hydro-ecologic Modeling in the Okavango: hydrologic uncertainty analysis &the development of a fish model<br />Anna Cathey...
Outline<br /><ul><li>Coursework
Introduction/Motivation
Research questions/objectives
Future work</li></li></ul><li>Coursework<br />Engineering Coursework and Requirements<br />Applied Math in Ag Engr (ABE 69...
Introduction andMotivation<br />
Uncertainty analysis (UA) is used to propagate parameter uncertainties onto the model output<br />Inputs<br />Output<br />...
Why do we care?  Policy Implications for Sensitivity and Uncertainty Analysis<br />Models are useful for policy makers <br...
Reasons for uncertainty
What parts of the system need to be better understood to produce better models.</li></li></ul><li>Sensitivity Analysis Met...
Interactions of inputs are not accounted for
Inherently assumes models are linear and additive
Global: multiple inputs are changed in each model run
Interactions of inputs are accounted for
Useful in complex nonlinear or non-additive models
Variance Based Global Sensitivity Analysis: parameter importance is tracked, E[Y|X]</li></li></ul><li>Monte Carlo versus V...
Global Sensitivity Analysis Roadmap<br />
Morris Method<br />Input factor 1<br />X(3)<br />X(2)<br />Input factor 2<br />X(0)<br />Global Sensitivity Analysis <br /...
Modified Morris Method results in two sensitivity measures<br />σ - estimates the higher-order effects of the parameter.<b...
Extended FAST (eFAST)<br /><ul><li>Global Sensitivity and Uncertainty Analysis
Quantitative
Calculates the variability in the output due to the uncertainty of input factors
Variance decomposition requires a large number of simulations per parameter, hence the need for initial screening (Morris)
Sensitivity index: Si = Vi / V </li></li></ul><li>eFASTSensitivty Decomposition<br />V(Y) is total variance of output (the...
GSA/GUA in the Okavango Basin<br />Largest inland delta in the world<br />Ramsar wetland of international significance<br ...
A fish model<br />Environmental flows are being set in the Delta<br />Recommendation for the development of a quantitative...
Research Objectives<br />Uncertainty Analysis of the Okavango Delta Hydrologic Model<br />The development of hydrologicall...
Objective 1Uncertainty analysis of the Okavango Delta hydrologic model<br />
HOORC Delta hydrologic model<br />(Wolski, 2006)<br />Structure <br />Monthly time step<br />Linked reservoir model<br />F...
The Delta Hydrologic Model<br />A reservoir model ~~~~~ linked to a ~~~~~ A GIS grid model<br />	Results are input into a ...
Step 1. Define pdfs<br />U = uniform continuous distribution, D = uniform discrete distribution, <br />
Step 2. Morris Method, Average Inundation Area<br />
Step 3. FAST GUA95% Confidence Interval for Average Flooding Extents<br />
Step 3. FAST GUA<br />
Step 3. FAST GSA<br />FAST 1st order indices<br />
Interesting Model Behavior<br />The maximum inundation for each of the reservoirs obtained during the GSA was mapped with ...
Objective 2A spatially explicit flood pulse driven fish model<br />
bucket versus spatial model<br />
Bucket model: Flood Pulse Concept<br />The main driver for riverine/ floodplain systems is the flood pulse<br />The aquati...
Okavango and the Flood Pulse Concept<br />Food availability (Hoberg et al., 2002)<br />“First flush” during advancing floo...
Everglades ALFISH model<br />Fish model build on top of a flood pulsed hydrologic model (ATLSS)<br />Periphyton, macrophyt...
Everglades ALFISH model<br />But it’s more complicated than that…<br />The coefficient of determination (R2) is only 0.35 ...
Murray-Darling Basin, Australia<br />Experiences a flood pulse from snow melt <br />Noted that floodplain utilization by f...
Okavango Fish Model<br />www.ag.auburn.edu/.../details.php?image_id=534 <br />Three-spotted tilapia (Oreochromisandersoni)...
von Bertalanffyage/weight/length relationships<br />Length from age<br />Lt,n = Lmax(1-e-n)<br />L is length (cm), n is ag...
Beverton and HoltMortality<br />Age class<br />Time step<br />Nn = R e(-Z*n)<br />Nt,n = Nt-1,n-1e(-Z*Δn)<br />N is number...
