Toward Optimal Rainfall – Hydrologic Correction of Precipitation to Close the Water Budget in Headwater Basins

Abstract

Quantitative Precipitation Estimation (QPE) is crucial in hydrology and water resources research and applications. QPE remains the most pressing challenge due to the lack of high-resolution precipitation measurements and, or inconsistencies among measurements across a wide range of hydrometeor sizes (e.g.; six order of magnitude from haze to raindrops) and large measurement uncertainty that is technology dependent (e.g., disdrometers, rain gauges, radars, satellite versus ground-based, etc) and often precipitation-regime dependent as well. This is a more significant issue in complex terrain because rain gauge networks are not adequate and radar measurements suffer from retrieval algorithm uncertainties and observing geometry artifacts that result from operations to avoid ground clutter effects. In models, QPF (Quantitative Precipitation Forecasts) result from incomplete model physics and physical parameterizations, coarse resolution that cannot capture storm dynamics and orographic flows, as well as uncertainty in boundary conditions. Therefore, QPE products are often associated with very large errors in mountainous regions. This is known from water budget analysis of hydrological prediction at watershed scales that show large discrepancies between simulated and observed hydrographs.The overarching goal of this study is to investigate the spatiotemporal structure of QPE error in observational data sets and develop a physics-based methodology to correct QPE with the goal of minimizing water budget closure errors in headwater basins from event-scales to the annual cycle. Traditionally, water budget studies estimate streamflow as an integrated residual, and the estimated streamflow is compared against streamflow observations to quantify the closure error. Statistical QPE error models on the other hand rely on statistical assumptions about the underlying statistics and in the case of data-driven models lack the physical underpinnings that are needed for predictive studies. In this work, QPE error is estimated as a dynamic residual using a distributed hydrology model. The underlying hypothesis is that the discrepancies between simulated and observed hydrographs result from the convolution of hydrologic processes with rainfall forcing and therefore it is necessary to deconvolve QPE errors in space and time to develop robust quantitative error models for correcting QPE. The principal research objective to construct a general framework for predictive QPE error modeling in complex terrain. This research leverages IPHEx (Integrated Hydrology and Precipitation Experiment observations) in the Southern Appalachian Mountains. Understanding scale-dependence and missing physics in the hydrologic model used for deconvolution is necessary toward improving QPE error estimates at multiple scales for both hydrologic operations and hydroclimatic studies, and this is the third objective of this research. Presently work has been completed for operational prediction of flood events in headwater basins in the SAM. Efforts currently are directed to error modeling regionalization and extension to seasonal and annual time-scales. In the first part of this work, Stage IV (STIV), a commonly used combined radar-raingauge NOAA product, is utilized to derive a reference precipitation product for the SAM by merging IPHEx raingauge observations. The merging process consists fractal downscaling for STIV data, bias correction, and geostatistical mapping techniques. In addition, hydroclimatic corrections to capture the diurnal and seasonal cycles of observed rainfall, and in particular the contribution of light rainfall (Liao and Barros, 2019). Hydrological simulations are conducted to assess the hydrological performance of the optimally combined QPE data show significant discrepancy between simulated streamflow and United States Geological Survey (USGS) streamflow observations. To resolve this problem and close the water budget, a Lagrangian-based backtracking algorithm was developed to deconvolve the signature of hydrologic processes and estimate the space-time dynamics of precipitation error that contributes to the streamflow error. This inverse process is hereafter referred to as Inverse Rainfall Correction or IRC. Hydrologic simulations using IRC corrected QPE exhibit significant improvements in Nash-Sutcliffe Efficiency (NSE) scores at hourly timescales that are dramatically increased from less than -0.5 to above 0.6 on average. Error attribution suggests that these hydrologic errors in QPE data are conditional on precipitation regime, and specifically separating cold and warm season processes. In the second part of this work, it is demonstrated that a predictive QPE error model can be derived from the climatology of derived IRC errors. Specifically, Multi-Layer Perceptron (MLP) network models were developed and applied to the 57 largest floods in the Cataloochee Creek, a USGS benchmark watershed, from 2008 to 2017. The results demonstrate a significant improvement in hydrologic response as the average NSE is improved from -0.4 to 0.5 consistent with the physically-constrained IRC results. Presently, the focus of ongoing efforts is on the regionalization of this approach with emphasis on expressing deconvolution kernels in terms of geomorphic parameters, precipitation regime, and eliminate systematic biases associated to measurement system operations. Simulated hydrographs show that the rising limb is too early in almost every event independently of storm regime and initial conditions. This behavior remains when the spatial resolution of the model increases to 85m. This error is embedded in the travel time distributions used in the IRC, which imposes space-time errors in the rainfall corrections resulting in excessive corrections along the stream network and overall shift of rainfall toward the beginning of the event. Further analysis suggest that unrealistically saturated river channel pixels cause rapid rising limbs and a Hillslope-Streamway Connectivity Parameterization (HSCP) is used to separate river channels from the pixels. Resulting hydrographs are characterized with an improved rising limb by reducing timing error by 2 hours, suggesting a need to investigating model structure errors proving to have great impacts on hydrological simulations. Model structure error comes from a wide variety of sources, including but not limited to model resolution, and small-scale physics parameterization. In the third part of this work, the effects of model spatial scale and sub-grid physics parameterization on hydrological simulation are analyzed. In hydrological modeling, higher spatial resolution does not necessarily produce better hydrological simulations against streamflow observations due to the limitation of understanding and parameterizing small-scale physics. It is true that sub-grid physics are usually parameterized or not represented entirely at coarse resolution in hydrological modeling and thus its effects on simulated hydrological processes are not fully understood. This is especially the case in the streamway and along the riverbanks where hillslope processes interact with river processes. After extensive analysis, it is hypothesized that the rapid rising limb are at least partially contributed by inadequate representation of riverbank and floodplain storage, and errors that result from poorly constrained bank-full conditions, hereafter referred to as dynamic River-Bank-Storage (RBS). A new RBS parameterization is developed and preliminary results from this study suggest that it can effectively delay streamflow travel time for approximately 2 hours, which is significant as flash floods usually occur within a few hours after extensive precipitation in mountainous regions. The final component of the research plan is to assess and improve model physics in the hydrologic model, and to characterize the impact of improved hydrograph simulation skill on QPE error modeling. In the future work, the structure of QPE error models derived from the DCHM incorporated with HSCP and RBS parameterization will be analyzed, and QPE error models will be used for operational forecasting in the Great Smoky National Park located in the SAM.