# Presentation: 364970

## III. Ground-Water Management Problem Used for the Exercises 

## Ground-Water Flow System

- The flow system is comprised of two confined aquifers separated by a confining unit.
- Inflow occurs primarily as areal recharge; there is also a very small amount of inflow across the boundary with the hillside.
- At steady-state, outflow occurs only as discharge to the river.

## Management Issues

**Ground-water management issues** related to this flow system:
**Pumping wells** for water supply are being completed in aquifers 1 and 2. The effect of pumping on the river is of concern, because there is a minimum required discharge from the ground-water system to the river.
- A **landfill** is proposed in one corner of the study area. The landfill developers claim
- (a) the landfill is outside the capture zone of the wells and
- (b) any leaking effluent will reach the river sufficiently diluted.
- We are developing a **flow model** to help evaluate these claims.

## Predicted transport from landfill

## Ground-Water Flow Model

- First, **steady-state model without pumping** will be developed and calibrated using available measurements of hydraulic-heads and discharge to the river, and will be used for preliminary evaluation of the issues.
- Then,** pumping wells will be installed**, a long-term aquifer test will be conducted using the wells, and a transient model of the system will be recalibrated using the steady-state measurements as well as the additional drawdown and river discharge data collected during the test.
- See flow model setup in Figure 2-1b (page 32) of Hill and Tiedeman.
- See model parameter definition and starting values in **Table 3-1** (**page 38**).
- See true simulated conditions in Figures 2-1c and 2-1d (**page 22-23**).

## MODFLOW Packages Used 

- Basic (BAS) and the Discretization input file
- Define model grid, including rows, columns, and layers
- Define types of model layer (confined; convertible)
- Layer Property Flow (LPF)
- Define hydraulic properties – K, Ss, Sy, Anisotropy
- Recharge (RCH)
- Define distribution of areal recharge
- River (RIV)
- General-Head Boundary (GHB)
- Well (WEL)
- Define pumpage
- Used here for prediction runs only

## Spatial Discretization -- Ground-Water Flow Model Grid

- Figure 2-1b of Hill and Tiedeman (page 22)

## Layer-Property Flow Package

- Figure 2-1a of Hill and Tiedeman (page 34)

- Define hydraulic properties – K, Ss, Sy, Anisotropy

- Model layer 1 is homogeneous
- Model layer 2 has K that increases linearly from beneath the river to the hillside

## Recharge Package

- Can apply recharge to model layer 1 or top active cell at each row, column location
- Input a flow rate (L/T). The program multiplies by area to get volume per time.
- Layer data.
- Parameters are used to define the recharge rate.
- For this problem, use 2 zones; no multiplication arrays.

## The River (RIV) and General-Head Boundary (GHB)Packages are used

- The River (RIV) and General-Head Boundary (GHB)Packages are used

- Both define head-dependent boundaries: q=C(H-h)

- GHB

- DRN

- RIV

## Well Package

- List data – layer, row, column, pumpage rate
- Input volume of discharge per time. Outflow is NEGATIVE.
- For this problem, no pumpage parameters need to be defined, but you can use the parameter capability to define them if you like. [Why might you want to do that?]

## Parameters and Starting Values

- Table 3-1 of Hill and Tiedeman (page 38)

## Slide 13

## True Simulated Conditions

- Figure 2-1 c and 2d of Hill and Tiedeman (page 22-23)

## Observations

**10 head observations**, 5 in each model layer.
- 	Observed values shown in Table 3-2 (page 38) of Hill and Tiedeman.
**1 steady-state flow observation**: ground-water discharge to the river of –4.4 m3/sec.

## Head Observations

- Table 3-2 of Hill and Tiedeman (page 38)

## Weighting is accomplished using UCODE_2005

- Here we break for a lecture introducing UCODE_2005

## Weights on Observations

**Weighted **residuals are squared and summed in the objective function:

**Prior**

**Heads**

**Flows**

- Need to weight the observations for two primary reasons:
- So that residuals for observations with **different units** (e.g. heads and flows) can be summed in the objective function.
- To account for different observations having **different degrees of measurement error**. Weighting is used to reduce the influence of observations that are less accurate, and to increase the influence of observations that are more accurate.

## Weights on Observations

- Defining the weights as being proportional to the **inverse of the variance of measurement error** meets both these needs:

- The variance of measurement error is an estimate of the uncertainty of the observation. How do we quantify this?
- Need to quantify the uncertainty using:
- A range that is symmetric about the measurement used for the observation.
- A probability with which the true value is expected to occur within the range.

