Gap-filling methods for CH 4 data Sigrid Dengel University of Helsinki
Outline - Ecosystems known for CH 4 emissions; - Why is gap-filling of CH 4 data not as easy and straight forward as CO 2 ; - Gap-filling methods applied so far; - What can we take over from CO 2? - Neural networks a suggested method;
Ecosystems with CH 4 emissions Concentrating on arctic and subarctic environments: - Boreal fens; - Tundra; - Mires; - Forests; - Bogs; - River plains/delta; - Water bodies -???
Variables influencing(?) CH 4 fluxes(?) - Soil temperature; - Water table level; - Soil moisture; - Air pressure - Soil type - Wind speed/velocity - Ebullition (bubbling effect) - Air temperature - Solar radiation;(?) - Vegetation type
Why is gap-filling of CH 4 data not as straight forward as CO 2? - Diurnal vs. non diurnal variation; - Seasonal complexity; - Ecosystem location; - Grazing patterns (ruminants);
Gap-filling methods applied so far - Always study dependent; - Majority gap-filled only daily values; - Data were split by season, even than still limited; - Non-linear relationship with soil temp (and water table level); - Always labour intensive;
CH 4 - example Dengel & Grace (2010) Peltola/Haapanala (unpublished data) Peltola (2011) Rinne et al. (2007?)
Gap-filling methods applied so far - Is filling daily values enough? - Which environmental factors are the right ones to use? - Non-linear regressions; - => No standardised method yet;
What can we take over from CO 2? - Linear interpolation short gaps; - Mean Diurnal Variation (MDV); - What else? Kalman filtering maybe?
What can we take over from CO 2? - Linear interpolation short gaps; - Mean Diurnal Variation (MDV); - What else? Kalman filtering maybe? - Feed-forward neural networks;
Can we apply Neural networks to gappy CH4 data? - History of neural networks; - Application of neural networks; - Where people have applied it; - How does it work (backpropagation);
Neural networks i 1 w 1 i 2 w 2 w 3 Neuron Output = f(i 1 w 1 + i 2 w 2 + i 3 w 3 + bias) i 3 bias Sigmoid function is the most commonly used function: f (x) = 1/(1+e -x )
Neural networks Input layer Hidden layer (neurons) Output layer 2.33-1.79 1 I 1 3.17 N 1 O Output 2 I 2-0.97 N 2-1.97
2.33-1.79 1 I 1 3.17 N 1 O Output 2 I 2-0.97 N 2-1.97 N1 = 1(3.17) + 2(-0.71) +2.33 = 4.08 = 1/(1 + e -4.08 ) = 0.983374 N2 = 1(2.67) + 2(-0.97) -1.97 = -1.24 = 1/(1 + e 1.24 ) = 0.224436 O = 0.983374(3.72) + 0.224436(-4.51) 1.79= 0.855944 Output = 1/(1 + e -0.855944 ) = 0.701812
2.33-1.79 1 I 1 3.17 N 1 O Output 2 I 2-0.97 N 2-1.97 N1 = 1(3.17) + 2(-0.71) +2.33 = 4.08 = 1/(1 + e -4.08 ) = 0.983374 N2 = 1(2.67) + 2(-0.97) -1.97 = -1.24 = 1/(1 + e 1.24 ) = 0.224436 O = 0.983374(3.72) + 0.224436(-4.51) 1.79= 0.855944 Output = 1/(1 + e -0.855944 ) = 0.701812
2.33-1.79 1 I 1 3.17 N 1 O Output 2 I 2-0.97 N 2-1.97 N1 = 1(3.17) + 2(-0.71) +2.33 = 4.08 = 1/(1 + e -4.08 ) = 0.983374 N2 = 1(2.67) + 2(-0.97) -1.97 = -1.24 = 1/(1 + e 1.24 ) = 0.224436 O = 0.983374(3.72) + 0.224436(-4.51) 1.79= 0.855944 Output = 1/(1 + e -0.855944 ) = 0.701812
How well do our data fit? - Is the result of 0.71 good enough??? - Common measure of error: - Pearson correlation coefficient; - Mean square error; - Backpropagation and re-adjustment the weights; - Under vs. over-fitting (quality of the data & network)
How well do our data fit? Training data set Test data set Well fitted Overfitted The number of neuron is very important! Too few underfit the data and NN can not learn the details; Too many overfit the data and NN learns insignificant details (outliers);