DataSimulated data

AMSREA, MODIS A-T

Cross-validation approach Full fields as input data and truth15 day sliding data windowRemove 3 or 5 days of dataCalculate error for middle day

2-D Bi-cubic 2-D Bi-cubic Smoothing SplineSmoothing Spline

Inoue (1986): tension parameter, roughness parameter

Tense splines (> 0.9) because of extrapolation

Very smooth splines can’t interpolate over large gaps

Interpolating splines whiten residuals & overfitting

.1 < rho (roughness parameter) < 1.0

Objective AnalysisObjective Analysis

Influential Data Points (IDP):•O(1,000,000) data pts to O(10) IDP at each OA location

•Computationally intensive part of OA code

•IDP should be the data most correlated with OA location

•PMOA algorithm was designed to efficiently find IDP

•New algorithm is finding IDP in local polar coordinates

•Goal: Find IDP most correlated that surround OA location reduce bias

Optical flow method• DT/dt=0 δT/δt=-(uδT/δx + vδT/δy)• Trend Field is used for input• Moore-Penrose Inverse Solution• Time derivative calculated with δt=2 days• Spatial derivatives weighted (1/4,1/2,1/4)• FDVs outliers are removed (large & near-zero)• Spline smoothing of FDV estimates

Cross-validation error estimates:Remove 3 input days of data in

sliding 15 day data window

Calculate estimation error for the middle day for 3 months

FDV-based estimates were 10%better, RMS of .51 vs .56

Input test Data

OA with FDV & zero FDV

3 days removed

5 days of data removed

Future Work

• Tune some parameters

• Influential Data Point Selection

• Estimation variance vs resolution/bias

• Merge FDV with MUR: FDV(scale)