Look-up Table Method Research Articles

Research on Optimal Coordination and Algorithms of Microprocessor-based Inverse Time Backup Protection

Backup protection plays an important role in the safe operation of power grid, and it has important research value in the field of power system relay protection. Firstly, the research status and development opportunities of inverse time limit protection are analyzed, and then the best cooperation between inverse time limit protection and distance protection is discussed theoretically. According to the time constraint relationship in the protection range, an objective function satisfying the selectivity and speed is proposed. Secondly, in view of the difficulty in calculating the inverse time characteristic curve, a processing algorithm combining Taylor expansion method and look-up table method is proposed. Finally, the effectiveness and practicability of the method are verified by simulation experiments.

Intelligent control and energy saving evaluation of highway tunnel lighting: Based on three-dimensional simulation and long short-term memory optimization algorithm

Traditional tunnel lighting luminance is calculated based on the designed hourly traffic volume and designed speed. This approach first determined the entrance section reduction factor and middle section’s luminance through the look-up table method, then calculated each section’s luminance in proportion. Since the designed value is often higher than the actual traffic flow value, and the calculated brightness value is so high which might lead to tunnel energy consumption. What’s more, the designed value in this method is the piecewise discrete value, which does not meet the requirement of continuous dimming for LED lighting. In this case, under the premise of satisfying operation safety, how to carry out continuous intelligent energy saving control research and energy saving evaluation based on actual traffic value is an urgent problem to be solved in tunnel lighting. This paper first proposed a luminance calculation model for each lighting section which can realize continuous dimming as needed. Using the least squares method fitting the reduction coefficient and the luminance of the middle section to solve the luminance of the entrance and middle sections under the condition of any speed and traffic flow, and realizing the continuous optimization of the luminance calculation. Second, in terms of the shortcomings of the traditional graded dimmer control, this paper offered a highway tunnel lighting intelligent control algorithm with traffic flow, speed and luminance out of the tunnel as the input matrix, which meets the requirement of LSTM (Long Short-Term Memory) neural networks, tunnel lighting characteristics and tunnel lighting section. Considering the objective function of optimization problem in LSTM, three gradient descent methods were introduced to optimize the model respectively. Third, this paper adopted equal proportion to arrange lamps and light distribution, and developed a tunnel lighting simulation environment based on DIALux to meet the energy conservation assessment requirements in operating tunnels. Roadway luminance and its total uniformity are selected as energy saving evaluation indexes. Finally, we established a three-dimensional tunnel model with the real environment of Jinding Lake 2# tunnel, then conducted simulations and experimental verifications of the intelligent control algorithm under sunny and cloudy weather conditions, and verified the performance of the intelligent lighting control algorithm under the three optimizers. The result of energy conservation evaluations shows that compared with traditional lighting design, the tunnel lighting energy conservation algorithm can save 23.61% of energy in sunny days and 31.40% in cloudy days.

Wheel–rail contact simulation with lookup tables and KEC profiles: a comparative study

This paper describes and compares the use and limitations of two constraint-based formulations for the wheel–rail contact simulation in multibody dynamics: (1) the use of contact lookup tables and (2) the Knife-edge Equivalent Contact constraint method (KEC-method). Both formulations are presented and an accurate procedure to interpolate within the data in the lookup table is also described. Since the wheel–rail constraint contact approach finds difficulties at simultaneous tread and flange contact scenarios, the lookup table method is implemented with a penetration-based elastic contact model for the flange, turning the method into a hybrid (constant in the tread and elastic in the flange) approach. To deal with the two-point contact scenario in the KEC-method, a regularisation of the tread–flange transition allows the use of the constraint approach in the tread and also in the flange. To show the applicability and limitations of both methods, they are studied and compared with special emphasis in the calculation of normal and tangential contact forces. Numerical results are based on the simulation of a two-wheeled bogie vehicle in different case studies that consider irregular tracks and two wheel–rail profiles combinations: profiles that do not show two-point wheel–rail contacts and profiles that do show two-point wheel–rail contacts. Although results show a good agreement between both approaches, the use of the KEC-method is more extensive since it allows to reproduce the wheel-climbing scenario that cannot be simulated with the lookup table method with the hybrid contact approach. It is concluded that simulations with this later method may not be on the safe side.

Dynamic AC Line Frequency Response Method for LUT-Based Variable On-Time Control in 360–800 Hz CRM Boost PFC Converter

To improve the input current total harmonic distortion (THD), the look-up table (LUT) method is used in the 360-800 Hz critical conduction mode (CRM) boost power factor correction (PFC) converter. When the ac line frequency changes drastically and suddenly, the zero-crossing detection method needs the half ac line period to follow the sudden frequency jump, causing a mismatching between the LUT and the ac line frequency. This mismatching in the time domain leads to a large current spike in the input current and even destruction in the PFC converter under some severe conditions. In this letter, a dynamic ac line frequency response method is proposed to eliminate this mismatching. The proposed method only needs to sample the input voltage, leading to a good performance in following the sudden frequency jump in a wide input voltage range. The effectiveness of the proposed method is verified with a 160 W GaN-based CRM boost PFC converter.

