On Evaluation of Recharge Model Uncertainty: a Priori and a Posteriori Page: 4 of 8
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different (Figure 2), the aggregated probabilities are more
or less uniform, considering that the equally likely prior
probability is 20%. The largest deviation from the equally
likely prior probability is only 10% for model DPW1.
This manifests the inherent uncertainty in the recharge
models, since they are developed independently based on
solid physical principles and assumptions, calibrated withsite measurements, and have all been applied to water
resource management in Nevada. Since none of the
models dominates over other models and all models have
prior model probabilities larger than 5%, there is no
justification to select one model and discard others, a
priori.Figure 2. Column chart of prior probabilities of the five models given by seven experts. Columns of each model represent
elicited prior model probability from one expert. Model names are explained in Table 1.
the recharge model is a component. DVRFS was modeled
by [5] using MODFLOW2000, and a three-dimensional
20 MEhydrogeologic framework based on characterization of
25% regional geology, hydrology, and hydrogeology. The
recharge model used in DVRFS is DPW1 developed by
[7]. Our study is to assess recharge model uncertainty in
the modeling framework of DVRFS, without modifying
13% its other components. DVRFS was calibrated using
MODFLOW2000 against a total of 4,963 observations of
head (2,227), head change (2,672), discharge (49), and
DPW1 constant-head flow (15). These observations are also used
11 i 31% in our calibration.
Figure 3. Prior probabilities of the five recharge models Our calibration process, however, is different from
obtained through an expert elicitation. Model names are that of DVRFS, which calibrated 55 model parameters, 23
explained in Table 1. in the steady-state model and 32 in the transient model.
Our model calibration is based on the transient model
IV. EVALUATE RECHARGE MODEL only, since there is insufficient information to identify
UNCERTAINTY: A POSTERIORI how the 23 parameters are calibrated in the steady-state
model. In addition, only some of the 55 parameters are
calibrated in our study, due to different purposes of our
Recharge model uncertainty is assessed, a posteriori, study. Specifically, 32 of the 55 parameters are calibrated
by maximum likelihood model calibration against site for DPW1 and DPW2. The two models estimate
observations. Results of model calibration are used to precipitation (not recharge), which is converted to
estimate model likelihood p(DlMk), which, in turn, is used recharge within DVRFS by dividing the top model layer
to evaluate posterior model probability p(MJD) in (4). into five recharge zones. Recharge coefficients in two
Whereas prior model probabilities must in our view zones are calibrated against site observations. Since the
remain subjective, the posterior model probabilities are other three models estimate recharge directly, recharge
modifications of these subjective values based on an coefficients are not used and therefore only 30 parameters
objective evaluation of each model's consistency with are calibrated. All other calibration parameters are the
available data. same as those used in DVRFS. Although MLBMA allows
different models having different numbers of calibrated
N.A. Model Calibration Using MODFLOW2000 parameters, we intend to calibrate the same model
parameters for all the recharge models so that model
Plausibility and uncertainty of each of the five ranking and uncertainty analysis are on the same basis. In
recharge models is evaluated by calibrating the Death the same line, model calibration is conducted in the same
Valley Regional Flow System (DVRFS) model, of which50.00
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L 25.00
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0 15.00
10.00
. 5.00
0. 0.00
ME DPW1 DPW2 CMB1 CMB2
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Ye, Ming; Pohlmann, Karl; Chapman, Jenny & Shafer, David. On Evaluation of Recharge Model Uncertainty: a Priori and a Posteriori, article, January 30, 2006; [Nevada]. (https://digital.library.unt.edu/ark:/67531/metadc881232/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.