## Weights on Observations: Example 1

- A head observation is thought to be “good to within 3 meters”.
- Quantify this as “there is a 95-percent chance the true value falls within 3 meters of the measurement.”
- Use a normal probability table to determine that a 95-percent confidence interval is a value plus and minus 1.96 times the standard deviation, ****.
- Thus, 1.96 x **** = 3 m, so **** = 1.53 m, and the variance ****2 = 2.34 m2.

## Weights on Observations: Example 2

- A measurement of stream loss to a ground-water system is derived by subtracting two streamflow measurements, an upstream value of 3.0 m3/s and a downstream value of 2.5 m3/s .
**Quantify uncertainty**: The first measurement is considered to be slightly worse than the second. For the upstream measurement, the hydrologist believes that there is a 90% chance that the true value falls within ± 5% of the measured value; for the downstream measurement, there is a 95% chance that the true value falls within ± 5% of the measured value.
- Using values from a **normal probability table**, a 90% confidence interval is a value ±1.65 times the standard deviation, ****.
**Upstream measurement**: 1.65 x **** = 0.05 x 3.0 m3/****, so **** = 0.091 m3/s.
**Downstream measurement**: 1.96 x **** = 0.05 x 2.5 m3/****, so **** = 0.064 m3/s.
- The loss of streamflow in the reach between these two measurements is 0.5 m3/s. How accurately is this loss known? **Add variances!!**
- The variance of the loss is 0.0912 + 0.0642 = 0.0124 (m3/****)2.

## Weights for the Steady-State Problem

**Head Observations**:
- Elevation of each observation well has a variance of measurement error of 1.00 m2.
- Each water-level measurement has a variance of measurement error of 0.0025 m2.
- Thus, total variance measurement error = 1.0025 m2
**Flow Observation**:
- Coefficient of variation of 10%; thus **** = 0.1 x 4.4 m3/s = 0.44 m3/s
- DO EXERCISE 3.2d: Calculate weights on hydraulic-head and flow observations.

## Model Fit Using Starting Parameter Values

** ****DATA AT HEAD AND FLOW LOCATIONS**
** ****OBSERVATION       MEASURED      SIMULATED                            WEIGHTED**
**    ****NAME            VALUE          VALUE      RESIDUAL   WEIGHT**.5   RESIDUAL**
** ****hd01.ss            101.804       100.225       1.579       0.999       1.577    **
** ****hd02.ss            128.117       139.331      -11.21       0.999      -11.20    **
** ****hd03.ss            156.678       174.363      -17.68       0.999      -17.66    **
** ****hd04.ss            124.893       139.331      -14.44       0.999      -14.42    **
** ****hd05.ss            140.961       157.132      -16.17       0.999      -16.15    **
** ****hd06.ss            126.537       139.632      -13.10       0.999      -13.08    **
** ****hd07.ss            101.112       102.868      -1.756       0.999      -1.754    **
** ****hd08.ss            158.135       173.956      -15.82       0.999      -15.80    **
** ****hd09.ss            176.374       190.300      -13.93       0.999      -13.91    **
** ****hd10.ss            142.020       157.041      -15.02       0.999      -15.00    **
** ****flow01.ss         -4.40000      -4.86060      0.4606        2.27       1.047    **
-  **STATISTICS FOR THESE RESIDUALS:**
** ****MAXIMUM WEIGHTED RESIDUAL:  0.158E+01  Observation: hd01.ss             **
** ****MINIMUM WEIGHTED RESIDUAL: -0.177E+02  Observation: hd03.ss             **
** ****AVERAGE WEIGHTED RESIDUAL: -0.106E+02**
** ****# RESIDUALS >= 0.  :       2**
** ****# RESIDUALS <  0.  :       9**
** ****NUMBER OF RUNS:        3  IN       11 OBSERVATIONS**
** ****SUM OF SQUARED WEIGHTED RESIDUALS           :    1752.4    **
** ****SUM OF SQUARED WEIGHTED RESIDUALS WITH PRIOR:    1752.4    **
** ****SUM OF SQUARED, WEIGHTED RESIDUALS:**
**   ****DEPENDENT VARIABLES:   1752.4    **
** **

- From UCODE-2005 output file.
- DO EXERCISE 3.3: Evaluate model fit using the starting parameter values.

- Least squares objective function

## Example Least-Squares Objective Function

**HEADS**
**FLOWS**
**PRIOR**

**Notes:**
Plyers: Vrugt, Hosin Gupta, oroosh Sorrooshian

## Basic Steps
for Model
Calibration
Italicized steps
are affected by
using regression

- for Model
- Calibration
***Italicized*** steps
- are affected by
- using regression