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Balaji Rajagopalan Katrina Grantz CIVIL, ENVIRONMENTAL AND ARCHITECTURAL ENGINEERING DEPARTMENT

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Ensemble forecasts of streamflows using large-scale climate information : applications to the trcukee-carson basin

Balaji Rajagopalan

Katrina Grantz

CIVIL, ENVIRONMENTAL AND ARCHITECTURAL ENGINEERING DEPARTMENT

UNIVERSITY OF COLORADO AT BOULDER

NCAR/ESIG Spring 2004

Inter-decadal

Climate

Decision Analysis: Risk + Values

Time

Horizon

- Facility Planning
- Reservoir, Treatment Plant Size

- Policy + Regulatory Framework
- Flood Frequency, Water Rights, 7Q10 flow

- Operational Analysis
- Reservoir Operation, Flood/Drought Preparation

- Emergency Management
- Flood Warning, Drought Response

Data: Historical, Paleo, Scale, Models

Weather

Hours

PYRAMID

LAKE

WINNEMUCCA

LAKE (dry)

CALIFORNIA

NEVADA

Nixon

Stillwater NWR

Derby

Dam

STAMPEDE

Reno/Sparks

Fernley

Fallon

TRUCKEE

RIVER

INDEPENDENCE

BOCA

Newlands

Project

PROSSER

Truckee

CARSON

LAKE

MARTIS

LAHONTAN

Carson

City

DONNER

Tahoe City

CARSON

RIVER

LAKE TAHOE

NEVADA

Truckee

Carson

CALIFORNIA

TRUCKEE

CANAL

Farad

Ft Churchill

Lahontan Reservoir

Prosser Creek Dam

- USBR needs good seasonal forecasts on Truckee and Carson Rivers
- Forecasts determine how
storage targets will be met

on Lahonton Reservoir to

supply Newlands Project

Truckee Canal

NEVADA

Truckee

Carson

CALIFORNIA

Average Annual Precipitation

- 1949-2003 monthly data sets:
- Natural Streamflow (Farad & Ft. Churchill gaging stations)
(from USBR)

- Snow Water Equivalent (SWE)- basin average
- Large-Scale Climate Variables (SST, Winds, Z500..)
from http://www.cdc.noaa.gov

- Natural Streamflow (Farad & Ft. Churchill gaging stations)

- Streamflow in Spring (April, May, June)
- Precipitation in Winter (November – March)
- Primarily snowmelt dominated basins

- Winter SWE and spring runoff in Truckee and Carson Rivers are highly correlated
- April 1st SWE better than March 1st SWE

- Past studies have shown a link between large-scale ocean-atmosphere features (e.g. ENSO and PDO) and western US hydroclimate (precipitation and streamflow)
- E.g., Pizarro and Lall (2001)
Correlations between peak

streamflow and Nino3

Climate

Diagnostics

- Climate Diagnostics
To identify relevant predictors to streamflow / precipitation

- Forecasting Model
stochastic models for ensemble forecasting - conditioned on climate information

Forecasting

Model

Decision

Support System

- Decision Support System (DSS)
Couple forecast with DSS to demonstrate utility of forecast

- Correlations between spring flows and winter (standard) climate indices (NINO3, PNA, PDO etc.) were close to 0!
- Need to explore other regions correlation maps of ocean-atmospheric variables?

Truckee Spring Flow

500mb Geopotential Height

Sea Surface Temperature

Carson Spring Flow

Sea Surface Temperature

500 mb Geopotential Height

- Use areas of highest correlation to develop indices to be used as predictors in the forecasting model
- Area averages of geopotential height and SST

500 mb Geopotential Height

Sea Surface Temperature

- SWE

- Geopotential Height

- Sea Surface Temperature

Strongest correlation in Winter (Dec-Feb)

Correlation statistically significant back to August

Vector Winds

Low Streamflow Years

High Streamflow Years

Sea Surface Temperature

Low Streamflow Years

High Streamflow Years

- Winds rotate counter-clockwise around area of low pressure bringing warm, moist air to mountains in Western US

L

- Winter/ Fall geopotential heights and SSTs over Pacific Ocean related to Spring streamflow in Truckee and Carson Rivers
- Physical explanation for this correlation
- Relationships are nonlinear

- Ensemble Forecast/Stochastic Simulation
/Scenarios generation – all of them are conditional probability density function problems

- Estimate conditional PDF and simulate (Monte Carlo, or Bootstrap)

- Forecast spring streamflow (total volume)
- Capture linear and nonlinear relationships in the data
- Produce ensemble forecasts (to calculate exceedence probabilities)

- Model selection / parameter estimation issues
Select a model (PDFs or Time series models) from candidate models

Estimate parameters

- Limited ability to reproduce nonlinearity and non-Gaussian features.
All the parametric probability distributions are ‘unimodal’

All the parametric time series models are ‘linear’

- Models are fit on the entire data set
Outliers can inordinately influence parameter estimation

(e.g. a few outliers can influence the mean, variance)

Mean Squared Error sense the models are optimal but locally they can be very poor.

