dt (GRACE) – R (GRDC)

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Evaluation of the basin- scale water budget closure

from 90 combinations of state-of-the-art datasets

for precipitation, evapotranspiration, and

water storage changes.

Large residuals in the long-term water budgets

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7 25.10.2016

Some agreement with observations...

Prof. Dr. Harald Kunstmann

Correlation w.r.t. GRDC

Number of catchments

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...but not enough for reasonable predictions

NSE w.r.t. GRDC

Number of catchments

Can we improve these combinations?

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• Simple and straightforward maths

• Framework based on an EnKF

• Purely data-driven

• Exploit the joint inter- and intra-catchment auto and cross covariances between the four major water cycle variables through LS-prediction

• Application of a constrained EnKF for ensuring water budget closure

Empirical hydrological model which is based on hydrometeorological data and their statistical

dependencies.

Development of a data-merging approach for the consistent combination, correction, and prediction of basin-scale water cycle

variables:

Cornerstones of the approach

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Tourian et al. (2013), WRR

Derivation of the observation equation

• State 𝑋_𝑡 with water cycle variables of the study

• Observations and uncertainties from global datasets

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= 𝐷 𝒓

_𝑡

, 𝒓

_𝑡−1

Prediction of the anomalies from 𝑡 − 1 to 𝑡

𝒓

_𝑡

= 𝑨𝒓

_𝑡−1

+ 𝜺

_𝑡 ^with

𝑨 = 𝚺

_Δ

𝚺

⁻¹

Prediction of the „full“ signal

• Study comprises 29 large river-basins like, e.g., Amazon, Mississippi, Ob, Mackenzie, ...

• Prediction of monthly runoff for 16 basins (blue)

• Compare runoff predictions against monthly observations from the GRDC- database

Overview of the study regions

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Performance of the EnKF-approach

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Performance of the EnKF-approach

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Ensemble Kalman Filter (EnKF), hard and soft Constrained Ensemble Kalman Filter (CEnKF_h, CEnKF_s), Ensemble Kalman Smoother (EnKS), and hard and soft Constrained

Ensemble Kalman Smoother (CEnKS_h, CEnKS_s)

Lorenz et al. (2015), WRR

Performance of the different configurations

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Full Signal Anomalies (w.r.t. MAC)

• Very good agreement of both the full signal and the runoff anomalies

• Shorter and longer term deviations from the mean annual cycle of runoff are well represented in the predicted time-series

• However: Problems in the representation of extremes

Exemplary time-series

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Conclusions

Decrease in the number of rain- and river-gauges

Large imbalances in the catchment-scale water budgets

 Analysis of an intensification of the water cycle or water budget studies not possible

 Urgent need for alternative approaches for

estimating/predicting/correcting our data sources for the water cycle variables

EnKF-based framework for predicting basin-scale runoff Very good agreement with monthly runoff observations

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Thank you for your attention.

Outlook

Representation of Extremes?

Application to climate models (CMIP5-ensemble) Prediction for other catchments

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