Effect of Precipitation Errors on Simulated Hydrological Fluxes and States

Bart NijssenUniversity of Arizona, Tucson

Dennis P. LettenmaierUniversity of Washington, Seattle

EGS-AGU-EUG Joint Assembly, Nice, FranceApril 11, 2003

Motivation

Precipitation is the single most important determinant of the fluxes and states of the land surface hydrological system

Most important atmospheric input to hydrological models

Distribution of surface stations is uneven and sparse in many area

NOAA CPC Summary of the Day 1987-1998

Satellite-based precipitation estimates hold great promise for application in hydrological applications

Usefulness will depend on error characteristics

Global Precipitation Measurement Mission

courtesy: NASA GSFC

• Currently in its formulation phase

• Primary spacecraft • Dual-frequency precipitation radar• Passive microwave radiometer

• Constellation spacecraft• Passive microwave radiometer

• Target launch date: 2007

Objectives:• Improve ongoing efforts to predict climate• Improve the accuracy of weather and precipitation forecasts• Provide more frequent and complete sampling of the Earth’s precipitation

… aims to improve water resources management (NASA/NASDA)

Satellite Precipitation Error

Errors in GPM precipitation products will result from

• Instrument error

• Algorithm error, e.g.• radar reflectivity - rainfall rate relationships • transfer of information from the primary spacecraft to

the constellation spacecraft

• Sampling error• result from a lack of temporal continuity in coverage

Objective

To quantify:

• the effect of precipitation sampling error on predictions of land surface evapotranspiration, streamflow, and soil moisture at the scale of large continental river basins and tributaries thereof

• the variation of the prediction error as a function of the drainage area and the averaging period

Error Model

Relative root mean squared error E in time-aggregated precipitation due to sampling error (Steiner, 1996)

€

E = 85P−0.6A−0.5ΔT30T

⎛ ⎝ ⎜

⎞ ⎠ ⎟0.5

P - Precipitation (mm/day)A - Domain size (km2)T - Sampling interval (hours)T - Accumulation period (days)

A = 2500 km2

T = 1 day

Perturb original precipitation by sampling from a log-normal distribution under the constraints that the corrupted precipitation

• is unbiased • has the specified relative error• has the same sequence of

wet and dry days

Error is uncorrelated in time

Methodology

Compare newly simulated fluxes and states with the baseline simulation

Simulate the hydrological fluxes and states in a large river basin (Ohio River Basin) using the station-based, gridded precipitation data set from Maurer et al., 2002

Simulated fluxes and states are taken as truth(baseline simulation)

Perturb station-based precipitation according to the adopted error model to produce a new time series of precipitation fields

Rerun the simulations with the new, error-corrupted precipitation

Monte Carlo framework

• 5 years• 1000

simulations

Perturbation of Precipitation Fields

Average precipitation (mm/day)

Station-based precipitationMaurer et al., 2002

Generate gaussian random fields for each day for each Monte Carlo simulation

Precipitation (mm)

Extract basin precipitation and aggregate to desired resolution (0.5º 0.5º) for day X

Corrupt precipitation for day X

Spatially correlated error

Spatially uncorrelated error

VIC Macroscale Hydrology Model

Ohio River Basin

Streamflow is routed to each red dot along the mainstem of the river (virtual gage locations)

Hydrological fluxes and states are averaged over the upstream area associated with each virtual gage location

Hydrological fluxes and states are averaged over periods ranging from 1 to 30 days

Mean annual precipitation

Ohio river basin:5.3105 km2

Model implementation:0.5º0.5º (about 50 km 50 km)

261 grid cellsDaily timestep

Analysis: Precipitation

RMSE and bias as a function of area for three sampling intervalsThe red dots indicate the virtual gage locationsThe dashed lines show the 10% and 90% quantiles

Precipitation

RMSE as a function of averaging period for three upstream areas (T = 1 hour)

The dashed lines show the 10% and 90% quantiles

For the spatially uncorrelated case, precipitation errors decrease rapidly with an increase in averaging period and averaging area

Streamflow

RMSE as a function of area for three sampling intervals

Dashed lines show 10% and 90% quantiles

RMSE as a function of averaging period for three upstream areas (T = 1 hour)

Streamflow errors decrease rapidly for areas greater than about 50,000 km2. At the mouth of the Ohio, the relative RMSE in the daily flow was 10-20% for sampling intervals of 1-3 hours

Soil Moisture

RMSE as a function of averaging period for three upstream areas (T = 1 hour)

Although an increase in the upstream area reduces the mean RMSE, an increase in the averaging period does not reduce the mean RMSE for the deeper soil layers

Spatially Correlated Error

RMSE as a function of area for the spatially correlated error (T = 1 hour)The mean RMSE for the uncorrelated error is shown in blue

Spatially correlated precipitation errors induce greater persistence in the errors in modeled fluxes when averaged over upstream area

Temporal Correlation in the Error

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Temporally uncorrelated errors in precipitation give rise to temporally correlated errors in simulated fluxes and states

Autocorrelation of the error as a function of the lag for the spatially uncorrelated case for three upstream areas(T = 1 hour)

Conclusions

• Errors in precipitation can be large even for hourly overpasses at 50 km resolution. However, the relative errors decrease rapidly for drainage areas larger than about 10,000 km2

• Because of non-linearities in the hydrological cycle, unbiased and temporally uncorrelated errors in precipitation give rise to biases and temporally correlated errors in other fluxes and states

• Errors in simulated fluxes and states decline with the averaging area and period. This decrease is less rapid when the errors are temporally and/or spatially correlated

• Streamflow errors decrease rapidly for areas greater than about 50,000 km2. At the mouth of the Ohio, the relative RMSE in the daily flow was 10-20% for sampling intervals of 1-3 hours

Manuscript available at:

http://www.hydro.washington.edu