Not flexible

- Not Portable across sites

- Any functional (probabiliity density, regression etc.) estimator is nonparametric if:
It is “local” – estimate at a point depends only on a few neighbors around it.

(effect of outliers is removed)

No prior assumption of the underlying functional form – data driven

- Kernel Estimators
(properties well studied)

- Splines
- Multivariate Adaptive Regression Splines (MARS)
- K-Nearest Neighbor (K-NN) Bootstrap Estimators
- Locally Weighted Polynomials (K-NN Polynomials)

- Find K-nearest neighbors to the desired point x
- Resample the K historical neighbors (with high probability to the nearest neighbor and low probability to the farthest) Ensembles
- Weighted average of the neighbors Mean Forecast
- Fit a polynomial to the neighbors – Weighted Least Squares
- Use the fit to estimate the function at the desired point x (i.e. local regression)

- Number of neighbors K and the order of polynomial p is obtained using GCV (Generalized Cross Validation) – K = N and p = 1 Linear modeling framework.
- The residuals within the neighborhood can be resampled for providing uncertainity estimates / ensembles.

k-nearest neighborhoods A and B for xt=x*A and x*B respectively

Logistic Map Example

4-state Markov Chain discretization

- Uses local polynomial for the mean forecast (nonparametric)
- Bootstraps the residuals for the ensemble (stochastic)

Benefits

- Produces flows not seen in the historical record
- Captures any non-linearities in the data, as well as linear relationships
- Quantifies the uncertainty in the forecast (Gaussian and non-Gaussian)

e

*

t

y

*

t

xt*

yt* = f(xt*) + et*

- Monthly Streamflow Simulation Space and time disaggregation of monthly to daily streamflow
- Monte Carlo Sampling of Spatial Random Fields
- Probabilistic Sampling of Soil Stratigraphy from Cores

- Hurricane Track Simulation
- Multivariate, Daily Weather Simulation
- Downscaling of Climate Models
- Ensemble Forecasting of Hydroclimatic Time Series
- Biological and Economic Time Series
- Exploration of Properties of Dynamical Systems
- Extension to Nearest Neighbor Block Bootstrapping -Yao and Tong

- Cross-validation: drop one year from the model and forecast the “unknown” value
- Compare median of forecasted vs. observed (obtain “r” value)
- Rank Probability Skill Score

- Cross-validation: drop one year from the model and forecast the “unknown” value
- Compare median of forecasted vs. observed (obtain “r” value)
- Rank Probability Skill Score
- Likelihood Skill Score (Rajagopalan et al., 2001)

- Predictors
- April 1st SWE
- Dec-Feb geopotential height

95th

50th

5th

95th

50th

5th

April 1st forecast

- Ensemble forecasts provide range of possible streamflow values
- Water manager can calculate exceedence probabilites

Wet Year

Dry Year

April 1st forecast

- Median skill scores significantly beat climatology in all year subsets, both Truckee and Carson
- Truckee slightly better than Carson

Extremely Wet Years

- In general, the boxes are much tighter with geopotential height (greater confidence)
- Underprediction w/o climate index– might not be fully prepared with flood control measures

95th

95th

50th

50th

5th

5th

95th

95th

50th

50th

5th

5th

SWEand Geopotential Height

SWE

Use of Climate Index in Forecast

Extremely Dry Years

- Tighter prediction interval with geopotential height
- Overprediction w/o climate index (esp. in 1992)
- Might not implement necessary drought precautions in sufficient time

95th

95th

50th

50th

5th

5th

95th

95th

50th

50th

5th

5th

SWEand Geopotential Height

SWE

Model Skills in Water Resources Decision Support System

Ensemble Forecasts are passed through a Decision Support (RIVERWARE) System of the Truckee/Carson Basin

Ensembles of the decision variables are compared against the “actual” values

- Physical Mechanisms
- Reservoir releases, diversions, evap, reach routing

- Policies
- Implemented with “rules” (user defined prioritized logic)