Preliminary Results<br />Steady state<br />Fish Biomass<br />Flooding Extent<br />
Flood pulse structural parameters<br />Recruitment increases on the advancing flood<br />R = R * At / At – 1<br />R is rec...
Calibration<br />(Mosepele et al., 2009)<br />
Age Classes Over Time<br />
Biomass Over Time<br />
The spatial model<br />Based on the flood pulse concept coupled with the foraging arena concept<br />(Murray-Hudson, 2009)...
Foraging Arena Concept<br />Traditional Mass Action Principle: two well mixed species<br />Number of encounters (predation...
Okavango and the Foraging Arena Theory <br />Mosepele (pers.comm., 2009) proposes vegetation related protection<br />survi...
Foraging arena concept coupled with flood pulse concept<br />High Flood<br />Nutrients,<br />Algae, and <br />zooplankton<...
Vegetation in the Delta<br />Vegetation types were modeled by Murray-Hudson (2009) based on the inundation duration of the...
Preliminary spatial model<br />Monthly survivability is based on annually determined vegetation types<br />No dynamics (Ex...
Objective 3Uncertainty analysis of the Pitman model in the Okavango Basin<br />
Pitman model (Pitman, 1973)<br />Structure<br />Rainfall runoff model<br />Uses historic rainfall and temperature<br />SPA...
GSA/GUA of the Pitman model <br />Will use the Morris/FAST GSA/GUA technique<br />GUA<br />Understand the impact of the un...
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  1. 1. hydro-ecologic Modeling in the Okavango: hydrologic uncertainty analysis &the development of a fish model<br />Anna Cathey <br />Department of Agricultural and Biological Engineering<br />University of Florida<br /> <br />
  2. 2. Outline<br /><ul><li>Coursework
  3. 3. Introduction/Motivation
  4. 4. Research questions/objectives
  5. 5. Future work</li></li></ul><li>Coursework<br />Engineering Coursework and Requirements<br />Applied Math in Ag Engr (ABE 6986)<br />*Simulation Ag Watersheds (ABE 6254)<br />*Bio and Ag Simulation (ABE5646)<br />Hydrology Field Lab (ENGR 6170)<br />Natural WWT Systems (ENGR 8980)<br />ABE Seminar (ABE 6931)<br />Intro to Probability I (STA 5325)<br />Intro to Probability II (STA 5328)<br />Electives<br />*Soil and Water Chemistry (SOS 5406)<br />*Forest Hydrology (FORS 6110)<br />Eco. and General Systems (EES 5305)<br />Wetlands Ecology (ENT 8150)<br />Ag Ecology Field Course (CRSS 6931)<br />*Limnology (ECOL 6310)<br />*Groundwater II (CWR 6525)<br />IGERT Coursework<br />*S Florida Ecosystems (SOS 5235)<br />Watersheds (ENV 6932)<br />Water Politics (POS 6933)<br />Com, Ethics, Leadership (ENV 6935)<br />AM Seminar (ENV 6935)<br />Systems Ecology (ECOL 8580)<br />AM Field Research (ENV 6932)<br />Other<br />Research<br />Individual Work<br />Teaching Assistant <br />Expected Graduation May 2011<br />*Hydrologic Sciences Academic Cluster Minor<br />
  6. 6. Introduction andMotivation<br />
  7. 7. Uncertainty analysis (UA) is used to propagate parameter uncertainties onto the model output<br />Inputs<br />Output<br />A<br />MODEL<br />B<br />C<br />B<br />A<br />Sensitivity analysis(SA) studies how the uncertainty in the output can be apportioned to the model inputs.<br />C<br />
  8. 8. Why do we care? Policy Implications for Sensitivity and Uncertainty Analysis<br />Models are useful for policy makers <br />They can indicate system response to management decisions and climate change.<br />Using GSA/GUA we can give a policy maker a probably range of probable system responses based on our understanding of the system.<br /><ul><li>By combining GUA with GSA we can also determine
  9. 9. Reasons for uncertainty
  10. 10. What parts of the system need to be better understood to produce better models.</li></li></ul><li>Sensitivity Analysis Methods<br /><ul><li>Local: inputs are varied one at a time
  11. 11. Interactions of inputs are not accounted for
  12. 12. Inherently assumes models are linear and additive
  13. 13. Global: multiple inputs are changed in each model run
  14. 14. Interactions of inputs are accounted for
  15. 15. Useful in complex nonlinear or non-additive models
