Historical Data Analysis

NWS Calibration Workshop, LMRFC March, 2009 slide 1

Historical Data AnalysisGeneral Information Needed

Analysis of PrecipitationInformation needed

Non Mountainous Mountains

PXPP

1 check consistency2 compute monthly means

MAP

1 recheck consistency2 generate time series of MAP

MAT

TAPLOT

MAT

MAPE

1. Station data2. Station history info: obs times, changes, location, moves3. Topographic data

1 isohyetal map2 station weights-basin boundary

Mountains

- check consistency

- get mean max/min for mean zone elev.

- generate time series of MAT.

- area vs elev. curve-basin boundary

1 evaporation maps2 station weights3 mean monthly evap.

1 check consistency2 generate daily time series of MAPE

- evap. vs elev. curve

Non Mountainous Non Mountainous Mountains

-compute 12monthly ETdemand values

Analysis of TemperatureInformation needed

Analysis of EvaporationInformation needed

MAPX1. ‘Poor man’s” reanalysis


Analysis of Precipitation

• Non-Mountainous Areas– Long Term Means Vary Slightly Across the Region– Station Weights Based Totally on Location

• Mountainous Areas– Long Term Means Vary Across the Region– Ratio of Monthly Normals Used when Estimating

Missing Data– Long Term Areal Mean Based on Isohyetal Analysis– Station Weights Typically Don’t Sum to 1.0


Analysis of Precipitation

Criteria for

Mountainous vs Non-Mountainous Area Analysis• Mountainous Areas: any area where the long-term mean

precipitation varies significantly over the area such that mean areal values cannot be computed as a weighted average based solely on the geographical location of the stations.

Station Variation0 1-10% >10%

Analysis MAP Use Judgment PXPP


Analysis of PrecipitationStation Selection

• Be conservative• All stations within basin• A few outside the basin for coverage and

estimation of missing data• At least 5, preferably 10 years of data• Complete as possible record• Hourly stations for time disaggregation of daily

stations• Go further out for mtn. areas to represent higher

elevations.


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Selection of Potential Precipitation Stationsin Non-Mountainous Areas


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HDaily station used as estimator for nearby daily station

Hourly station needed to distribute nearby daily station values

Selection of Potential Precipitation Stationsin Non-Mountainous Areas


Standard Rain Gauge

Boundary of drainage area

Main river channel

Precipitation data


Data Quality Control

• Method: Double Mass Analysis (DMA)• Reasons

– Station moves– Equipment changes

• (e.g., add wind shield)

– Site Changes (vegetation, buildings, etc)

• Legacy Programs that use DMA– PXPP/MAP/MAT/MAPE

Need station history

Wind Shield


Accumulation of the group of stations.

Acc

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sta

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Standard Double Mass Analysis


Analysis of PrecipitationNWS Double Mass Analysis

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Accumulation of Average Precipitation of Group BaseDe

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estimated data

documented station change

More logical that a single gage is inconsistent rather than entire group



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calibration verificationA

Goal: • one set of parameters that is good for entire period• real inconsistencies are removed, not natural variations

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Documented station change

Station 1

Given: Station 1 receives 50% of the weight for MAP. Without correction, it catches20% more precip in verification period. MAPA< MAPB ,hard to calibrate


NWS Double Mass Analysis:Definitions

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Acc. of Average Precip. of Group BaseDev

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Average precip. of group

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Px= station analyzedPi= all stations other than Px

n = total no. of stations; n-1 stations in the group; group base acc. varies slightly for each station.M = no. of months

Average precip. of group

Acc precip. of station


What is the IDMA Tool?

• A GUI that aids in the quality control of hydrologic data– point observations of rainfall, temperature etc.

• Links legacy NWS pre-processors and a data base of historical data/metadata

• Uses Double Mass Analysis (DMA) as primary quality check

• Main output: multiplicative correction factors– Typical range .90 < cf < 1.5


LegacyCalibration Pre-processor-MAP-PXPP-MAT-MAPE

IDMA

Point time series dataStation HistoryMetadata Historical data

inventories(Postgres)

Mean areal Time series

Accumulated point time series(‘dma’ file)

Pre-processor controls

Pre-processor controls

Current correctionFactors

Current correctionFactors

Pre-processorInput file

New correction factors

Pre-processor: program for analyzing precipitation, temperature, evaporation data

IDMA Linkages to Historical Data and Preprocessors


IDMA Steps

• Group stations geographically

• Identify missing data (white lines in IDMA)

• Identify station moves

• Pick period to correct to (usually the most recent)



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Simple Case

Early period Later period


CF > ? CF =?

CF = correction factor



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Accumulation of Average Precipitation of Group Base

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Simple Case

Early period Later period


CF > 1.0 CF =1.0

CF = correction factor



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Complex case

CF>1.0 CF<1.0 CF=1.0


Analysis of PrecipitationNWS Double Mass Analysis - Cases

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estimated data




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estimated data (can’t be corrected explicitly)


Check for bad data in raw time series

Good candidate forcorrection



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Given: no documented station changes



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Given: documented station change in recent period


Accumulated Simulation Error (mm of depth) : North Fork American RiverSimulation Period 10/1998 to 8/2006

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Accum error

Analysis of OHD Basic QPE for DMIP 21987 – 2006

Output from STAT-QME Operation

Inconsistent Precipitation?

