Cathey Quals

hydro-ecologic Modeling in the Okavango: hydrologic uncertainty analysis &the development of a fish model Anna Cathey Department of Agricultural and Biological Engineering University of Florida

Uncertainty analysis (UA) is used to propagate parameter uncertainties onto the model output Inputs Output A MODEL B C B A Sensitivity analysis(SA) studies how the uncertainty in the output can be apportioned to the model inputs. C

Why do we care? Policy Implications for Sensitivity and Uncertainty Analysis Models are useful for policy makers They can indicate system response to management decisions and climate change. Using GSA/GUA we can give a policy maker a probably range of probable system responses based on our understanding of the system. ,[object Object]

What parts of the system need to be better understood to produce better models.,[object Object]

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],[object Object]

Global Sensitivity Analysis Roadmap

Morris Method Input factor 1 X(3) X(2) Input factor 2 X(0) Global Sensitivity Analysis Qualitative Screening Tool Requires few simulations to map relative sensitivity Ranks input factors according to their effects on model output Two indices of sensitivity Main effect (mean µ): the direct effect of the input factor on a given output Interactions (standard deviation σ): the higher-order effects X(1) Input factor 3

Modified Morris Method results in two sensitivity measures σ - estimates the higher-order effects of the parameter. σ- Interactions μ* -Importance μ* - estimates the overall effect of the parameter on a given output.

Extended FAST (eFAST) ,[object Object]

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 ,[object Object]

GSA/GUA in the Okavango Basin Largest inland delta in the world Ramsar wetland of international significance Future development in Angola and Climate change may pose threats Ecology, tourism, fisheries, and collection of veld products all rely on hydrology Environmental flows are currently being set for the Delta No formal GSA/GUA has been run on the hydrologic models in the Okavango GUA can aid policy decisions GSA can reveal the most important processes in the system

A fish model Environmental flows are being set in the Delta Recommendation for the development of a quantitative relationship between the flood pulse and fish populations (Mosepele, 2009. Environmental Flow Specialist Report for the Okavango Delta) 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. Models can let us simulate experiments that are too big to conduct development climate change

Research Objectives Uncertainty Analysis of the Okavango Delta Hydrologic Model The development of hydrologically driven fish model Bucket model Spatial model Uncertainty analysis of the Pitman Model in the Okavango Basin Putting it all together: Scenarios in the linked Okavango modeling environment

Objective 1Uncertainty analysis of the Okavango Delta hydrologic model

HOORC Delta hydrologic model (Wolski, 2006) Structure Monthly time step Linked reservoir model Flow is input from Okavango River Groundwater flow and infiltration is represented sub-reservoirs Volume thresholds move water from one reservoir to another Represents Flood duration Flood frequency Flooding extents Outflow from the Boro River Model parameters for each reservoir include Area (surface, groundwater, island) Topography Evapotranspiration Rainfall ratio Flow resistance Extinction coefficient Volume threshold From Wolski (2006)

The Delta Hydrologic Model A reservoir model ~~~~~ linked to a ~~~~~ A GIS grid model Results are input into a grid model that inundates cells based on flood area Volume thresholds route water. Output is area of inundation Wolski Wolski, 2006

Step 1. Define pdfs U = uniform continuous distribution, D = uniform discrete distribution,

Step 2. Morris Method, Average Inundation Area

Step 3. FAST GUA95% Confidence Interval for Average Flooding Extents

Step 3. FAST GSA FAST 1st order indices

Interesting Model Behavior The maximum inundation for each of the reservoirs obtained during the GSA was mapped with interesting results. Degree to which the water is being moved around the system Future calibration may focus on refining the volume thresholds Panhandle Nqoga1 Thaoge Xudum

Objective 2A spatially explicit flood pulse driven fish model

Bucket model: Flood Pulse Concept The main driver for riverine/ floodplain systems is the flood pulse The aquatic/terrestrial transition zone (ATTZ) is a ‘moving littoral’ high inputs of nutrients from dry land is dynamic and flowing Resulting high primary productivity in the ATTZ Impacts for fish utilization of floodplains Taken from Junk et al., 1989.

Okavango and the Flood Pulse Concept Food availability (Hoberg et al., 2002) “First flush” during advancing flood, nutrients released (4 mg/l N, 560 μg/l P) Burst in primary production (300 μg C/ ld, 24 μgchla/l) 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) Fish spawn with the burst in zooplankton, providing food for the fry Spawning period (Merron, 1991) The larger the flood, the longer water is on the floodplain Leads to a longer spawning period and greater overall production of fish. (Mosepele et al., 2009) (Mmopelwa et al., 2009)

Everglades ALFISH model Fish model build on top of a flood pulsed hydrologic model (ATLSS) Periphyton, macrophytes, detritus, meso- and macro-invertebrates, and big and small fish are simulated Recruitment is based on fecundity and number of mature fish Fish move into floodplain as flood rises and into refugia as it recedes 3 types of mortality: background, predation, density dependant, failure to find refugia Growth is simulated by the von Bertalanffy relationships DeAngeles et al., 1997