  16. 16. Variance Based Global Sensitivity Analysis: parameter importance is tracked, E[Y|X]</li></li></ul><li>Monte Carlo versus Variance Methods<br />FAST<br />Monte Carlo<br />Variance based methods go one step further and also provide a quantitative value for the direct and indirect sensitivities (importance of parameters)<br />Monte Carlo simulations calculate the uncertainty of model outputs given the uncertainty of model inputs<br />
  17. 17. Global Sensitivity Analysis Roadmap<br />
  18. 18. Morris Method<br />Input factor 1<br />X(3)<br />X(2)<br />Input factor 2<br />X(0)<br />Global Sensitivity Analysis <br />Qualitative<br />Screening Tool<br />Requires few simulations to map relative sensitivity<br />Ranks input factors according to their effects on model output<br />Two indices of sensitivity <br />Main effect (mean µ): the direct effect of the input factor on a given output<br />Interactions (standard deviation σ): the higher-order effects<br />X(1)<br />Input factor 3<br />
  19. 19. Modified Morris Method results in two sensitivity measures<br />σ - estimates the higher-order effects of the parameter.<br />σ- Interactions<br />μ* -Importance<br />μ* - estimates the overall effect of the parameter on a given output.<br />
  20. 20. Extended FAST (eFAST)<br /><ul><li>Global Sensitivity and Uncertainty Analysis
  21. 21. Quantitative
  22. 22. Calculates the variability in the output due to the uncertainty of input factors
  23. 23. Variance decomposition requires a large number of simulations per parameter, hence the need for initial screening (Morris)
  24. 24. Sensitivity index: Si = Vi / V </li></li></ul><li>eFASTSensitivty Decomposition<br />V(Y) is total variance of output (the whole pie)<br />Vi is direct variance from input factor Xi<br />R is residual (interactions)<br />
  25. 25. GSA/GUA in the Okavango Basin<br />Largest inland delta in the world<br />Ramsar wetland of international significance<br />Future development in Angola and Climate change may pose threats<br />Ecology, tourism, fisheries, and collection of veld products all rely on hydrology<br />Environmental flows are currently being set for the Delta<br />No formal GSA/GUA has been run on the hydrologic models in the Okavango<br />GUA can aid policy decisions <br />GSA can reveal the most important <br /> processes in the system<br />
  26. 26. A fish model<br />Environmental flows are being set in the Delta<br />Recommendation for the development of a quantitative relationship between the flood pulse and fish populations <br />(Mosepele, 2009. Environmental Flow Specialist Report for the Okavango Delta) <br />There is a theory that the flood pulse is a major driver for fish population has yet to be tested. This model will be used to test that hypothesis.<br />Models can let us simulate experiments that are too big to conduct <br />development <br />climate change<br />
  27. 27. Research Objectives<br />Uncertainty Analysis of the Okavango Delta Hydrologic Model<br />The development of hydrologically driven fish model<br />Bucket model<br />Spatial model<br />Uncertainty analysis of the Pitman Model in the Okavango Basin<br />Putting it all together: Scenarios in the linked Okavango modeling environment<br />
  28. 28. Objective 1Uncertainty analysis of the Okavango Delta hydrologic model<br />
  29. 29. HOORC Delta hydrologic model<br />(Wolski, 2006)<br />Structure <br />Monthly time step<br />Linked reservoir model<br />Flow is input from Okavango River<br />Groundwater flow and infiltration is represented sub-reservoirs <br />Volume thresholds move water from one reservoir to another<br />Represents <br />Flood duration<br />Flood frequency<br />Flooding extents<br />Outflow from the Boro River <br />Model parameters for each reservoir include <br />Area (surface, groundwater, island)<br />Topography<br />Evapotranspiration<br />Rainfall ratio<br />Flow resistance<br />Extinction coefficient<br />Volume threshold<br />From Wolski (2006)<br />
  30. 30. The Delta Hydrologic Model<br />A reservoir model ~~~~~ linked to a ~~~~~ A GIS grid model<br /> Results are input into a grid model that inundates cells based on flood area<br /> Volume thresholds route water. Output is area of inundation<br />Wolski<br />Wolski, 2006<br />
