Surface Hydrology Research Group Università degli Studi di Cagliari Evaluation of Input Uncertainty in Nested Flood Forecasts: Coupling a Multifractal Precipitation Downscaling Model and a Fully-Distributed Hydrological Model Giuseppe Mascaro 1,2, Enrique R. Vivoni 2 and Roberto Deidda 1 H14C: Physically Based Hydrologic Models, Remote Sensing, and Uncertainty II 1. Dipartimento di Ingegneria del Territorio, Università di Cagliari 2. Department of Earth and Environmental Sciences, New Mexico Tech AGU Fall 2006 Conference 1 December 11, 2006
Motivation Use of Coarse-Scale Precipitation Data in Hydrology A major limitation towards use of coarse satellite and NWP products is the lack of a formal framework for downscaling precipitation fields in space and time over a catchment of interest. Assessment of Input Uncertainty in Hydrologic Models Knowledge is limited regarding the propagation of precipitation input uncertainty into hydrological model response, in particular for spatiallydistributed forecasting systems. Evaluation of Ensemble Hydrologic Products Rigorous statistical tests are required for assessing ensemble methods used to evaluate precipitation uncertainty and its propagation to hydrological model response. 2
An Example of the Approach Satellite or NWP Fields L L Coarse Scale: NWP or satellite sensors provide rainfall volume at a coarse scale (L x L x T). Hydrologic Model: Rainfall forcing used to generate hydrograph ensemble via model physics Ensemble Members λ λ Fine Scale: Downscaling used to generate an ensemble of rain fields at fine scale (λ x λ x τ). 3
Outline Study Site and Data Sets Precipitation Downscaling Model Ensemble Streamflow Forecasting Conclusions and Future Work 4
Outline Study Site and Data Sets Study Watershed Precipitation Data Streamflow Data Precipitation Downscaling Model Ensemble Streamflow Forecasting Conclusions and Future Work 5
Study Site and Data Sets NEXRAD Stage III Precipitation Estimates (June, 21 st 2000 21-22 UTC) Study Watershed: Baron Fork at Eldon, OK (808 km 2 ) with two nested USGS streamflow gauges. Large topographic variability in basin. Peacheater Creek (64 km 2 ) Baron Fork at Dutch Mills, AK (108 km 2 ) Precipitation Data: Stage III NEXRAD data over Arkansas Red River Basin for the summer periods in 1997-2002 (4 km, 1 hour). 6
Study Site and Data Sets 512 km Precipitation (mm/hr) Aggregation of NEXRAD Stage III (June, 23 rd 2000 14-15 UTC) Nested USGS Discharge Observations (June 1 July 31, 2000) NEXRAD Aggregation: To mimic a coarse-scale product, we aggregated 4-km, 1-hr NEXRAD data up to 512-km, 16-hr (space-time events). Streamflow Data: USGS streamflow observations at three gauging stations (15-min) over summer periods 1997-2002. 7
Outline Study Site and Data Sets Precipitation Downscaling Model Ensemble Streamflow Forecasting Conclusions and Future Work 8
Outline Study Site and Data Sets Precipitation Downscaling Model Downscaling Procedure Application to Study Site Precipitation Ensemble Verification Ensemble Streamflow Forecasting Conclusions and Future Work 9
Precipitation Downscaling Time A precipitation downscaling model was used to generated high space-time resolution (λ x λ x τ) rainfall field from coarse (L x L x T) aggregations. Space Space Space-time binary cascade: Each father generates 2 d sons, with d = 3 (2 in space x, y + 1 in time t). STRAIN Model: Log-Poisson generator η = β y where y is a random i.i.d. Poisson variable with mean c. R j+1 = R j η β and c are the only downscaling parameters. A (velocity) parameter (U = L/T) is also used to homogenize the space and time scales. Deidda et al. (1999), Water Resources Research, 35 Deidda (2000), Water Resources Research, 36 10
Precipitation Downscaling Space-time sequences were analyzed in a self-similarity framework. Evidence of scale invariance and multifractal behavior were found in 400 events which were then used to calibrate the downscaling model. Downscaling Parameters Coarse resolution L x L x T L = 512 km, T = 16 hr Four downscaling levels Fine resolution λ x λ x τ λ = 32 km, τ = 1 Relation between parameters c and β and the coarse precipitation rate R [mm/h] Results for Case Study c(r) = a e -γr + c inf a = 0.644, β(r) = 0.18 γ = 2.782, cinf = 0.824 11
Precipitation Ensemble Verification We test whether the ensemble members and the observed fields are drawn from the same distribution (Consistency Hypothesis). This is achieved using the Verification Rank Histogram (Wilks, 2006). 1. CDF of precipitation rates i [mm/h] at fine resolution (32 km, 1 hr). For a rainfall threshold (i * ), Exceedence Probability is obtained from N ENS members. 2. CDF of the Exceedance Probabilities y i. For each k event, a rank r k determined at observed frequency y obs. 3. Verification Rank Histogram for r k ranks is constructed for all observed events (N EV ). Rank Histogram ranks CDF of Precipitation Rate i * I [mm/h] y obs y i r k Uniform distribution Consistency hypothesis 12
