Constraining monthly GRACE-solutions with hydrological mass estimates .... negligible ETa, but only twenty-eight catchments were usable due to data gaps.
Constraining monthly GRACE-solutions with hydrological mass estimates B. Devaraju1, N. Sneeuw1, H. Kindt2, J. Riegger2, and C. Lorenz1 1. Institute of Geodesy, Universit¨at Stuttgart; 2. Institute of Hydraulic Engineering, Universit¨at Stuttgart. [devaraju,sneeuw]@gis.uni-stuttgart.de
1. Hydrology and GRACE he GRACE satellite mission provides high resolution time-variable gravity-field information, which has considerably improved the knowledge of mass distribution and redistribution. In terms of hydrological applications, GRACE provides information on monthly changes of continental water storage. This information can be used in the continental water balance equation given below;
T
∂S ETa = ∂t
P−
R
1e3
60˚
30˚
1e1 0˚
2. Methodology
0˚
(2)
!60˚
1e!3
(a)
.
.
(b)
Constraining GRACE solutions with hydrology
Observed hydrology
Precipitation (P )
Run-off (R)
P − R − ETa =
• Spherical harmonic coefficients (Klm ) and their formal errors (σKlm )
∂S ∂t
(1)
Simulating covariance matrices. L # WA − WB = Λl Ylm (θA , λA )Klm −
Finding catchments with negligible ETa ∂S ∂t
l,m
(negligible for deserts during dry seasons; during winters for tundric and arctic areas.)
(c)
• GRACE L1B orbit data (positions of both GRACE A and B)
Actual evapotranspiration ETa is unknown.
⇒ P − R ≈
L # l,m
L #
∆TAB =
Λl Ylm (θB , λB )Klm
This smoothing of the adjacent area is conspicuous around north-eastern Africa, parts of the Indian subcontinent, Mongolia, Tibet and China. In order to quantify this contribution of hydrology the redundancy numbers were investigated. Redundancy numbers provide the percentage contribution to the whole sequential estimate from each of the input datasets 4. Full covariance matrix
Block!diagonal covariance matrix
[mm/month]
Negligible precipitation. ET can be ignored. Total a
E
change negligible.
()
ˆ (1) x y2
*+
=
,
I A2
-
x;
D
()
ˆ (1) x y2
*+
=
.
Qx ˆ (1) 0
0 Q2
/
40
ˆ (2) = x
20 0
Qx ˆ (2)
Precipitation Run−off 100
ˆ (1) x y2
Very low run−off. Indicates very cold weather. ET can a
60
be ignored.
−1 AT 2 Q2 A2
&
+
Q−1 ˆ (1) x
−1 −1 AT 2 Q2 A2 + Qx ˆ
Rx = Qx ˆ (2)
Yukon catchment
80
=
&
(1)
&
−1 AT 2 Q2 A2
'
'−1 &
−1 AT 2 Q2 y 2
+
'−1
ˆ (1) Q−1 ˆ (1) x x
'
−1 Ry = Qx ˆ (2) Qx ˆ
(1)
– GRACE covariance matrix. – GRACE solution from data centres. Qx ˆ (1) – Mass constraints from hydrology. Q2 – Hydrology covariance matrix. Rx & Ry – Redundancy contribution of GRACE & hydrology, respectively..
20
0.6 0.4
40 60 !60 !40 !20
0.2 0
20
40
60
!60 !40 !20
S
0
20
| Order | C
40
!60 !40 !20
60
0
20
40
0
60
lm
Figure 3: Redundancy contribution of the hydrological mass constraints. It is apparent from figure 3 that the contribution of hydrology increases with increase in order. However; there is also substantial contribution to the degree two elements. The contribution naturally indicates that hydrology provides GRACE with information about the small-scale features. Also, it can be seen that the different GRACE covariance structures provide more or less the same redundancy contribution. However, this is not the case when the difference between those estimates are investigated. U
U
U
0 May 02
Sep 02
Jan 03
May 03
Sep 03
Jan 04
May 04
Sep 04
2,005
GRACE and hydrology common data period
Figure 1: Circled regions in Sahara show the dry periods, and in Yukon run-off in the circled periods stay constant even if precipitation fluctuates, indicating frozen conditions. The water storage change from (2) can now be directly compared with GRACE water storage change estimates. Such information is available for EGU General Assembly 2008, 13-18 August 2002, Vienna, Austria.
1e!1 1e!3
1e3
CSR release 04 Constrained solution using full covariance Constrained solution using block diagonal covariance Constrained solution using diagonal covariance
10 1e!1 1e!3 1e!5
Filtered with Gauss 500km filter
Catchments used for constraining GRACE solution
Figure 5: Misclosure between the observed mass estimates and the mass estimates from GRACE solutions. Good estimates must be close to zero.
