Research Interests

Research

Dr. Kavvas’ areas of specialization include assessment of climate change impact by mathematical modeling of the coupled hydrologic-atmospheric processes at watershed, regional and continental scales. The in-house-developed regional and watershed-scale coupled hydrologic-atmospheric numerical models are also used for the simulation and forecasting of hydrologic water balances and hydrologic extremes toward quantifying and estimating phenomena such as  floods and droughts, and forecasting water supply at watershed and regional scales. The mathematical modeling of hydrologic processes at regional, watershed and hillslope scales are also used toward planning and management of water resources at these scales. Physics-based stochastic models are developed for investigating river flow, snow accumulation/melting, unsaturated soil water flow, unconfined and confined groundwater flow, and contaminant transport. Physical modeling of fish ecological hydraulics are performed at J. Amorocho Hydraulics Laboratory.

Major research areas of Dr. Kavvas are as follows:

  • Climate change impact assessment at regional and watershed scales by means of coupled numerical hydrologic-atmospheric process modeling

Since mid-1990s Dr. Kavvas and his team of graduate students and postdocs have been working on the development of numerical computer models for the assessment of the impacts of climate change with respect to water balances and hydrologic extremes (floods and droughts) in California and over various regions of the world in collaboration with various government agencies.

 

  • Physics-based quantification and assessment of extreme precipitation, floods, droughts and wildfires by means of numerical atmospheric-hydrologic modeling

In this focus area, starting in early 1990s and continuing to the present, we have been studying the physics of droughts, floods, maximum precipitation and wildfires over geographical regions and watersheds in order to understand their underlying causal mechanisms to be able to simulate such systems for their management toward the engineering planning and design of hydraulic structures.

 

  • Numerical modeling of hydrologic and environmental processes at watershed scale by means of WEHY (Watershed Environmental Hydrology) Model for the Assessment of Flow and Environmental Conditions

Since the beginning of 2000s Dr. Kavvas and his graduate students and postdocs at Hydrologic Research Laboratory (HRL) and J. Amorocho Hydraulics Laboratory have been developing numerical modeling tools for simulating the hydrologic and environmental processes in time and space at watershed scale for the assessment of flow, sediment and contaminant (mercury) conditions at various watersheds within California.

 

  • Modeling Hydrologic, Hydraulic and Environmental Processes Under Uncertainty

Hydrologic, hydraulic and environmental processes have uncertain parameters as function of spatial location within a specified modeling domain. For example, in soil water flow or in groundwater aquifer flow the hydraulic conductivity, the fundamental parameter of these processes, is uncertain as function of spatial location within a specified model domain. For surface flow processes, the surface roughness, which is a fundamental parameter of these processes, again has uncertain variation with spatial location within a model domain. The source/sink terms for these processes are again uncertain in time and space. For example, the recharge to a groundwater aquifer is an uncertain function of time and space. Similarly, the pumping rates from an aquifer are generally uncertain. Precipitation, which is the main source of overland flow, river flow, soil water flow and unconfined aquifer flow processes, is an uncertain function of time and space over a specified modeling domain. Furthermore, due to the scarcity or lack of data, the initial and boundary conditions of hydrologic-hydraulic-environmental processes are generally uncertain. In the mathematical modeling of these processes one solves their corresponding governing equations under specified initial and boundary conditions in time and space. Within the above framework, this so-called initial-boundary value problem solution must be performed under the appropriately quantified uncertainties with respect to their parameters, sources-sinks, initial values and boundary values. As such, these uncertain systems become stochastic initial-boundary value problems that need to be treated in general as stochastic partial differential equation systems, the governing equation of the process becoming a stochastic partial differential equation. Dr. Kavvas and his students and research associates at HRL and J. Amorocho Hydraulics Laboratory have been developing solutions to such uncertain systems since early 1990s. Below, these efforts will be described.

 

  • Development of a New Scaling Theory for Modeling the Self-similarity of Hydrologic and Hydraulic Processes in Time and Space

Since the beginning of 1900’s engineers recognized that it is possible to scale the real-life (prototype) flow processes in reduced dimensions in a laboratory (model) in order to be able to investigate the behavior of such processes for the planning and design of hydraulic structures. Such scaling was possible due to Buckingham’s pi–theorem (Buckingham, 1914) which was based on dimensional analysis. By means of this theorem it is possible to scale any flow process, but not its initial and boundary conditions. Nevertheless, it was used successfully in hydraulics and fluid mechanics laboratories for more than a century. In the case of hydrologic processes, while the scaling of the process, analyzed in terms of its governing equation, is essential in order to investigate the process within a framework of different time-space dimensions, the initial and boundary conditions of the process are also very important in determining the behavior of the process. Accordingly, Dr. Kavvas and his team of graduate students and research associates have developed a new scaling theory that is based on mathematician Sophus Lie’s symmetry theory for transformations. This scaling theory does not only develop the scaling relationships for the process, in terms of its governing equation, but also the scaling relationships of its initial and boundary conditions. A simple presentation of this new scaling theory is here:  A presentation of the scaling theory as applied to the scaling of hydrologic processes . The introductory paper on the scaling of various hydrologic processes is here:  Scale invariance and self-similarity of hydrologic processes . After this initial development, the new scaling theory was applied to various hydrologic and hydraulic processes. For example, this new scaling theory was applied successfully to the scaled modeling of sediment transport while keeping the original material fixed ( Scaling and self-similarity in suspended sediment transport with fixed sediment material ). Development of the scaling relationships of various flow processes culminated in the development of the scaling relationships of the governing Navier-Stokes equations of fluid flow in multi-dimensional space and time ( Scaling relationships and self-similarity of the averaged Navier-Stokes equations ). This new scaling theory, coined as “Lie scaling theory” by our group, can be applied to any flow process in order to develop the scaling relationships for the process.

 

  • Development of the fractional governing equations of hydrologic and hydraulic processes in fractional time and multi-fractional space in order to quantify the effect of long memory in time and space on these processes

The conventional governing equations of hydrologic and hydraulic processes are expressed as partial differential equations with integer power derivatives. As such, these conventional governing equations can only address finite memories in time and space within a process. As shown in this presentation on the fractional governing equations of unsteady open channel flow in fractional time-space: Fractional governing equations of unsteady open channel flow in fractional time-space – presentation , the conventional governing equations of hydrologic and hydraulic processes are essentially local, expressing the nearest-neighbour interactions among the grid cells of a modeling domain. However, as explained in the above presentation, in order to accommodate the long memories in time and/or in space in hydrologic-hydraulic processes it is necessary to have their governing equations as non-local. Such non-local structures for the governing equations of hydrologic-hydraulic processes can be achieved by developing these governing equations as partial differential equations with fractional powers (explained in the above presentation). When their fractional powers revert to integer powers, the developed fractional governing equations transform into the corresponding conventional governing equations of the processes. Besides the above-presented fractional governing equations of unsteady open channel flow, Dr. Kavvas and his team of graduate students and research associates have also developed fractional governing equations of confined groundwater flow ( Fractional governing equations of confined groundwater flow – presentation  ;  Fractional governing equations of confined groundwater flow in fractional time-space – paper ), unconfined groundwater flow ( Fractional governing equations of unconfined groundwater flow in fractional time-space – paper ) and soil water flow ( Fractional governing equations of soil water flow in fractional time-space – paper ) in fractional time-space. This effort has recently culminated in the development of fractional governing equations of fluid flow which are the generalizations of the Navier-Stokes-Euler governing equations of fluid flow ( Generalizations of the Navier-Stokes-Euler governing equations of fluid flow to fractional time-space- paper ).

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