  31. 31. Step 1. Define pdfs<br />U = uniform continuous distribution, D = uniform discrete distribution, <br />
  32. 32. Step 2. Morris Method, Average Inundation Area<br />
  33. 33. Step 3. FAST GUA95% Confidence Interval for Average Flooding Extents<br />
  34. 34. Step 3. FAST GUA<br />
  35. 35. Step 3. FAST GSA<br />FAST 1st order indices<br />
  36. 36. Interesting Model Behavior<br />The maximum inundation for each of the reservoirs obtained during the GSA was mapped with interesting results. <br />Degree to which the water is being moved around the system <br />Future calibration may focus on refining the volume thresholds<br />Panhandle<br />Nqoga1<br />Thaoge<br />Xudum<br />
  37. 37. Objective 2A spatially explicit flood pulse driven fish model<br />
  38. 38. bucket versus spatial model<br />
  39. 39. Bucket model: Flood Pulse Concept<br />The main driver for riverine/ floodplain systems is the flood pulse<br />The aquatic/terrestrial transition zone (ATTZ) is a ‘moving littoral’<br />high inputs of nutrients from dry land<br />is dynamic and flowing<br />Resulting <br />high primary productivity in the ATTZ<br />Impacts for fish utilization of floodplains<br />Taken from Junk et al., 1989.<br />
  40. 40. Okavango and the Flood Pulse Concept<br />Food availability (Hoberg et al., 2002)<br />“First flush” during advancing flood, nutrients released (4 mg/l N, 560 μg/l P)<br />Burst in primary production (300 μg C/ ld, 24 μgchla/l) <br />Resting zooplankton eggs hatch when submerged and feed on the phytoplankton (10 mg DW/l and up to 90 mg DW/l in near-shore edges)<br />Fish spawn with the burst in zooplankton, providing food for the fry<br />Spawning period (Merron, 1991) <br />The larger the flood, the longer water is on the floodplain<br />Leads to a longer spawning period and greater overall production of fish. <br />(Mosepele et al., 2009)<br />(Mmopelwa et al., 2009)<br />
  41. 41. Everglades ALFISH model<br />Fish model build on top of a flood pulsed hydrologic model (ATLSS)<br />Periphyton, macrophytes, detritus, meso- and macro-invertebrates, and big and small fish are simulated<br />Recruitment is based on fecundity and number of mature fish<br />Fish move into floodplain as flood rises and into refugia as it recedes<br />3 types of mortality: background, predation, density dependant, failure to find refugia<br />Growth is simulated by the von Bertalanffy relationships<br />DeAngeles et al., 1997<br />
  42. 42. Everglades ALFISH model<br />But it’s more complicated than that…<br />The coefficient of determination (R2) is only 0.35 for fish population and 0.88 for water depth <br />Empirical findings show that depth only accounts for 20-40% of the variability in fish population<br />Other factors like availability of prey and the frequency and size of the flood may be important<br />Gaff et al., 2004<br />
  43. 43. Murray-Darling Basin, Australia<br />Experiences a flood pulse from snow melt <br />Noted that floodplain utilization by fish was less than expected and that the relationships may be more complicated than previously thought<br />Temperature, flood predictability, as well as inundation duration and area may also need to be considered<br />King et al., 2003<br />http://www.sas.usace.army.mil/50/Images/drought.jpg<br />http://www.mda.asn.au/<br />
  44. 44. Okavango Fish Model<br />www.ag.auburn.edu/.../details.php?image_id=534 <br />Three-spotted tilapia (Oreochromisandersoni) is an indicator species for floodplain migratory fish in the Delta<br />120 age classes are simulated and tracked<br />Beverton and Holt mortality equation<br />von Bertalanffy age/weight/length relationships<br />Flood based recruitment and additional mortality<br />Based on monthly time step HOORC model of Delta inundation area<br />Recruitment increases on the advancing flood (but is otherwise constant)<br />Mortality increases on the receding flood (but is otherwise constant)<br />
  45. 45. von Bertalanffyage/weight/length relationships<br />Length from age<br />Lt,n = Lmax(1-e-n)<br />L is length (cm), n is age (years)<br />Lmax is 53cm (Mosepele and Nengu, 2003)<br />Biomass from length<br />Bt,n = aLnb<br />a and b are empirical parameters<br />a is 0.004, and b is 3.242 (Mosepele and Nengu, 2003)<br />(von Bertalanffy, 1957)<br />