Precipitation Ensemble Verification Do our downscaling ensembles (from NEXRAD aggregation) represent statistically the fine-scale observation? We test N ENS = 1000 ensemble members for N EV = 400 events during summer 1997-2005 for three fine-scale thresholds (i * = 10, 30, 40 mm/h). i* = 10 mm/h i* = 30 mm/h i* = 40 mm/h N ENS = 1000 N ENS = 1000 N ENS = 1000 + 1 σ -1 σ Results Indicate: For all i *, higher values of r are more populated, implying that the the downscaling model underestimates the exceedance probability. The degree of underestimation decreases as the fine-scale threshold value increases (more intense local events). Verification was performed for N ENS = 20 and 100 with similar results. 13
Outline Study Site and Data Sets Precipitation Downscaling Model Ensemble Streamflow Forecasting Conclusions and Future Work 14
Outline Study Site and Data Sets Precipitation Downscaling Model Ensemble Streamflow Forecasting Model Setup and Calibration Ensemble Flood Forecasting Streamflow Ensemble Verification Conclusions and Future Work 15
Hydrological Simulations A distributed hydrologic model was used to generate flood forecasts at three nested gauging sites with the ensemble precipitation forcing. tribs Model: A coupled surface-subsurface watershed model using triangulated irregular network (TIN) representation of terrain. Model Setup: Landscape descriptions (soil, vegetation) used for model parameterization. Hourly weather station and downscaled rainfall forcing. TIN Topography Land Cover Downscaled Rainfall 32 km Virtual Gauge Grass Forest Urban Ivanov et al. (2004), Water Resources Research, 40; Ivanov et al. (2004), Journal of Hydrology, 298; Vivoni et al. (2005), Hydrological Processes, 19 16
Hydrological Simulations Model Observed Ensemble Flood Forecasting Observed Precipitation Downscaled Ensemble 16 hr Zero Padding Calibrated Model Output with NEXRAD (4-km, 1-hr) tribs Model Calibration at Nested Gauges (15 Summer 2000 storm events) Ensemble Flood Forecast Experiment Design (Summer 2000 Event: June 11, 07-23 UTC) Model Calibration: Manual calibrations for each summer (1997, 2000) at each gauge. Calibrated model is ground-truth for ensemble verification. Ensemble Streamflow Forecasts: Twenty rainfall ensemble members used as forcing for 30 storms (16 hour duration) for summer 1997, 2000. The storm events selected based on the highest coarse-scale intensity. 17
Streamflow Ensemble Verification Using the Verification Rank Histogram, we test if the observed and ensemble maximum and mean streamflow during each event are drawn from the same distribution (Consistency Hypothesis). 1. CDF of ensemble streamflow metrics (maximum or mean) from tribs model output Qi (in m 3 /s) during 32- hr flood forecast event. CDF of Streamflow Measure r k 2. For each k event, a rank r k given by the Exceedance Probability determined at the observed value Q obs. 3. Verification Rank Histogram for r k ranks is constructed for all observed events (N EV ). Q obs Q [m 3 /s] Rank Histogram Uniform distribution ranks Consistency hypothesis 18
Streamflow Ensemble Verification Maximum Streamflow + 1 σ Baron Fork Dutch Mills Peacheater Creek -1 σ Mean Streamflow Results Indicate: Underdispersion or overconfident ensembles (especially Baron Fork) which imply that members are too alike and do not adequately capture observation. Lower ranks r are more populated in the ensemble indicating that the ensemble values underestimate the observed streamflow. 19
Outline Study Site and Data Sets Precipitation Downscaling Model Ensemble Streamflow Forecasting Conclusions and Future Work 20
Outline Study Site and Data Sets Precipitation Downscaling Model Ensemble Streamflow Forecasting Conclusions and Future Work 21
Conclusions and Future Work Implications Our study aims to implement an ensemble hydrometeorological forecasting chain and a robust and general approach for ensemble verification. Approach is designed to use a large number of storm and flood events to draw conclusions that are statistically significant. Other Ensemble Metrics Reliability Diagrams and Brier Skill Score will be used to test the forecasting chain at different precipitation and streamflow thresholds. Minimum Spanning Tree will be used to test multiple scalar predictants at the same time in the forecasting chain. Improvements to Forecasting Chain Use of higher temporal resolution radar data set (15-min) to reach spatial resolutions that are more suitable for the distributed hydrological model. Adjust the precipitation downscaling procedure based on feedbacks obtained through the verification process (e.g. tune downscaling model parameters). 22