Lab Report on Water Resources
Introduction: The water cycle is essential to life, and therefore it is very important to fully
understand the implications of the relationships between the different reservoirs. The cycle
can be modeled using Stella with six reservoirs: ground water, surface water, marine
atmosphere, terrestrial atmosphere, snow/ice, and oceans. The relationships between the six
reservoirs are outlined in Figure 1. Modeling can be helpful in exploring the impacts of change
on the cycle, because it would be dangerous and impossible to experiment with the actual
water cycle.
Groundwater
Land Atmosphere
Marine Atmosphere
Surf ace Water
Snow and Ice
Oceans
Land Atmosphere
Marine Atmosphere
Ev aporation f rom land
Adv ection
Ev aporation
Surf ace Water
Percolation
Rain 1
Surf ace runof f to oceans
Oceans
Groundwater
Discharge
Rain 2
Precipitation snow on land
Sea Lev el
Snow and Ice
Melting
Figure 1: Interrelatedness of resevoirs of the water cycle.
The values used for the resevoirs’ initial amounts are summarized in Table 1.
Inventory of Water
Total amount of water: 1,385,990.5 x 1015 kg
Reservoirs
Oceans
Mass of Water in 1015 kg
Approximate %
1,350,000
97.4
11
0.0008
4.5
0.0003
275
0.02
8,200
0.59
27,500
1.98
Marine atmosphere
Land atmosphere
Surface Water
Ground Water
Snow & Ice
Table 1. Reservoir values for model.
Estimated Flows of Water in the Global Water Cycle
Flows given in units of 1015 kg/year
Process
Evaporation from oceans
Evaporation from land
Precipitation on oceans
Transfer from marine to land atmosphere
Precipitation (rain) on land
Precipitation (snow) on land
Melt-water return to surface water
Surface runoff to oceans
Surface percolation into groundwater
Groundwater flow into oceans
Flow (note: this is a rate)
435
71 (mainly from soil water)
398
37 (also known as advection)
107
1
1
34
2
2
Table 2. Flow rates for inflow/outflows.
Using the equations in table 2 for the inflows and outflows, the following equation was used,
where 10 is the flow rate. The equation for sea level is also shown below.
Sea_Level = 100*((Oceans-INIT(Oceans))*1E12/3.61E14) {cm}
PART A:
Based on these equations, the following graphs were generated. They represent a steady state
in which the inflows of the reservoirs equal the outflows.
1: Groundwater
1:
8201
1:
8200
1:
8199
1
0.00
1
3.00
Page 1
1
6.00
Time
1
9.00
12.00
11:45 AM Fri, Mar 13, 2009
Groundwater
1: Land Atmosphere
1:
5
1:
5
1:
4
1
0.00
Page 1
1
3.00
1
6.00
Time
1
9.00
12.00
11:45 AM Fri, Mar 13, 2009
1: Marine Atmosphere
1:
12
1:
11
1:
10
1
0.00
1
3.00
1
1
6.00
Time
Page 1
9.00
12.00
11:45 AM Fri, Mar 13, 2009
1: Oceans
1:
1350001
1:
1350000
1:
1349999
1
0.00
Page 1
1
3.00
1
6.00
Time
1
9.00
12.00
11:45 AM Fri, Mar 13, 2009
1: Snow and Ice
1:
27501
1:
27500
1:
27499
1
0.00
1
3.00
1
6.00
Time
Page 1
1
9.00
12.00
11:45 AM Fri, Mar 13, 2009
1: Surf ace Water
1:
276
1:
275
1:
274
1
0.00
1
3.00
Page 1
1
6.00
Time
1
9.00
12.00
11:45 AM Fri, Mar 13, 2009
Fig. 2 Graphs of the Steady States.
PART B:
Residence Times
Reservoir
Ice
Groundwater
Oceans
Land (Surface Water)
Terrestrial Atmosphere
Marine Atmosphere
Residence Time (in Years)
27500
4100
3110
2.57
0.042
0.025
Table 3: Residence Times for reservoirs.