U
U
U
U
(a)
The constrained unfiltered GRACE solutions are closer to zero than the CSR release 4 dataset, which is what the technique was expected to do. But, the misclosure increases as soon as the constrained data is low-pass filtered. This can be traced to figure 3, where the contribution of the constraints are only beyond degree 40. Therefore further low-pass filtering after constraining removes what has been restored. 4. Summary and Outlook Mass constraints from reliable hydrology data can be used for improving the signal quality of GRACE. The constrained signal can be used without further filtering. Hydrology contributes significantly for improving the signal content in the higher harmonic degrees. It has to be investigated as to how the hydrological mass constraints map into the higher harmonic degrees.
U
40
In the analysis carried out, sixty catchments matched the criterion of negligible ETa, but only twenty-eight catchments were usable due to data gaps. The stochastic information for this hydrological data was mainly taken from hydrology literature. In general, precipitation data can be considered accurate to 5–30% 1 and the discharge data is accurate to 30% 2 in the Arctic regions. So, for the analysis the upper limit error of 30% of the mass estimate was chosen uniformly for all the catchments. Further, three different structures of GRACE covariance matrices were used in the analysis. It is widely believed that the full covariance matrix is closely approximated by the block-diagonal covariance matrix 3. It was intended to verify if this holds true in general, and specifically for the case of GRACE.
1e1
0
U
20
1e3
Variances
Sequential estimation
100
Destriped
1e!5 1e5
0.8
∆TAB = YΛK & '−1 T T Λ Y YΛ QGRACE =
∂S of the Deriving stochastics for ∂t catchments with negligible ETa
(d)
Figure 2: (a) Catchments that constrain the GRACE solution. Constrained solutions obtained using (b)full covariance information; (c) block diagonal covariance information; and (d) only variance information of the GRACE solutions.
Λl ∆Ylm Klm
l,m
Western Sahara catchment
60
1e!5 1e5
GRACE
lm
80
1e!1
!30˚
!60˚
;;;
Initially, it was thought that such information could be used for calibrating hydrological models. However; GRACE has not met the expected level of accuracy. This inaccuracy is the contribution of the large errors due to aliasing in the higher harmonic degrees of the GRACE solutions. In order to counteract these erroneous higher harmonic degrees, various filtering techniques tailor-made for GRACE data have been developed. While these filters remove noise they also remove a good part of the signal. So, these filtered datasets have to be validated with other reliable hydrological datasets. The problem with hydrology datasets has always been that evapotranspiration measurements are difficult to obtain and hence, only information from models is available. This makes it difficult for validating filtered GRACE data. On the flip side, for particular catchments evapotranspiration is negligible due to their geographical setting and hence their climatic regime. This is true for catchments in the Arctic regions where the winters are extremely cold with sub-zero temperatures; for catchments in dry regions like deserts where the precipitation is very meagre that evapotranspiration can be completely neglected; and for catchments fed by seasonal rivers, which go dry when there is no precipitation and hence, evapotranspiration can be neglected. This reduces the continental water balance equation to, ∂S ∂t
60˚
(1)
Actual Evapotranspiration = Water storage change
1e5 Without filtering and destriping
!30˚
,
Finally, to verify the constrained estimates a closed-loop analysis was carried out. The mass estimates from the constrained and unconstrained GRACE solutions for the twenty-eight catchments were compared with the corresponding hydrological mass estimates.
dM/dt [mm/month]
Run-off −
In figures 2(b), 2(c), and 2(d) the constraints that were applied to GRACE solutions have taken care of the noise in the regions where they were applied and also smoothing out some of the adjacent areas.
Degree
Precipitation −
3. Results and Discussion
30˚
Constraints
P − R−
about 20% of the land mass. However; only part of this 20% can be used for a particular time-period, because of the climatic regime of each of those catchments. In this contribution, this reliable hydrology information is used for constraining the GRACE monthly solutions, and there-by re-estimate the spherical harmonic coefficients via sequential estimation techniques. This technique is illustrated for the month of Januray 2003 with GRACE CSR release 4 dataset.
U
(b)
Figure 4: Difference between unfiltered sequential mass estimates using (a) full covariance information and block diagonal information; (b) full covariance information and variance information of GRACE. It is evident from figures 4(a) and 4(b) that using only the blockdiagonal covariance information of GRACE is as good as using the full covariance information of GRACE.
Simulated block diagonal covariance matrices were shown to closely approximate the simulated full covariance matrices. Additional reliable data sources other than hydrology can also be used for constraining GRACE solutions. References 1. Xie, P. and Arkin, P. A. Journal of Climate 9, 840–858 (1996). 2. Shiklomanov, A. I. et al. Journal of Hydrology 326, 231–256 (1996). 3. Han, S. -C. OSU Geodetic Reports 467, (2003). 4. Bouman, J. Publications on Geodesy, Netherlands Geodetic Commission 48, (2000).