Possible cause: bad data for the Blue Canyon station: “a lot of rain in Jan 95” wasrecorded as zeros in the NCDC data. CNRFC set these values to ‘missing’ in their calibration.

March 1998

Dec 2005


OHDDistributed

Observed

Lumped

DMIP 2: North Fork American RiverOHD Streamflow Simulations

Flo

w (

cms)

March 25, 1998


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cms)

Dec 19-26, 2005

OHD

Observed

North Fork American RiverStreamflow Simulations


Guidelines for Consistency Adjustments• Use Seasonal Plots in Regions with Snowfall

– Winter - Months when Snowfall Predominates– Summer - Months with Mostly Rainfall– Snowfall Affected more by Station Changes

• Large Spikes in Plot Indicate Bad Data• Group Stations by Location/Elevation

– Changes in Storm Track or Type will Alter the Relationship between Stations (All Stations in Portion of the Area will Show a Similar Shift in their Double Mass Plot -- This is Real and Should Not be Corrected)

• If Any Doubt, Don’t Make an Adjustment– Precipitation is Naturally Quite Variable– Double Mass Plots Should Contain Wobbles

• Identify periods of missing data: these can’t be adjusted explicitly• Station history files not always complete


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Double Mass AnalysisGrouping of Precipitation Stations

in Non-Mountainous Areas

Group stations geographicallyin sets of 5


Tests for Precipitation Homogeneity: Graphical procedures

Isolated Station Analyses Neighborhood Analyses

1.a Plot of pure data: (Rhoades & Salinger, 1993)1.b Cusums of isolated data: (Rhoades & Salinger, 1993)

Double Mass Analysis

Compare one station to ‘reference’ or ‘base’ series (absolute homogeneity)(Kohler, 1949; WMO, 1971)

Single Cusum Plots(Kohler, 1949; Arndt and Redmond, 2004;Craddock, 1979)

Parallel Cusums Plots(Rhoades and Salinger, 1993)

Specialized Parallel Cusums Plots (Rhoades and Salinger, 1993)1. Deviations2. Ratio3. Ratio of log

Compare one station to another station(relative homogeneity)

Specialized Single Cusums(Cumulative deviations) (Craddock, 1979) 1. Ratio2. Deviation from mean3. Deviation from user defined

line segment (Arndt and Redmond, 2004)

Plots of test statistcs(Potter, 1981)

Reference series network constant in time

Reference series networkchanges with time(Peterson and Easterling, 1994)

Unweighted mean of ref. stations(Alexandersson, 1986)N-1 stations (NWS)20 stations5 stations

Weighted mean ofref. stations. 1.Using correlation coeffs.(Alexandersson, 1986)

Specialized Cusum plots(deviations)1. Difference 2. Ratio3. Ratio of logs

NWS

NWS

Where do the NWS procedures fit in relation to peer-reviewed, published methods?


Historical Data AnalysisGeneral Information Needed

Analysis of PrecipitationInformation needed

Non Mountainous Mountains

PXPP

1 check consistency2 compute monthy means

MAP

1 recheck consistency2 generate time series of MAP

MAT

TAPLOT

MAT

MAPE

1. Station data2. Station history info: obs times, changes, location, moves3. Topographic data

1 isohyetal map2 station weights-basin boundary

Mountains

- check consistency

- get mean max/min for mean zone elev.

- generate time series of MAT.

- area vs elev. curve-basin boundary

1 evaporation maps2 station weights3 mean monthly evap.

1 check consistency2 generate daily time series of MAPE

- evap. vs elev. curve

Non Mountainous Non Mountainous Mountains

-compute 12monthy ETdemand values

Analysis of TemperatureInformation needed

Analysis of EvaporationInformation needed


Grid Point Weighting1. Overlays HRAP grid2. For each grid pt. Finds closest station

in each of 4 quadrants; compute distance d

3. Compute weight of each station 1/d4. Normalize 4 weights5. Sum all weights for each station6. Normalize station weights to sum to 1.0

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HRAP grid

Thiessen Polygon

Precipitation station2

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Mean Areal Precipitation (MAP) Program

MAP weighting options: Grid Thiessen Predetermined


Thiessen Weighting

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HRAP grid

Precipitation station

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1. Overlays HRAP grid2. Examines each grid point3. Assigns grid point to closest

station4. Station weight =

no. assigned points/Total no. of grid points.

Mean Areal Precipitation (MAP) Program MAP weighting: Grid Thiessen Predetermined


MAP3 Computational Sequence1. Read in data and corrections2. Applies corrections to observed data3. Estimates missing hourly data using only other hourly stations.