  46. 46. Beverton and HoltMortality<br />Age class<br />Time step<br />Nn = R e(-Z*n)<br />Nt,n = Nt-1,n-1e(-Z*Δn)<br />N is number of fish, R is recruits, Z is mortality, and n is age class<br />Z is 3.99 per year (Mosepele and Nengu, 2003) <br />Z is divided into two parts<br /> natural (M) 1.39 <br /> fishing mortality (F) 2.60 per year<br /> Indicates that fishing pressure is relatively high (Mosepele and Nengu, 2003) <br />(Beverton and Holt, 1956)<br />
  47. 47. Preliminary Results<br />Steady state<br />Fish Biomass<br />Flooding Extent<br />
  48. 48. Flood pulse structural parameters<br />Recruitment increases on the advancing flood<br />R = R * At / At – 1<br />R is recruitment, A is area<br />Mortality increases on the receding flood<br />Nt,n = Nt-1,n-1e(-Z*Δn *(At / At-1))<br />N is number of fish, Z is mortality, and n is age in years<br />
  49. 49. Calibration<br />(Mosepele et al., 2009)<br />
  50. 50. Age Classes Over Time<br />
  51. 51. Biomass Over Time<br />
  52. 52. The spatial model<br />Based on the flood pulse concept coupled with the foraging arena concept<br />(Murray-Hudson, 2009)<br />
  53. 53. Foraging Arena Concept<br />Traditional Mass Action Principle: two well mixed species<br />Number of encounters (predation) = density of sp1 *density sp2<br />Results in <br />Strong top–down controls by predators <br />Unstable community structure - predation affects biodiversity<br />Field data from complex systems show mixed top-down and bottom–up controls<br />Biodiversity is maintained in the face of predator/prey relationships<br />Random distribution does not occur<br />The Foraging Arena Theory addresses this discrepancy<br />Organisms make spatial habitat choices that minimize the risk of predation<br />Populations are divided into vulnerable (V) and safe (B-V) stocks<br />Flux (v) between these states v(B-V) and vV<br />Biomass flow rate from prey to predator Q = aVB. <br />(Walters, 2006)<br />
  54. 54. Okavango and the Foraging Arena Theory <br />Mosepele (pers.comm., 2009) proposes vegetation related protection<br />survivability is increased in denser vegetation types <br />dense vegetation provides protection from predators<br />Large predators typically reside in the stream channels, not in the floodplain <br />
  55. 55. Foraging arena concept coupled with flood pulse concept<br />High Flood<br />Nutrients,<br />Algae, and <br />zooplankton<br />High Predation<br />Med Predation<br />Low Predation<br />Low Flood<br />Crowding<br />Dry, fish are forced to refugia<br />
  56. 56. Vegetation in the Delta<br />Vegetation types were modeled by Murray-Hudson (2009) based on the inundation duration of the HOORC grid model<br />Four classes of functional vegetation types<br />Mosepele proposes that predation varies among vegetation types<br />Aquatic communities (Model survivability = N*0.8)<br />Seasonally flooded sedgeland (Model survivability = N*0.95)<br />Seasonally flooded grassland (Model survivability = N*0.9)<br />
  57. 57. Preliminary spatial model<br />Monthly survivability is based on annually determined vegetation types<br />No dynamics (Ex. exchange between cells)<br /><ul><li>Reduces the total population based on average vegetative cover</li></ul>The lighter the shade the lower the survivability<br />
  58. 58. Objective 3Uncertainty analysis of the Pitman model in the Okavango Basin<br />
  59. 59. Pitman model (Pitman, 1973)<br />Structure<br />Rainfall runoff model<br />Uses historic rainfall and temperature<br />SPATSIM GUI<br />Applications to Okavango<br />Has been calibrated in the Okavango River (Hughes, 2006)<br />Results can be used to drive the HOORC Delta model<br />http://www.ru.ac.za/static/institutes/iwr/software/reserve/helpdss/model_frame.htm<br />
  60. 60. GSA/GUA of the Pitman model <br />Will use the Morris/FAST GSA/GUA technique<br />GUA<br />Understand the impact of the uncertainty of model inputs on streamflow<br />Useful for decision making<br />GSA<br />Determine which inputs are most important<br />Focus on the most important parameters<br />Help to refine model structure<br />
