INSTITUTE OF METEOROLOGY AND CLIMATE RESEARCH, ATMOSPHERIC ENVIRONMENTAL RESEARCH, IMK-IFU REGIONAL CLIMATE AND HYDROLOGY
Development of a Copula-based data merging framework forcombining spaceborne soil moisture
and ancillary data
1 Karlsruhe Institute of Technology, Institute for Meteorology and Climate Research, Garmisch-Partenkirchen, Germany 2. Forschungszentrum Jülich GmbH, Agrosphere Institute (IBG-3), Jülich, Germany
3. German Aerospace Center, Microwaves and Radar Institute, Oberpfaffenhofen, Germany
Christof Lorenz1, Carsten Montzka2, Thomas Jagdhuber3, Harald Kunstmann1,4
Homogenization – improved resolution – gap filling – enhancement of time-series – bias
correction
Many products for hydrometeorological variables BUT different
Sensors – resolutions – time-periods – spatial coverage – quality
Why data fusion?
DATA FUSION TECHNIQUES
Data fusion – some examples
Gauge- and radar based precipitation data (Goudenhoofdt & Delobbe, 2009)
Development of multi-satellite products (Huffman et al. 2007, Hou et al.
2014)
Active and passive microwave data (Das et al. 2011, Liu et al. 2011) Bias correction of RCM-data using in situ observations (Laux et al.
2011) ...
Linear techniques (simple/weighted average, ...)
Semi-statistical (empirical) techniques (Kriging, Kalman Filter, ...) Statistical techniques (CDF matching, COPULAS)
Data fusion – typical methods
Sklar‘s Theorem (1959): For any bivariate distribution function 𝐹𝑋𝑌 𝑥, 𝑦 with univariate marginals 𝐹𝑋 𝑥 and 𝐹𝑌 𝑦 there exists a Copula 𝐶 such that
𝐹
𝑋𝑌𝑥, 𝑦 = 𝐶 𝐹
𝑋𝑥 , 𝐹
𝑌𝑦
= 𝐶 𝑢, 𝑣
with density
𝑐 𝑢, 𝑣 =
𝜕2𝐶 𝑢,𝑣𝜕𝑢𝜕𝑣
The multivariate (here: bivariate) PDF of 𝐹𝑋𝑌 𝑥, 𝑦 is then given by
𝑓 𝑥, 𝑦 = 𝑐 𝐹
𝑋𝑥 , 𝐹
𝑌𝑦 ∙ 𝑓
𝑋𝑥 ∙ 𝑓
𝑌𝑦
Copula-based data fusion – Background
The Copula describes the full dependency between 𝒙 and 𝒚
Archimedian Copula families
Different Copula families for different dependency structures
Methodology – Step 1
Use parameteric, non-parametric, or empirical methods for estimating the marginals
Methodology – Step 2
Ce
( )
u,v = m1 I mr+i1£ u, si
m+1 £v æ
èç ö
ø÷
i=1
å
mFind a suitable Copula and (for archimedian models) fit the Copula parameter
Empirical Copula Theoretical Copula
Methodology – Step 3 & 4
Prof. Dr. Harald Kunstmann
Compute the Conditional Copula and draw random samples
Cq,v=V
( )
u = ¶¶vC u
( )
,vv=V
Transform samples back to the data space using the inverse
marginals
Experiment #1: Active-Passive Combination
Background: Evaluate methods for combining SMAP AP data
SMAP-Type data from active FSAR (DLR) and passive PLMR2 (FZJ) Data from flight campaign over the Rur catchment during 2013
Combine high-resolution (active, FSAR) with high accuracy (passive, PLMR2) microwave data
Are Copulas a valid alternative to „classical“ AP-
Algorithms?
Benefit of active-passive combination?
High resolution (SAR) is combined with high accuracy (radiometer) for an improved soil moisture
estimation.
Similar patterns in active (top) and passive (bottom) data
Retrievals from a flight campaign using DLR‘s DO228 aircraft over the Rur-Catchment during three dates in 2013.
Approach: Transform radar backscatter into brightness temperature using Copula
models
Dependence on Land Use Classes (LUCs)
Different LUCs show different marginal
distributions
Different LUCs show different dependencies
Generation of one Copula for each LUC using
• One date (spatial approach)
Estimated TB from radar backscatter
Transforming radar backscatter to TB using Copulas yields
similar patterns and data
ranges (at least for the spatial approach)
Ensemble standard deviation
Comparison with „standard“ AP-approaches
Left: Disaggregation of the radiometer soil moisture product (SMAP baseline;
Das et al. 2011)
Middle: Disaggregation of radiometer brightness temperature (SMAP alternative;
Das et al. 2014)
Right: Copula-based active-passive fusion
Experiment #2 – Fusion of SM-products
SMAP (radiometer) and SMOS provide global satellite based soil moisture estimates from passive microwave data
Can we use Copulas to combine the data from the two satellites for
estimating a consistent SMAP/SMOS soil moisture dataset?
Fill spatial gaps?
Can we use Copulas to combine data from SMAP/SMOS with in situ data
for correcting biases in the soil moisture fields?
for temporal downscaling?
Combine SMAP with SMOS?
Correlation between SMAP and SMOS during Apr. 2015 to March 2016
Number of (approx.) simultaneous SM retrievals
Temporal downscaling of SMAP/SMOS data
Transform 3-daily SMAP-snapshots (blue) to daily time-series (red) using in situ data (black)
Top-level soil moisture at Jordan (SCAN)
Correcting SMAP/SMOS-data with observations
SMOS-based SM data before (blue) and after (red) bias correciton using in situ data over the SCAN (150 stations)
and COSMOS (61 stations) networks.
Merging SMAP and SMOS data at the SM-level
Improve SMOS-based soil moisture during the pre-SMAP period
…results look promising, but need to be further investigated
Conclusion
State-of-the-art framework for data fusion
Application does not require any pre-knowledge of the data No requirements w.r.t. distribution of the data
Simple to use
...but needs careful implementation, application, and validation