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ix,d

w1

i estimator to x station from distanced

weightstationw

i station for ionprecipitat monthly meanP

x station for ionprecipitat monthly meanP

estimator an as used being station i

stations estimating of number n

station estimator the at ionprecipitatP

estimated being station at ionprecipitatP

ix,

ix,

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x

i

x


4. Time distribute observed daily amounts into hourly values based on surrounding hourly stations.

1. Procedure uses 1/d2 weighting for surrounding hourly stations.2. If all hourly stations = 0, then all precipitation is put in last hour of the

daily station. Hour of the observation time. NFAR example5. Estimate missing daily amounts using both hourly and daily gages; time

distribute these amounts-If all estimators are missing, then uses 0.0

6. Generates file of station and group accumulated precipitation for IDMA7. IDMA

1. -Compute correction factors2. -Preliminary check of correction factors3. -Insert correction factors into input file4. -Re-run MAP3 for final check of consistency

8. Applies weights to station for each area9. Computes hourly MAP time series10. Sums to selected time interval, e.g., 3hr, 6hr.

MAP3 Computational Sequencecontinued


Calibration MAP vs Operational MAPTwo Different Algorithms

Calibration MAP Operational MAP

1. Uses hourly and daily precipitation amounts

1. Uses sub-daily and daily amounts.

2. Computes hourly MAP, then sums to any time step.

2. Computes 24 hr. MAP, then distributes into 4 6-hr. periods based on hourly stations. Will use uniform distribution if hourly not available.

3. OFS Techniques available for various conditions.


Importance of Mountainous Area Analysis


Precipitation AnalysisObjectives of Mountainous Area Procedure

• Compute Unbiased Estimate of Mean Areal Precipitation• Ratio of Monthly Normals Used to Estimate Missing Data• Long Term Areal Averages Based on Isohyetal Analysis• Allow for Operational and Historical Estimates of MAP to

be Unbiased• Same Method Used for Both Historical and Real Time

Data• Exact Same Areal Averages Used in Both Cases• Requires Good Definition of Monthly Station Normals


Mountainous Area AnalysisSteps

• Select stations, perform quality control• Determine mean monthly precipitation for each station for

the period of record (Program PXPP)• Determine annual or seasonal station weighting• Determine mean annual precipitation for area or sub area• Determine station weights (adjust the relative weights)

=> predetermined weights• Compute MAP time series


Program PXPP

• Function: compute monthly means for stations having different periods of record

• Uses monthly time step• If any hour or day is missing, sets entire month to

missing• Computes correlation tables to assist with station

weights.

time

stat

ion

Base station


Analysis of Precipitation in Mountainous Areas

Derivation of Isohyetal Maps

• Use existing map

• Derive using method of Peck (1962)

• Use NRCS PRISM data– Note:

• May not have used all data NWS uses• Data may not be consistent• May need water balance analysis.


Verification of Isohyetal Maps

• Compare station means, seasonal and annual, from PXPP to values from isohyetal maps– Plot Ratio of PXPP mean to isohyetal map value– Tabulate values, compute differences and average

ratio over the entire region– Determine isohyetal map adjustment(s) for

historical data period of record• Perform water balance computations

– Compute actual ET, from MAP and runoff, for headwaters and local areas with minimal complications

– Determine if actual ET values are reasonable (Can adjust MAPs that are clearly in error at this point)


Determining Relative WeightsMAP weighting options: Grid Thiessen Predetermined

• Information to Consider– Precipitation - Elevation Relationships, Seasonal and

Annual– Correlation Relationships (from PXPP)– Knowledge of Prevailing Storm Types and Tracks

(Anomaly Maps can Assist in Understanding)

• Typical Results– Seasonal Weights in Intermountain West– Winter Weights Based More on Elevation– Summer Weights Based More on Distance– Annual Weights in East and along West Coast


Mtn Area AnalysisExamples

• Juniata River, Pennsylvania– Uses available isohyetal map

• Oostanaula River, Georgia– Derivation of isohyetal map


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OHD UTS UWO End Calib

Effects of Inconsistent Radar QPEDMIP 1

Period of known underestimationand algorithm changes

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• Analysis of Monocacy River observed and simulated flows shows reduction in cumulative bias and improved consistency when bias corrected precipitation is used

• A consistent bias can be removed through calibration or through DHM-TF approach

Monocacy at Jug Bridge (2116 km2)

• Bias detected in MARFC MPE archives prior to 2004• Bias corrected precipitation needed to support unbiased simulation statistics for a reasonable historical period (can extend to ~9 years)

Bias Correction of Archived Precipitation: Example of ‘Poor Man’s’ Reanalysis

Cumulative Bias, Monocacy River at Jug Bridge (2100 km2)


Monthly RFC MPE Precipitation 03/97 (mm)

Monthly PRISM Precipitation 3/97 (mm)

Monthly Bias (ratio)RFC Hourly MPE Precipitation

03/01/97 12z (mm)

Adjusted RFC Hourly MPE Precipitation 03/01/97 12z (mm)

Yu Zhang

Bias Correction of Precipitation


Re-analysis

Original

Example of typical improvements, particularly for small-medium events.

Monocacy River

Bias Correction of Precipitation

Re-analysis

Original

Historical Data Analysis

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