Table 3 summarizes the different residence times of the six reservoirs. The residence time is the
average amount of time that a water molecule would spend in that particular reservoir. As the table
shows, there is a large degree of variance between the different reservoirs. The marine atmosphere is
the smallest, with just .025 years and ice is the longest, with 27500 years. While the solid reservoirs,
such as ice, tend to have the longest times, the gaseous phase reservoirs, such as marine and terrestrial
atmospheres have the smallest. Because of the detailed interrelatedness of the water cycle, a
significant change in residence time could substantially impact the rest of the cycle. For example, if one
residence time decreased, all the reservoirs that it flows into would not be prepared for the sudden
influx. This could throw off the entire cycle because all of the cycles are dependent on each other. This
could result in one of the reservoirs being depleted, having disastrous consequences.
PART C:
In order to model ground water mining, an outflow called ‘withdrawal’ was added going from
groundwater to surface water. To simply matters, this outflow was assigned a rate of 0.2 (2.0 * 10^14
kg/year). When the model ran for 100 years, the groundwater decreased from 8200 to 8180, the
marine and land atmosphere and snow/ice increased very slightly, and oceans increased from 1350000
to 1350020. Sea level also increased from .001 to approximately 4.7 cm. The results are summarized in
Table 4.
Reservoir
Initial
Final
Ocean
1350000
1350020
Marine Atmosphere
11
11
Land Atmosphere
4.5
5.3
Surface Water
275
276
Groundwater
8200
8180
Snow/Ice
27500
27500
Table 4: Changes in reservoir levels when modeling ground water mining.
Change
20
0
0.8
1
20
0
Ground water does not seem to stabilize during the 100 year period that was modeled. This is
due to the fact that the response time can be calculated as 4100 years, based on the change that we
made, by the following equations:
Because this is substantially longer than 100 years, the ground water did not stabilize.
In order to observe the stabilization of the ground water, the initial can be modified to 100 and
the outflow:
.
This time, the graphs visually level off, as seen in Figure 3.
1: Groundwater
1:
100
1
1:
75
1
1
1
1:
50
0.00
25.00
Page 1
50.00
Y ears
75.00
100.00
9:53 PM Mon, Mar 16, 2009
Groundwater
1: Land Atmosphere
1:
5
1:
5
1
1
1
1
1:
5
0.00
25.00
50.00
Y ears
Page 1
75.00
100.00
9:53 PM Mon, Mar 16, 2009
1: Marine Atmosphere
1:
11
1
1
1:
11
1
1:
11
1
0.00
Page 1
25.00
50.00
Y ears
75.00
100.00
9:53 PM Mon, Mar 16, 2009
1: Oceans
1:
1350040
1
1
1:
1350020
1:
1350000
1
1
0.00
25.00
Page 1
50.00
Y ears
75.00
100.00
9:53 PM Mon, Mar 16, 2009
1: Snow and Ice
1:
27503
1:
27502
1
1
1
1:
Page 1
27500
1
0.00
25.00
50.00
Y ears
75.00
100.00
9:53 PM Mon, Mar 16, 2009
1: Surf ace Water
1:
290
1
1
1
1:
280
1
1:
270
0.00
25.00
50.00
Y ears
Page 1
75.00
100.00
9:53 PM Mon, Mar 16, 2009
1: Sea Lev el
1:
20
1:
10
1
1
1
1:
Page 1
0
1
0.00
25.00
50.00
Y ears
75.00
100.00
9:53 PM Mon, Mar 16, 2009
Figure 3. Graphs of Ground Water Mining experiment leveling off.
Although we have withdrawn the same amount of water, the sea level rise is a lot less and the
decrease in groundwater is a lot less. This is because the outflow was defined as a function of the
reservoir, creating a negative feedback because the outflow changes in response to the amount in the
reservoir, making it level off.
In conclusion, the water cycle is dynamic and easily offset system. Because of this, it is
important to understand the interrelations between the different reservoirs so we can fully evaluate the
human impact on the cycle. Though these models, various human impacts may be explored and the
water cycle can be better understood.