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Results
Pre-analysis showed that hydraulic conductivity (Kf) and groundwater recharge (RCH) were the
most sensitive parameters over the entire area. Therefore, they were chosen to be split into
four regions. Within the consequent spatial analysis, the most sensitive parameter for overall
model efficiency is Kf in 3 regions, followed by the DRN and CHD boundary conditions.
Parameters of the conduit system and recharge are less sensitive. While the ranking of discharge
sensitivity is quite similar to overall sensitivity, the prediction of hydraulic heads is more strongly
dominated by Kf, and less by RCH or CHD. Among the conduit parameters, Exch and d are most
influential for hydraulic heads.
Spatially distributed sensitivity indices of Kf and RCH for different output measures are shown
below. The greater the Kf parameter value in one region is, the bigger is its sensitivity index. The
hydraulic head sensitivity indices are generally higher than those for spring discharges. For RCH,
sensitivity indices have a different pattern. Discharge indices are highest in regions that
contribute to all springs’ discharge, head indices are highest where model fit is worst.
Model & Data
The study uses an existing MODFLOW-CFP mode 1 model including discrete conduits and a
porous matrix. It evolved over many years with several model versions by different authors.
Input data and model parameters were derived from a steady-state model run by Gallegos
et al. (2013) for one time period in 1991, published by Kuniansky (2016). Observation data
from three karst springs and 13 observation wells are available for that time.
Gallegos, J. J. , Hu, B.X., Davis, H. (2013): Simulating flow in karst aquifers in laboratory and sub-regional scales using MODFLOW-CFP: Hydrogeology
Journal, v. 21, no. 8, p. 1749-1760.
Kuniansky, E. L. (2016): MODFLOW and MODFLOW Conduit Flow Process data sets for simulation experiments of the Woodville Karst Plain, near
Tallahassee, Florida with three different approaches and different stress periods: U.S. Geological Survey Data Release, http://dx.doi.org/10.5066/F7PK0D87
Method
With the given model and calibrated parameters, a sensitivity analysis was conducted
using the Elementary Effects test (Morris’ method). The sensitivity analysis results
(hydraulic heads and spring discharges) were evaluated with the observations by the Nash-
Sutcliffe-Efficiency (NSE). To compare both heads and discharges, their NSEs were
standardized with their mean and standard deviation. With the resulting values NSEnorm,
input parameter sets X for “initial” and altered points, and parameter range R, Elementary
Effects EE of each parameter i were calculated:
𝐸𝐸𝑖=|𝑁𝑆𝐸𝑛𝑜𝑟𝑚,𝑖 −𝑁𝑆𝐸𝑛𝑜𝑟𝑚,𝑖𝑛𝑖𝑡𝑖𝑎𝑙|
|𝑋𝑖− 𝑋𝑖𝑛𝑖𝑡𝑖𝑎𝑙|∙ 𝑅𝑖
The mean of all Elementary Effects for each parameter is the sensitivity index used for
parameter ranking. Uncertainty ranges were derived with the bootstrapping method. The
detailed workflow is given below:
Sensitivity analysis of a distributed karst
hydrological model at a Floridan karst aquifer
Schima, B.1, Reimann, T.2 , Xu, Z.3, Hu, B.4, Hartmann, A.1,5
1) Albert-Ludwigs-Universität, Freiburg, Germany 2) Technische Universität Dresden, Dresden, Germany 3) Lawrence Berkeley National Laboratory, Berkeley, CA, USA
4) Florida State University, Tallahassee, FL, USA 5) University of Bristol, Bristol, UK
Motivation & Objectives
Karst aquifers are a significant source of drinking and irrigation water in many countries
worldwide. For a proper water management, knowledge of the processes controlling the
available amounts of water is crucial. A valuable to support water management are
distributed simulation models. However, their input parameters are often subject to large
uncertainties. Sensitivity analysis methods are able to analyze these uncertainties and to
provide directions for uncertainty reduction. The aim of this study is to conduct a sensitivity
analysis to rank the parameters according to their influence on the model performance. A
spatial breakdown of the most influential parameters is supposed to additionally rank the
most important regions of the simulation area.
Conclusion
The study shows that, under the assumption of steady-state conditions, hydraulic conductivity,
boundary conditions and, to a lesser degree, certain conduit parameters are influential for the
efficiency of a distributed groundwater model of the Woodville Karst Plain. Most notably, the
contribution of different model regions varies. The spatial pattern of the regions’ sensitivities
strongly depends on the regarded output variable and the distribution of monitoring stations.
Consequently, the model performance obtained by NSE is dominated by the regions with high
sensitivity and the capability of the model to provide reliable simulations at regions with low
sensitivity remains questionable.
Variable
Explanation
K
f B1 – B4
Hydraulic
conductivity in regions 1 to 4
RCH B1
–
B4
Groundwater
recharge in regions 1 to 4
DRN
cond
Conductivity
of drains (representing
rivers
)
DRN
elev
Elevation
of drains
CHD
Elevation
of constant head boundary
condition
Define parameters and ranges Generate input parameter samples
(Latin Hypercube Sampling)
Create MODFLOW input files
.cfp .chd .drn .lpf .rch .wel .nam Matrix X
Run model
RCLOSE
HCLOSE
Water budget
M parameters
Inspect results
Sort out invalid runs
Criteria for valid runs
Calculate objective
function
Simulated discharge
and head
NSEnorm
Calculate „Elementary
Effects“ Plot results
Analyse uncertainty
Determine convergence
Repeat r(M+1)
times
Variable
Explanation
Exch
Exchange
parameter between
matrix
and conduits
d
Conduit
diameter
Roug
Conduit
wall roughness
Tort
Conduit
tortuosity
Temp
Water
temperature
WEL
Various
other recharge sources
(
implemented with WEL
boundary
condition)
Study site
The Woodville Karst Plain is located in northwest Florida,
bordered by Tallahassee in the north and the Gulf of
Mexico in the south. Topography is hilly with elevations not
exceeding 200 ft. The general flow direction of the water is
from the north to the Gulf of Mexico. The modelled layers
represent the Upper Floridan Aquifer, which consists
mostly of different limestones. Due to the geologic
properties, there are many sinkholes, an extensive
submerged cave system and three major springs.
Woodville Karst Plain
Open Street map, www.osm.org
Model
evaluation
Nash-Sutcliffe-Efficiency:
Schima ● 0.68
Gallegos et al. Δ 0.70