Local to Regional Hydrological Model Calibration for the Okavango River Basin from In-situ and Space Borne Gravity Observations

Transcription

1 Local to Regional Hydrological Model Calibration for the Okavango River Basin from In-situ and Space Borne Gravity Observations Lars Christiansen (1), Pernille E. Krogh (2), Peter Bauer-Gottwein (1), Ole B. Andersen (2), Silvia Leirião (1), Philip J. Binning (1), Dan Rosbjerg (1) (1) Institute of Environment & Resources, Technical University of Denmark Bygningstorvet, DTU Building 1, DK-28 Kgs. Lyngby, Denmark (Christiansen) (Bauer-Gottwein) (Leirião) (Binning) (Rosbjerg) (2) Danish National Space Center, Technical University of Denmark Juliane Maries Vej 3, DK-21 København Ø, Denmark (Krogh) (Andersen) Introduction The Okavango Delta in Botswana, Southern Africa, is one of the World s largest wetlands. Placed in a semi-arid region, the delta and its rich flora and fauna are under constant pressure due to human water abstraction and climate variations. The recently started HYDROGRAV research project ( focuses on the use of gravity data for hydrological model calibration at continental to local scales, with the Okavango Delta as one of two model areas. Changes in total water storage in hydrological systems provide a strong constraint on model calibration, but are difficult to monitor with traditional methods. As a change in total water storage translates directly into a change in gravity, the introduction of more precise measurement methods over the past years provides a new data type for hydrological model calibration. The Okavango Delta Mohembo Gauging Station 2km Fig. 1. Location of the Okavango Delta and Mohembo Gauging Station. Project Objectives In the early stage of the HYDROGRAV project, the objectives are to: Use time-lapse remote sensing gravity data (GRACE) to calibrate a large scale hydrological model covering the Okavango Delta and surroundings. Show that in-situ gravity data provide new information for the calibration of local-scale hydrological models by performing a pump test as a proof-of-concept. We here present our initial analysis of the ability of GRACE data to resolve the lateral movement of water in the Okavango Delta, and then move on to analyse the in-situ gravity response from a simulated pump test. Space Borne Gravity Observations The twin GRACE satellites (Gravity Recovery And Climate Experiment) have now completed more than five successful years in orbit since their launch on March 17 th 22 through the joint partnership between the US National Aeronautics and Space Administration (NASA) and the German Deutschen Zentrum für Luft- und Raumfahrt (DLR) [1]. GRACE is capable of measuring large-scale mass re-distributions within the entire Earth system with

2 unprecedented accuracy [2], but it is not capable of discriminating between the different contributors such as atmosphere, ocean, water-storage on land, or solid earth contributions. Amplitude 2 Phase GRACE BGI GRACE mascon a b [cm H2] [cm H2] d e GLDAS c Longitude 1 [cm H2] f Longitude Fig. 2. Amplitude and phase of the semi-annual change in terrestrial water storage over Southern Africa from the hydrological model GLDAS and two differently processed sets of GRACE data. Data used in Fig. 3 is marked with a 2 GLDAS GRACE mascon GRACE BGI Discharge Jan3 Jan4 Jan Jan6 Jan7 Fig. 3. Semi-annual variations of the two GRACE solutions, a hydrological model (GLDAS), and the discharge at Mohembo Gauging Station (see Fig. 1 for location). GRACE and GLDAS time series locations are marked with a square in Fig. 2.

3 GRACE Data in Southern Africa 6 sub-monthly (1-day) gravity field solutions from GRACE, processed by the French International Gravimetric Bureau (BGI), have been studied and compared with a mass concentration solution (mascon), also sub-monthly, developed by NASA/Goddard Space Flight Center (GSFC) and a hydrological model GLDAS, developed jointly by NASA/GSFC and National Oceanic and Atmospheric Administration (NOAA)/National Centers for Environmental Prediction (NCEP) [3]. Fig. 2 shows the amplitude and the phase of the semi-annual variations. BGI GRACE gravity solutions have been corrected for several undesired effects, and the time-lapse gravity models only differ from the static field by un-modelled effects, which in Southern Africa mainly is due to hydrology [4]. The studied data span the period of Aug-22 to Feb-27 and is presented in a 1 grid resolution. Mass concentration (mascon) solutions provide measures of the change in continental water storage over the land areas with a 4 gridded resolution. Mass anomalies are directly solved and require no additional a posteriori processing or smoothing, thus preserving high spatial resolution []. The presented data span the period of Mar-23 to Apr-27. The Global Land Data Assimilation System (GLDAS) uses satellite and ground-based precipitation and evapotranspiration measurements to model the gravitational signal. Spatial and temporal characteristics are identical with those of the mascon solutions []. Lateral water flow is not considered in the model. Annual Variations in the Okavango Delta The largest annual variations in terrestrial water storage in the southern part of Africa occur around latitude 1- S (Fig. 2a, b, c), but also in the area of the Okavango Delta the fluctuations are noticeable (Fig. 3 and table 1). The water flowing through the Okavango Delta mainly originates from the highlands of Angola (located -1 km NW of the delta, constituting 9% of the catchment) where the rainy season occurs from November to March. The peak of the flood reaches the delta panhandle in April, as can be seen by the peak in discharge at Mohembo Gauging Station (table 1), but does not reach the extremity of the seasonal floodplains until August-September. The GLDAS model, not considering lateral water movement, reflects the timing of the rainy season, which in the Okavango Delta coincides with that of Angola (November-March), and hence water levels peak in late March. Table 1. Amplitude, phase, and peak timing of the semi-annual signals shown in Fig. 3. GRACE BGI GRACE mascon GLDAS Discharge Amplitude 4.4 cm H cm H 2 9. cm H 2 Phase 98 = 7-April 112 = 21-April 86 = 26-March 11 = 1-April Considering the NW-SE lateral movement of water in the delta during April to September, the gravitational anomaly will follow the flood wave, and hence the timing of peak water flow advances from NW towards SE. The GRACE satellites, however, have a very large footprint area and the Okavango Delta only accounts for about 12.% of the total effect measured by GRACE in the area. For this reason the temporal variation in the timing of flood wave peak within the catchment and delta cannot be resolved by GRACE. In-situ Gravimetry and Hydrology Motivation Calibration of local-scale groundwater models is usually done using point data such as head observations, discharge, and precipitation. By using in-situ high-precision ( nms -2 with a Scintrex CG- instrument) relative, time-lapse gravimetric measurements, true volume data is introduced as an additional constraint, adding new information to the calibration process. Objectives Improve hydrological model calibration at local scale using time-lapse relative gravimetry. Investigate the information content of gravity data in relation to hydrological models. Where should we measure to add most possible additional information to the calibration? Develop a new method for measuring evapotranspiration using direct observations of mass loss. Establish field routines for gravity data suitable for hydrological model calibration (e.g. sample rate and density).

