basin-scale runoff prediction: an ensemble kalman filter ...€¦ · prof. dr. harald kunstmann nse...

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 Kunstmann1,4

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



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



4 25.10.2016

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

Robs GRDC - - -



5 25.10.2016

Water budgets are not closed

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



6 25.10.2016

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



7 25.10.2016

Some agreement with observations...

Prof. Dr. Harald Kunstmann

Correlation w.r.t. GRDC

Nu

mb

er

of

catc

hm

en

ts




8 25.10.2016

...but not enough for reasonable predictions


NSE w.r.t. GRDC

Nu

mb

er

of

catc

hm

en

ts

Can we improve these combinations?




9 25.10.2016

• 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



10 25.10.2016

Tourian et al. (2013), WRR

Derivation of the observation equation

• State 𝑋𝑡 with water cycle variables of the study • Observations and uncertainties from global datasets



11 25.10.2016

Unconstrained vs. Constrained correction

Unconstrained observation equation

𝒀𝑡 = 𝑯𝑡𝑿𝑡 + 𝝂𝑡

Constrained observation equation

𝒀𝑡𝟎

=𝑯𝑡

𝑮𝑿𝑡 +

𝝂𝑡𝝎𝑡

with 𝑮 = 𝑰 −𝑰 −𝑰 −𝑰

𝟎 = 𝑷𝒕 − 𝑬𝑻𝒕 −𝑴 𝒕 −𝑹𝒕 +𝝎𝑡

1. Hard constraints: 𝝎𝑡 = 𝟎 water budgets are closed

2. Soft constraints: 𝝎𝑡 ~ 𝓝 𝟎,𝑸𝑤𝑏 small imbalances are allowed



12 25.10.2016

Derivation of the prediction equation

Anomalies at time-step 𝑡

𝒓𝑡 = 𝑿𝑡 − 𝑿 𝑡

with 𝑋 𝑡 being the long-term mean annual cycle.

Auto- and cross-covariance of the water cycle variables

𝚺 = 𝐷 𝒓𝑡 , 𝒓𝑡 , 𝚺Δ = 𝐷 𝒓𝑡 , 𝒓𝑡−1

Prediction of the anomalies from 𝑡 − 1 to 𝑡

𝒓𝑡 = 𝑨𝒓𝑡−1 + 𝜺𝑡 with 𝑨 = 𝚺Δ𝚺−1

Prediction of the „full“ signal

𝑿𝑡 = 𝑨𝑿𝑡−1 + −𝑨 𝑰𝑿 𝑡−1𝑿 𝑡

+ 𝜺𝑡



13 25.10.2016

• 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



14 25.10.2016

Performance of the EnKF-approach



15 25.10.2016

Performance of the EnKF-approach



16 25.10.2016

Ensemble Kalman Filter (EnKF), hard and soft Constrained Ensemble Kalman Filter (CEnKFh, CEnKFs), Ensemble Kalman Smoother (EnKS), and hard and soft Constrained

Ensemble Kalman Smoother (CEnKSh, CEnKSs)

Lorenz et al. (2015), WRR

Performance of the different configurations



17 25.10.2016

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



18 25.10.2016

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




19 25.10.2016

Thank you for your attention.

Outlook

Representation of Extremes?

Application to climate models (CMIP5-ensemble)

Prediction for other catchments



20 25.10.2016

basin-scale runoff prediction: an ensemble kalman filter ...€¦ · prof. dr. harald kunstmann nse...

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