Hybrid optical turbulence models using machine-learning and local measurements

Christopher Jellen; Charles Nelson; John Burkhardt; Cody Brownell

doi:10.1364/AO.487280

Applied Optics
Vol. 62,
Issue 18,
pp. 4880-4890
(2023)
•https://doi.org/10.1364/AO.487280

Hybrid optical turbulence models using machine-learning and local measurements

Christopher Jellen, Charles Nelson, John Burkhardt, and Cody Brownell

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Christopher Jellen, Charles Nelson, John Burkhardt, and Cody Brownell, "Hybrid optical turbulence models using machine-learning and local measurements," Appl. Opt. 62, 4880-4890 (2023)

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Abstract

Accurate prediction of atmospheric optical turbulence in localized environments is essential for estimating the performance of free-space optical systems. Macro-meteorological models developed to predict turbulent effects in one environment may fail when applied in new environments. However, existing macro-meteorological models are expected to offer some predictive power. Building a new model from locally measured macro-meteorology and scintillometer readings can require significant time and resources, as well as a large number of observations. These challenges motivate the development of a machine-learning informed hybrid model framework. By combining a baseline macro-meteorological model with local observations, hybrid models were trained to improve upon the predictive power of each baseline model. Comparisons between the performance of the hybrid models, selected baseline macro-meteorological models, and machine-learning models trained only on local observations, highlight potential use cases for the hybrid model framework when local data are expensive to collect. Both the hybrid and data-only models were trained using the gradient boosted decision tree architecture with a variable number of in situ meteorological observations. The hybrid and data-only models were found to outperform three baseline macro-meteorological models, even for low numbers of observations, in some cases as little as one day. For the first baseline macro-meteorological model investigated, the hybrid model achieves an estimated 29% reduction in the mean absolute error using only one day-equivalent of observation, growing to 41% after only two days, and 68% after 180 days-equivalent training data. The data-only model generally showed similar, but slightly lower performance, as compared to the hybrid model. Notably, the hybrid model’s performance advantage over the data-only model dropped below 2% near the 24 days-equivalent observation mark and trended towards 0% thereafter. The number of days-equivalent training data required by both the hybrid model and the data-only model is potentially indicative of the seasonal variation in the local microclimate and its propagation environment.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter	Data Source	Unit	Measurement Frequency	Number of Observations
$C_{n}^{2}$	BLS 450	$[m^{- \frac{2}{3}}]$	1 min	1,246,802
Water Temperature	NOAA Weather Station, NDBC Data Buoy	[°C]	1-hour	21,946
Air Temperature	Davis Weather Station	[°C]	10 min	125,569
Atmospheric Pressure		[mBar]		126,510
Relative Humidity		[%]		125,583
Solar Radiation		$[\frac{W}{m^{2}}]$		125,633
Wind Speed		$[\frac{m}{s}]$		126,512

	Air–Water Temperature Difference [°C]	Measured $C_{n}^{2}$ $[m^{- \frac{2}{3}}]$	Eq. (3) Predicted $C_{n}^{2}$ $[m^{- \frac{2}{3}}]$
Count	1,241,037	1,246,802	1,156,426
Mean	−0.4	$1.845 \times 10^{- 14}$	$2.862 \times 10^{- 15}$
Std.	4.34	$3.646 \times 10^{- 14}$	$4.350 \times 10^{- 15}$
Min.	−12.25	$1.642 \times 10^{- 17}$	$6.200 \times 10^{- 17}$
25%	−2.66	$2.871 \times 10^{- 15}$	$3.087 \times 10^{- 16}$
Median	−0.07	$8.326 \times 10^{- 15}$	$1.193 \times 10^{- 15}$
75%	3.11	$2.091 \times 10^{- 14}$	$3.652 \times 10^{- 15}$
Max	18.8	$2.404 \times 10^{- 12}$	$5.339 \times 10^{- 14}$

Description	Hyper-Parameter Name [12,18]	Possible Values
Number of leaves for each constituent tree node.	`num_leaves`	8, 128, 512, 1024, 4096
Model learning rate under the gradient boosting framework.	`learning_rate`	0.5, 0.2, 0.1, 0.01
Minimum number of training observations in each leaf node of each constituent tree.	`min_data_in_leaf`	32, 128, 512, 2048, 4096