4 Calculation of Gravity Signal In order to calculate the gravity response associated to the temporal changes in hydraulic head in a discretized groundwater model, the conventional methods developed for terrain correction (see e.g. [6]) are applied directly. Since calibration of the model, might involve thousands of model runs, model run time in particular is a critical factor when considering method applicability. Therefore methods for calculating the contribution to the gravity potential from each model cell are selected based on a precision criteria: At close distances to the gravimeter an exact prism formula is applied, whereas more time efficient, approximate methods are used at larger distances [6]. The gravity data is fed into groundwater model calibration along with other observations, but no geophysical inversion of the gravity signal is performed at this time. Example: Pump Test Model As initial preparation for a planned pump test, a homogeneous, isotropic, 2D groundwater model is set up in MODFLOW with a 2 m 3 h -1 pump in the centre, a specific yield of.2, initial water level m below ground level, and a transmissivity of.3 m 2 s -1 (see Fig. 4). The model simulation time is 7 days, with a data output in the form of hydraulic head and gravimetric signal every hour (168 hours). During the pump test, the gravimeter is moved around in the area in order to investigate the spatial distribution of the gravitational signal. Before calibration, Gaussian noise with a standard deviation of nms -2 is added to the resulting gravity data. At this early stage, calibration is done with respect to one parameter, transmissivity, using PEST [7]. Later specific yield will be included also. Monitoring well Gravimeter Mass removal T =.3 m 2 s -1 S y =.2 Fig. 4. Pump test model. The model has one layer and a 94 m x 94 m x 6 m domain with growing cell size from the model centre and towards the rim. Gravimeter position is varied to investigate the spatial distribution of the gravitational signal. Preliminary Results As expected the gravitational signal is largest above the pumping well, since the most mass is removed from the system directly below that point. The signal gets weaker with the distance, r, from the well, following the combined effect of the shape of the drawdown cone, which is proportional to ln(r), and the change in the gravitational signal, which goes as r -2. Fig. shows the gravity signal according to distance and time of pumping. After one hour, the change in gravity near the well is twice the instrument precision. After one week, the change is 12 times the precision. The limits of detection after seven days are around m from the pumping well. When calibrating the model using gravity data only (no head values) from a position at the pumping well, the true, known transmissivity is found with only 4% error. Calibration of the model with more parameters, dividing the model into areas of separate transmissivity, and using a combination of gravity and hydraulic head data has been performed, but is still at a too early stage to be conclusive.

5 Gravity change [μgal] hour hours 1 day 7 days Distance from well Fig.. Change in gravity as a function of distance, r, from the pumping well. With an instrument precision of nms-2 (horizontal black line) the limits of detection after seven days of pumping are at around m. Note the use of a logarithmic horizontal scale. Conclusion The hydrological signal of the NW-SE lateral movement of the annual flood wave in the Okavango Delta is not resolved by GRACE. A hydrological model covering the surrounding catchments must be build and the contribution from this area calculated and subtracted from the GRACE data in order to isolate the signal originating from the flood wave in the delta. The difference in foot print of GRACE and the ground based instrument is several orders of magnitude and ground based data thus cannot be expected to be used to improve the resolution of GRACE data. Simulations show that gravity data can be used to calibrate a homogeneous, isotropic pump test model without the use of other data (e.g. hydraulic head). A proof-of-concept pump test, for which a more complex model will be build, is planned for early 28 in Denmark. Acknowledgement The article is a contribution to the HYDROGRAV project funded by the Danish Agency of Science, Technology and Innovation under contract number References [1] Tapley, B.D. and C. Reigber (2) The GRACE mission status and future plans, EOS Trans AGU, 81, Fall meeting Supp., Abstract F311. [2] Tapley, B.D., S. Bettadpur, M. Watkins, and C. Reigber (24) The Gravity Recovery and Climate Experiment: Mission overview and early results, Geophys. Res. Lett., 31, L967, doi:1.129/24gl1992. [3] Rodell, M., P.R. Houser, U. Jambor, J. Gottschalck, K. Mitchell, C.-J. Meng, K. Arsenault, B. Cosgrove, J. Radakovich, M. Bosilovich, J.K. Entin, J.P. Walker, D. Lohmann, and D. Toll. (24) The Global Land Data Assimilation System, Bull. Amer. Meteor. Soc., 8 (3), [4] bgi.cnes.fr [] grace.sgt-inc.com [6] Forsberg, R. (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling, Ohio State University, scientific report no.. [7] Doherty, J. (2) PEST: Model Independent Parameter Estimation, fifth edition of user manual. Watermark Numerical Computing, Brisbane, Australia.