  61. 61. Preliminary Pitman Morris Results<br />GW: Max rate of GW recharge<br />R: Evap storage coefficient<br />GPOW: Power storage-recharge curve<br />FT: Runoff rate at ST<br />ST: Max soil water storage<br />POW: storage-runoff curve<br />AFOR: % basin in type 2 veg<br />FF: evaporation scaling factor<br />RDF: Rainfall distribution factor<br />*<br />
  62. 62. Regionalization<br />Based on varying characteristics that are spatially dependant<br />East and West have difference geology resulting in different hydrographs<br />South has less rainfall and can be a loosing reach<br />Eastern<br />sub-basins<br />Southern<br />sub-basins<br />Western<br />sub-basins<br />
  63. 63. Preliminary Pitman GSA regionalized results<br />E: Eastern watersheds<br />W: Western watersheds<br />S:Southern watersheds<br />GW: Max rate of GW recharge<br />R: Evap storage coefficient<br />GPOW: Power storage-recharge curve<br />
  64. 64. Objective 4<br />Putting it all together<br />
  65. 65. OkaSIMThe Okavango Delta Modeling Environment<br />OkaFLOW<br />OkaVEG<br />OkaFISH<br />
  66. 66. The whole systemPutting it all together<br />The linked Okavango modeling environment will be run<br />Pitman watershed model<br />Delta hydrologic model<br />Delta vegetation model<br />Delta fish model<br />Climate change and development scenarios will be simulated in the river basin along with GSA/GUA<br />
  67. 67. Future Work<br />
  68. 68. Future work on Objective 2: the fish model<br />Data will be collected for model calibration and testing<br />The data that is available so far shows an annual signal <br />Simulations of fishing, closed season, and other management strategies<br />Alternative equations to compute mortality<br />More spatially dynamic methods<br />Alternatives to modeling responses to the flood <br />food web based trophic models<br />The GSA/GUA analysis will be refined<br />(Mosepele et al., 2009)<br />(Mmopelwa et al., 2009)<br />
  69. 69. Future work on Objective 3: the Pitman GSA/GUA<br />Refine the regionalization approach<br />Run and analyze FAST GSA/GUA<br />
  70. 70. Papers, Presentations, Posters<br />Papers<br />Cathey, A.M., R. Munoz-Carpena, P. Wolski, G. Kikers, (In edits) Global Uncertainty and Sensitivity Analysis of the Okavango Delta Reservoir Model, Botswana<br />Kiker, G.A., R. Muñoz-Carpena, P. Wolski, A. Cathey, A. Gaughan, & J. Kim. (2008) Incorporating uncertainty into adaptive, transboundary water challenges: a conceptual design for the Okavango river basin. Int. J. of Risk Assessment and Management Vol. 10, No.4 pp. 312 – 338.<br />Presentations<br />Cathey, A., G. Parent, A. Gaughn, W. Kanapaux, D. Wojick. 2009. Living with Thirst: People and Wildlife in Southern Africa’s Variable Climate. Video case study for the Ecological Society of America Case Millennium Conference. Athens, Georgia. <br />Cathey, A., R. Muñoz-Carpena, P. Wolski. 2009. Global Uncertainty and Sensitivity Analysis of Hydro-Ecologic Models of the Okavango Basin, Botswana. Presentation at the University of Botswana Harry Oppenheimer Research Center. Maun, Botswana. <br />Cathey, A., R. Muñoz-Carpena, G. Kiker. 2009. Uncertainty Analysis Using the Method of Morris on a Hydrologic Model of the Okavango Basin, Botswana. Presentation at the AWRA Summer Specialty Conference: Adaptive Management of Water Resources II. Snowbird, Utah.<br /> <br />Cathey, A., R. Muñoz-Carpena, G. Kiker. 2009. Uncertainty Analysis of a Reservoir Model in the Okavango Delta, Botswana. Presentation at the Florida Section ASABE. Daytona Beach, Florida <br />Cathey, A., R. Muñoz-Carpena, G. Kiker. 2009. Adaptive Management and Global Uncertainty and Sensitivity Analysis of Hydro-Ecologic Models of the Okavango Basin, Botswana. Presentation at the University of Botswana Harry Oppenheimer Research Center. Maun, Botswana. <br />Posters<br />Cathey A, Kiker, GA, Muñoz-Carpena,R. (2008) Incorporating Uncertainty into Adaptive, Transboundary Water Challenges: A Conceptual Design for the Okavango River Basin. Poster presented at University of Florida Water Institute Symposium, Gainesville, Florida and NSF IGERT Sustainability Conference, Fairbanks, Alaska. <br />
  71. 71. Thanks!<br />

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