GEOG 110 – Lab #5 – Modeling Ecosystem Energy and Water InteractionsConstructing and Running the STELLA ModelEvaporation can be specified using:GEOG 110 – Lab #5 – Modeling Ecosystem Energy and Water InteractionsDue Date: 11:59 pm November 18, 2005Objectives: Energy and water flows through terrestrial ecosystems are closely related.On the one hand, the amount of evapotranspiration from an ecosystem islimited by the amount of energy available when there is a sufficientamount of water; on the other hand, the availability of water in the soilimposes a limit on evapotranspiration. The primary objective of this lab isto understand interactions of energy and water fluxes through forestecosystems using STELLA. In this lab, we will also learn how to link aSTELLA model with external data so that the model parameters areupdated through the course of a simulation.Background: We will model two closely related processes in this laboratory exercise:(1) The propagation of solar radiation through a forest canopy, and (2) thewater budget in the ecosystem. The model will simulate the propagationof solar radiation through forest canopy using the Beer’s Law:KLeII0where I0 and I are downward insolation at the top and bottom of a forestcanopy, respectively. K is the light extinction coefficient (K = 0.35 in thisexercise), L is leaf area index (LAI) for the canopy, as can be seen in thefollowing diagram:To simulate the water budget of the same forest ecosystem, we will use abucket model, treating water in soil as water in a bucket. When the bucketis full, it can no longer hold any more water. Therefore, all precipitationentering the bucket will overflow after the bucket is full, creating run-off.The depth of the bucket is called field capacity, the maximum amount of1KLeII0I0IaIrFigure 1: Radiation propagation through forest canopywater that the soil layer can hold. However, plants cannot use up all thewater in the bucket to make it empty. Plants begin to wilt well before thesoil water becomes zero. The amount of water in the bucket at this level iscalled the wilting point. Before the bucket is full, water in the bucket canleave the system through the process of evaporation on the forest floor,and through the biophysical processes of transpiration through the leafstoma. The following diagram illustrates the processes:The water balance equation in the diagram above can be written as:RSETPPT Using the hydrologic theory described above and radiation balanceequation, this lab will allows us to examine how energy and water fluxesare linked in a forest ecosystem. In your lab write-up, you will need todiscuss factors in forest ecosystems that enhance this linkage.Resources: The background provided above, along with your lecture notes andassigned readings from Botkin & Keller and Aber & Melillo shouldprovide sufficient grounding in the theory of modeling this sort of system.We will use STELLA (as always) to create a representation of the systemthat can perform the computation. At this point, you should be quitecomfortable using STELLA to build models of this sort.2Wilting pointField capacityEvaporationEvapotranspirationRun-offPrecipitationWater availableFigure 2: Water Balance for a bucket modelProcedure: This exercise will require you to first use Excel to calculate the energyavailable to the canopy for evapotranspiration each month. We will thenuse that information as input to run a STELLA model that you will build.Creating Input Values in Excel1. In this modeling exercise, we will do a simulation of energy and waterinteraction for a forest over an entire year on a monthly time step. Tosimplify the problem, we will treat incoming energy as converters thatcontrol the rates of transpiration and evaporation, and we will updatevalue of the converters each month. First we need to figure out theamount of energy coming to from the sun to the top of the canopy eachmonth.2. Get Excel started and open up the lab5data.xls Excel Workbookprovided for this exercise. The workbook will be saved inj:/isis.unc.edu/html/courses/2005fall/geog/110/001/data.3. First we need to calculate the sun declination angle. We can do this ona monthly basis, using the 15th day of the month to provide areasonable average value for the entire month. You’ll find Row 2 isalready has the Julian date of the 15th day of each month filled in thecells. In Row 3, we will calculate the sun declination angle using theformula, shown previously in lecture:δ = 23.5 sin(2π (284+jday)/365) degreesIn Excel, enter the following formula in Cell C3:=23.5*SIN(2*3.14149*(284+C2)/365)and then copy this value to cells D3 through N3 to calculate the sundeclination angles for each month.4. Make a line plot of Jday of 15th day (x axis) with Sun declination angle(y axis). Include this graph into your lab report and explain your graph.5. Next, we will calculate the solar elevation angles. Recall that these area function of both the location of the site and the hour of the day. Wewill run this model for Chapel Hill, at (latitude, longitude) of (36,-79)as is shown in Rows 4 & 5. We will calculate the solar elevationangles for 6 AM through 6 PM each day using the following formula,shown previously in lecture:sin(h0) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(ω)In Excel, enter the following formula in Cell C7:=SIN($D$4*3.14159/180)*SIN(C$3*3.14159/180)+COS($D$4*3.14159/180)*COS(C$3*3.14159/180)*COS($B7*3.14159/180)3and then copy this value to cells C8 through C19 to calculate the sundeclination angles for each hour in the days in the month of January.Then, copy the values in C7 through C19 to each of the other monthlyrows (so cells D7 through N19 are filled in with values).6. Note that some of the solar elevation angles in the early and latemonths of the year are less than zero, which indicates that the sunwould be below the horizon at that time of the day. You MUSTreplace these values with 0 values, since we do not want to include‘negative’ insolation in our calculations.7. We now have the angle we need to use as an input to calculating thehourly total insolation at the top of the canopy. We know that at thetop of the atmosphere, the irradiance of the sun is 1367 W/m2 (W/m2reads as watts per