Research

Machine Learning - Flood Prediction

In Bartlett et al. 2022, we propose an approach where the physical mechanisms of flooding are distilled into the machine learning features through the use of Buckingham Pi Theorem. We apply this concept for creating dimensionless predictors for mapping the likelihood of flooding over a landscape for both the pluvial and fluvial flood processes. In both cases, the fluvial and pluvial process complexities are subsumed through this new theory that is amenable to empirical testing and analytical developments. In particular, we test the use of these predictors for a probabilistic determination of flood risk using a logistic regression model. The corresponding flood risk well compares to existing Federal Emergency Management Agency (FEMA) maps, while also expanding existing FEMA maps to new areas and a wider spectrum of flood flows and precipitation amounts. Our results demonstrate how existing hydrology and hydraulic modeling may create a data driven model for rapidly estimating flood risk on a global scale. We anticipate that such an approach will find general utility in assessing geohazard risk, as well as become a starting point for rapid flood warning systems for mitigating flood impacts.

Figure 1: The machine learning model performs well (with an F1 Score of 0.8) for predicting flood extents outside of region on which the model was trained. For a model trained on New York state watersheds, the model captures the FEMA 1% annual chance event floodplain for the North Fork river in Kentucky (shown in the figure).

Statistical Mechanics - Jumps

The abrupt changes that are ubiquitous in physical and natural systems often are well characterized by shot noise (i.e. jumps) with a state dependent recurrence frequency and amplitude. In Bartlett and Porporato (2018), we present a comprehensive overview of the theory for state dependent jump transitions. For exponentially distributed inputs, we present a novel class of transient solutions, as well as a generic steady state solution in terms of a potential function and the Pope-Ching formula. Ongoing work uses the jump characterization to quantify natural processes, e.g., soil salinity dynamics, hydrological processes, etc..

Figure 2: The general solutions of Bartlett and Porporato (2018), allow for a unique description of jump process dynamics within the classic double well potential paradigm. The double well potential description may be especially useful in describing natural processes such as abrupt changes between two climatic states.

Noisy Controls in Noisy Systems

Bartlett and Porporato (2019) considers the dynamics of a one-dimensional system evolving according to a deterministic drift and randomly forced by two types of jump processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously resets the system according to specified protocols (either deterministic or stochastic). We develop a general theory, which includes a different formulation of the master equation using antecedent and posterior jump states, and obtain an analytical solution for steady state.

Figure 3: Bartlett and Porporato (2019) example of stochastic control of a process forced by random jumps and a deterministic drift. Shown are the simulation distribution (histogram bars), and the steady-state PDF (black line). The stochastic control is based on the antecedent and posterior PDFs for the respective initialization and termination of the control forcing.

Physical Systems Modeling - Ecohydrology

Climate and earth systems models require reasonable estimates of plant functioning. Critically, of the three types of photosynthesis on earth (C3, C4, and CAM), Crassulacean acid metabolism (CAM) photosynthesis hitherto lacked a comprehensive model. Bartlett et al. 2014, created the first model of CAM photosynthesis that was both consistent with existing models of other photosynthetic processes and fully connected to the soil-plant-atmosphere-continuum. This model is a first step towards a more accurate quantification of CAM productivity. We currently are exploring the potential benefits of CAM as a biofuel feedstock at the nexus of energy, climate, and economic conditions. Crassulacean acid metabolism (CAM) plants are highly water efficient and thus are of environmental and economic importance in the arid and semiarid regions of the world. Many CAM plants (e.g., Agave tequilana) also have attractive qualities for biofuel production such as a relatively low lignin content and high amount of soluble carbohydrates.

Figure 4: Daily results for well watered conditions: Net C uptake (solid line) in comparison to experimental data (symbols) for Agave tequilana (Nobel et al. 1987). Plant transpiration and WUE are displayed in the second and third rows, respectively

Figure 5: Evolution of an unconfied aquifer water table, h, and flow rate, q, over 60 days for a sloping aquifer.