- Water Rights
- Implemented in accounting network

Method to test the utility of the forecasts and the role they play in decision making

Model implements major policies in lower basin (Newlands Project OCAP)

Seasonal timestep

- Use Carson water first
- Max canal diversions: 164 kaf
- Storage targets on Lahontan Reservoir: 2/3 of projected April-July runoff volume
- Minimum Lahontan storage target: 1/3 of average historical spring runoff
- No minimum fish flows

Lahontan Storage Available for Irrigation

Truckee River Water Available for Fish

Diversion through the Truckee Canal

- Irrigation Water less than typical– decrease crop size or use drought-resistant crops
- Truckee Canal smaller diversion-start the season with small diversions (one way canal)
- Very little Fish Water- releases from Stampede coordinated with Canal diversions

Ensemble forecast results

Climatology forecast results

Observed value results

NRCS official forecast results

Seasonal Model Results:1993

- Irrigation Water more than typical– plenty for irrigation and carryover
- Truckee Canal larger diversion-start the season at full diversions (limited capacity canal)
- Plenty Fish Water- FWS may schedule a fish spawning run

Ensemble forecast results

Climatology forecast results

Observed value results

NRCS official forecast results

- Irrigation Water pretty average: business as usual
- Truckee Canal diversions normal: not full capacity, but don’t hold back too much
- Plenty Fish Water- no releases necessary to augment low flows, may choose a fish spawning run

Ensemble forecast results

Climatology forecast results

Observed value results

NRCS official forecast results

- Interannual/Interdecadal variability of regional hydrology (precipitation, streamflows) is modulated by large-scale ocean-atmospheric features
- Incorporating Large scale Climate information in regional hydrologic forecasting models (Seasonal streamflows and precipitation) provides significant skill at long lead times
- Nonparametric methods offer an attractive and flexible alternative to traditional methods.
- capability to capture any arbitrary relationship
- data-drive
- easily portable across sites
- Significant implications to water (resource) management and planning

- Couple ensemble forecasts with RiverWare model
- Temporal disaggregation
- Forecast improvements
- Joint Truckee/Carson forecast
- Objective predictor selection

- Compare results with physically-based runoff model (e.g. MMS)

Summary & Conclusions

- Climate indicators provide skilful long-lead forecast
- Water managers can utilize the improved forecasts in operations and seasonal planning
- Nonparametric methods provide an attractive and flexible alternative to parametric methods.

- Couple ensemble forecasts with RiverWare model
- Temporal disaggregation
- Forecast improvements
- Joint Truckee/Carson forecast
- Objective predictor selection

- Compare results with physically-based runoff model (e.g. MMS)

Funding

- CIRES Innovative Reseach Project
- Tom Scott of USBR Lahontan Basin Area Office

Technical Support

- CADSWES personnel

K-Nearest Neighbor Estimators

A k-nearest neighbor density estimate

A conditional k-nearest neighbor density estimate

f(.) is continuous on Rd, locally Lipschitz of order p

k(n) =O(n2p/(d+2p))

A k-nearest neighbor ( modified Nadaraya Watson) conditional mean estimate

Classical Bootstrap (Efron):

Given x1, x2, …... xn are i.i.d. random variables with a cdf F(x)

Construct the empirical cdf

Draw a random sample with replacement of size n from

Moving Block Bootstrap (Kunsch, Hall, Liu & Singh) :

Resample independent blocks of length b<n, and paste them together to form a series of length n

k-Nearest Neighbor Conditional Bootstrap (Lall and Sharma, 1996)

Construct the Conditional Empirical Distribution Function:

Draw a random sample with replacement from

Define the composition of the "feature vector" Dt of dimension d.

(1) Dependence on two prior values of the same time series.

Dt : (xt-1, xt-2) ; d=2

(2) Dependence on multiple time scales (e.g., monthly+annual)

Dt: (xt-t1, xt-2t1, .... xt-M1t1; xt-t2, xt-2t2, ..... xt-M2t2) ; d=M1+M2

(3) Dependence on multiple variables and time scales

Dt: (x1t-t1, .... x1t-M1t1; x2t, x2t-t2, .... x2t-M2t2); d=M1+M2+1

Identify the k nearest neighbors of Dt in the data D1 ... Dn

Define the kernel function ( derived by taking expected values of distances to each of k nearest neighbors, assuming the number of observations of D in a neighborhood Br(D*) of D*; r0, as n , is locally Poisson, with rate (D*))

for the jth nearest neighbor

Selection of k: GCV, FPE, Mutual Information, or rule of thumb (k=n0.5)