Everglades ALFISH model But it’s more complicated than that… The coefficient of determination (R2) is only 0.35 for fish population and 0.88 for water depth Empirical findings show that depth only accounts for 20-40% of the variability in fish population Other factors like availability of prey and the frequency and size of the flood may be important Gaff et al., 2004

Murray-Darling Basin, Australia Experiences a flood pulse from snow melt Noted that floodplain utilization by fish was less than expected and that the relationships may be more complicated than previously thought Temperature, flood predictability, as well as inundation duration and area may also need to be considered King et al., 2003 http://www.sas.usace.army.mil/50/Images/drought.jpg http://www.mda.asn.au/

Okavango Fish Model www.ag.auburn.edu/.../details.php?image_id=534 Three-spotted tilapia (Oreochromisandersoni) is an indicator species for floodplain migratory fish in the Delta 120 age classes are simulated and tracked Beverton and Holt mortality equation von Bertalanffy age/weight/length relationships Flood based recruitment and additional mortality Based on monthly time step HOORC model of Delta inundation area Recruitment increases on the advancing flood (but is otherwise constant) Mortality increases on the receding flood (but is otherwise constant)

von Bertalanffyage/weight/length relationships Length from age Lt,n = Lmax(1-e-n) L is length (cm), n is age (years) Lmax is 53cm (Mosepele and Nengu, 2003) Biomass from length Bt,n = aLnb a and b are empirical parameters a is 0.004, and b is 3.242 (Mosepele and Nengu, 2003) (von Bertalanffy, 1957)

Beverton and HoltMortality Age class Time step Nn = R e(-Z*n) Nt,n = Nt-1,n-1e(-Z*Δn) N is number of fish, R is recruits, Z is mortality, and n is age class Z is 3.99 per year (Mosepele and Nengu, 2003) Z is divided into two parts natural (M) 1.39 fishing mortality (F) 2.60 per year Indicates that fishing pressure is relatively high (Mosepele and Nengu, 2003) (Beverton and Holt, 1956)

Preliminary Results Steady state Fish Biomass Flooding Extent

Flood pulse structural parameters Recruitment increases on the advancing flood R = R * At / At – 1 R is recruitment, A is area Mortality increases on the receding flood Nt,n = Nt-1,n-1e(-Z*Δn *(At / At-1)) N is number of fish, Z is mortality, and n is age in years

Calibration (Mosepele et al., 2009)

The spatial model Based on the flood pulse concept coupled with the foraging arena concept (Murray-Hudson, 2009)

Foraging Arena Concept Traditional Mass Action Principle: two well mixed species Number of encounters (predation) = density of sp1 *density sp2 Results in Strong top–down controls by predators Unstable community structure - predation affects biodiversity Field data from complex systems show mixed top-down and bottom–up controls Biodiversity is maintained in the face of predator/prey relationships Random distribution does not occur The Foraging Arena Theory addresses this discrepancy Organisms make spatial habitat choices that minimize the risk of predation Populations are divided into vulnerable (V) and safe (B-V) stocks Flux (v) between these states v(B-V) and vV Biomass flow rate from prey to predator Q = aVB. (Walters, 2006)

Okavango and the Foraging Arena Theory Mosepele (pers.comm., 2009) proposes vegetation related protection survivability is increased in denser vegetation types dense vegetation provides protection from predators Large predators typically reside in the stream channels, not in the floodplain

Foraging arena concept coupled with flood pulse concept High Flood Nutrients, Algae, and zooplankton High Predation Med Predation Low Predation Low Flood Crowding Dry, fish are forced to refugia

Vegetation in the Delta Vegetation types were modeled by Murray-Hudson (2009) based on the inundation duration of the HOORC grid model Four classes of functional vegetation types Mosepele proposes that predation varies among vegetation types Aquatic communities (Model survivability = N*0.8) Seasonally flooded sedgeland (Model survivability = N*0.95) Seasonally flooded grassland (Model survivability = N*0.9)

Preliminary spatial model Monthly survivability is based on annually determined vegetation types No dynamics (Ex. exchange between cells) ,[object Object],The lighter the shade the lower the survivability

Objective 3Uncertainty analysis of the Pitman model in the Okavango Basin

Pitman model (Pitman, 1973) Structure Rainfall runoff model Uses historic rainfall and temperature SPATSIM GUI Applications to Okavango Has been calibrated in the Okavango River (Hughes, 2006) Results can be used to drive the HOORC Delta model http://www.ru.ac.za/static/institutes/iwr/software/reserve/helpdss/model_frame.htm

GSA/GUA of the Pitman model Will use the Morris/FAST GSA/GUA technique GUA Understand the impact of the uncertainty of model inputs on streamflow Useful for decision making GSA Determine which inputs are most important Focus on the most important parameters Help to refine model structure

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