Statistics - Rainfall runoff modeling

In Bartlett et al. 2016b, we use statistics to unify various model approaches with a general equation that highlights the commonality of the rainfall-runoff response. The general equation differs for each model based on the model statistical assumptions of spatial heterogeneity and watershed properties. With this approach, we currently are linking model types and assumptions to different hydro-geographic and climatic settings.

Stochastic Processes - Hydrology

Hydrologists have yet to derive analytical distributions of runoff explicitly linked to mechanistic environmental descriptions and distributions of rainfall. In Bartlett et. al 2015, we outline a framework for deriving distributions of storm runoff from precipitation statistics and a mechanistic model of plant functioning. This framework provides high fidelity representations of runoff statistics with minimal parameterization. Furthermore, this framework is provides a tangible connection between the soil moisture status, hydro-climatic variables (e.g., rainfall frequency) and the runoff response. We are currently expanding this approach to common semi-distributed horological models such as the variable infiltration capacity model (VIC), the Topographic based model (TOPModel), the probability distribution model (PDM), as well as the classic SCS-CN method.

Figure 6: Rainfall and runoff data (black dots) of the Upper Little Tennessee River watershed at USGS stream gauge 03500000 with a contributing area of 363 km2.

Figure 7: Quantile–quantile (Q–Q) plots (grey line) comparing the data distribution to the theoretical distributions for (a) normalized rainfall, z, and (b) stormflow runoff q, which are displayed with the 1:1 line (dashed) and the 95% confidence bands (red, curved lines). (c) Comparison between the theoretical stormflow distribution PDF (dotted-dashed lines) and the data distribution of stormflow (histogram bars) where (d) shows a log scale plot.

Crop modeling

Agricultural crop productivity results from either C3, C4, or CAM photosynthesis. For all three plant photosynthetic types, carbon and water fluxes may be consistently compared with the Photo3 model (Hartzell et al. 2018) which builds upon Bartlett et. al 2014. Photo3 is one of the only platforms for consistently comparing different photosynthetic plant types and the associated the carbon and water fluxes . With Photo3, we currently are evaluating the trade offs between C3, C4, and CAM photosynthesis and developing Photo3 into a full crop model for assessing agricultural productivity under various climatic scenarios.

For the full Photo3 code see the Tools.

Figure 8: Photo3 model schematic. The Photo3 model is based on a core model of C3 photosynthesis with options to represent C4 photosynthesis, CAM photosynthesis, and plant water storage.

Figure 9: Comparison of Photo3 model results with experimental data. (a) Comparison of modeled carbon assimilation, An (μmol/m2 /s) for Opuntia ficus-indica (solid line) with data from Nobel and Hartsock (1983) (circles). (b) Comparison of modeled decrease in stomatal conductance gs as a fraction of maximal stomatal conductance gs,max for O. ficus-indica during a drydown period with data from Acevedo et al. (1983) (circles). (c) Comparison of modeled carbon assimilation as a function of maximal carbon assimilation, An,max, for S. bicolor with published ranges in laboratory experiments according to Peng, Peng (1990), Resende et al. (2012) (gray shading). (d) Comparison of modeled decrease in carbon assimilation with leaf water potential for S. bicolor and data from Contour-Ansel et al. (1996) for two cultivars: ICSV 1063 (circles) and MIGSOR (squares).

Engineering Systems Modeling - Stormwater Management

In Parolari, Pelrine and Bartlett (2018), we derive the stochastic water balance model and develop analytical expressions for the steady-state water level probability density functions (PDFs) for stormwater basins with both passive and actively-controlled outflow structures. These PDFs are then used to define water level and flow duration curves that provide a probabilistic description of the full range of basin performance. The model provides a basis for evaluating how changes in the rainfall-runoff process, affected by land use and climate change, will impact the variability of stormwater basin function. The model provides a framework for designing resilient stormwater systems that perform optimally under urbanization and changing rainfall intensities.

Figure 10: Ensemble average (a) water level and (b) overflow volume as a function of rainfall frequency and different values for the setpoints, hs, for initiating valve opening for basin outflow. On the x-axis of (a), the total runoff volume is kept constant while the rainfall frequency is varied.

Non-Stationarity in Extreme Value Distributions

More information coming soon

Ungauged basin predictions

More information coming soon