Model	Target	Metric	Features	Number of Days-Equivalent Observations in Training Set	Hyper-Parameters
Data-Only	${L o g}_{10} C_{n}^{2}$	MAE	Air–Water	1	`learning_rate: 0.5 min_data_in_leaf: 32 num_leaves: 8`
			Temperature	2
			Difference,	3
			Wind Speed,	4
			Humidity,	5
Hybrid	Target correction		Pressure,	6	`learning_rate: 0.1 min_data_in_leaf: 128 num_leaves: 8`
	(tc in Eq. (1))		Solar Radiation,	7
			Temporal Hour,	8
			Air–Water	9
			Temperature	10
			Difference	12	`learning_rate: 0.1 min_data_in_leaf: 128 num_leaves: 8`
				14
				16
				18
				21
				24	`learning_rate: 0.1 min_data_in_leaf: 128 num_leaves: 8`
				27
				30
				45
				60
				75	`learning_rate: 0.01 min_data_in_leaf: 128 num_leaves: 8`
				90
				120
				150
				180
				210	`learning_rate: 0.01 min_data_in_leaf: 512 num_leaves: 128`
				240
				270
				300
				330
				360	`learning_rate: 0.01 min_data_in_leaf: 128 num_leaves: 1024`
				390
				420
				450
				480

Number of	Mean Absolute % Error (validation set)				MAE ${L o g}_{10} C_{n}^{2}$ (validation set)
Days-Equivalent	Hybrid Model		Data-Only Model		Hybrid Model		Data-Only Model
Observations in Training Set	Bootstrap mean	Bootstrap Std.	Bootstrap mean	Bootstrap Std.	Bootstrap mean	Bootstrap Std.	Bootstrap mean	Bootstrap Std.
1	4.92%	0.78%	4.30%	0.74%	0.700	0.110	0.610	0.109
2	4.10%	0.70%	3.89%	0.43%	0.581	0.102	0.549	0.057
3	3.91%	0.54%	4.21%	0.58%	0.553	0.076	0.593	0.080
4	3.91%	0.50%	4.08%	0.52%	0.555	0.071	0.577	0.073
5	3.77%	0.71%	3.92%	0.61%	0.534	0.101	0.555	0.085
6	3.53%	0.52%	3.49%	0.39%	0.499	0.073	0.493	0.053
7	3.16%	0.44%	3.43%	0.50%	0.448	0.061	0.484	0.069
8	3.03%	0.14%	3.23%	0.25%	0.430	0.018	0.457	0.033
9	3.07%	0.23%	3.31%	0.24%	0.435	0.032	0.468	0.033
10	3.02%	0.24%	3.30%	0.27%	0.429	0.033	0.468	0.037
12	2.93%	0.19%	3.08%	0.28%	0.416	0.027	0.437	0.038
14	2.96%	0.30%	3.15%	0.29%	0.419	0.042	0.445	0.039
16	2.80%	0.18%	2.99%	0.25%	0.398	0.025	0.424	0.034
18	2.85%	0.16%	2.94%	0.24%	0.405	0.021	0.417	0.033
21	2.80%	0.20%	2.87%	0.20%	0.397	0.028	0.406	0.027
24	2.63%	0.11%	2.80%	0.12%	0.375	0.016	0.398	0.016
27	2.55%	0.14%	2.66%	0.14%	0.363	0.020	0.379	0.019
30	2.53%	0.09%	2.63%	0.11%	0.360	0.013	0.375	0.015
45	2.45%	0.08%	2.53%	0.09%	0.349	0.011	0.361	0.012
60	2.38%	0.05%	2.46%	0.06%	0.339	0.008	0.350	0.009
75	2.31%	0.05%	2.39%	0.07%	0.329	0.008	0.341	0.009
90	2.30%	0.05%	2.35%	0.05%	0.327	0.008	0.336	0.007
120	2.25%	0.03%	2.27%	0.04%	0.321	0.005	0.324	0.006
150	2.20%	0.04%	2.22%	0.05%	0.314	0.006	0.316	0.008
180	2.19%	0.03%	2.22%	0.03%	0.312	0.005	0.317	0.005
210	2.15%	0.03%	2.18%	0.03%	0.307	0.004	0.311	0.004
240	2.16%	0.03%	2.18%	0.04%	0.308	0.004	0.311	0.006
270	2.15%	0.03%	2.16%	0.04%	0.306	0.004	0.309	0.006
300	2.14%	0.03%	2.16%	0.04%	0.306	0.004	0.308	0.005
330	2.12%	0.03%	2.14%	0.03%	0.303	0.004	0.305	0.004
360	2.17%	0.02%	2.21%	0.03%	0.309	0.003	0.315	0.004
390	2.16%	0.02%	2.19%	0.02%	0.308	0.003	0.312	0.004
420	2.15%	0.01%	2.18%	0.03%	0.307	0.002	0.311	0.004
450	2.15%	0.02%	2.16%	0.02%	0.306	0.002	0.309	0.003
480	2.14%	0.02%	2.16%	0.02%	0.306	0.003	0.309	0.004

Abstract

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Applied Optics