Outlier-robust tri-percentile parameter estimation of K-distributions

K-distribution is one of the most popular sea clutter amplitude models where the scale and shape parameters reflect the power level and non-Gaussianity of the clutter. In real oceanic environments, the two spatial-temporally varying parameters are estimated from sea clutter data with outliers. Outliers are probably from sea-surface ships, reefs, or abnormal scattering phenomena. Existing moment-based, numerical maximum likelihood, and [zlog(z)]-based estimators are sensitive to outliers, which results in abrupt degradation of parameter estimation precision in real clutter environments. This paper proposes an outlier-robust tri-percentile parameter estimator of K-distributions. It is shown that the ratio of two percentiles is a monotonically decreasing function of the shape parameter and independent of the scale parameter. In this way, the shape parameter is estimated from the ratio of two sample percentiles by the look-up table method and interpolation method. Moreover, an empirical formula on the optimal setup of the two percentiles is given by numerical computation. Next, the scale parameter is estimated by the third sample percentile whose position depends on the estimated shape parameter. Finally, the tri-percentile estimator is evaluated by using simulated and measured data, showing that it is rather robust to outliers in simulated data and raw sea clutter data.

Compact full-color holographic 3-D display based on undersampled computer-generated holograms and oblique projection imaging.

A compact full-color electro-holographic three-dimensional (3-D) display with undersampled computer-generated holograms (US-CGHs) and oblique projection imaging (OPI) is proposed. For its realization, undersampling conditions of the CGH enabling the complete recovery of image information are derived, and the OPI-based longitudinal-to-lateral depth conversion (LTL-DC) scheme allowing the simple reconstruction of full-color images is also proposed. Three-color off-axis US-CGHs are generated with their center-shifted principle fringe patterns (CS-PFPs) of the novel look-up table (NLUT) method, where center-shifts are calculated with the derived undersampling conditions of the CGH based on the generalized sampling theorem, and then multiplexed into the color-multiplexed hologram (CMH). The CMH is loaded on a SLM (spatial light modulator) and reconstructed by being illuminated with a multi-wavelength light source, where an original full-color image is reconstructed being spatially separated from the other color-dispersed images on the projected image plane with the OPI-based LTL-DC process, which enables us to view the original full-color image just with a simple filter mask. Performance analysis and successful experiments with the test 3-D objects in motion confirm the feasibility of the proposed system.

Fast calculation of high-definition depth-added computer-generated holographic stereogram by spectrum-domain look-up table [Invited

High-definition depth-added computer-generated holographic stereogram (DA-CGHS) is superior in its high quality, easy realization, and auto-shading effect. However, its computing cost is extremely high because numerous scenes together with depth information must be calculated. Here, we proposed a fast calculation scheme of DA-CGHS by the spectrum-domain look-up table (SDLUT) method. In SDLUT, diffraction fields on the hogel plane of selected reference points in the object space are calculated. Subsequently, the fields are Fourier transformed to the spectrum domain. Because the signal energy always concentrates in a small spectrum region, these regions are cropped as the elemental tables. In the computing of the hogels, the field superposition is conducted in the spectrum domain by using the elemental tables. In our demonstration, the table size of SDLUT is only 0.44% that of the look-up table (LUT). Because the table size is very small, the computing time of SDLUT method can be nearly 80 times faster than that of conventional LUTs in the spatial domain, while the image quality is comparable.

Phase modulation depth setting technique of a phase-generated-carrier under AOIM in fiber-optic interferometer with laser frequency modulation.

The phase modulation depth (PMD) in phase-generated-carrier demodulation is determined by the laser frequency modulation amplitude and working distance of a fiber-optic interferometer and must be set at a certain value. Active setting of the amplitude is unsuitable, especially for high-speed modulation, owing to variations in the laser source tuning coefficients. Existing calculation schemes for passive setting cannot work both owing to carrier phase delay (CPD) and the accompanied optical-intensity modulation (AOIM). Herein, a modified phase modulation depth calculation and setting technique is proposed. Double photoelectric detection and signal division are optimized to eliminate AOIM using a fiber delay chain and phase-locked amplifier module. Fast Fourier-transform and look-up table methods are used to calculate phase modulation depth without adding the carrier, which is unaffected by CPD. A fiber-optic Michelson interferometer is constructed to verify the feasibility of the proposed method. The experimental results show that AOIM can be eliminated; moreover, PMD can be calculated and set precisely. The displacement deviation is less than 1.03 nm. The resolution of measurement is considerably lesser than 1 nm and nanoscale accuracy is achieved in displacement measurement.

Look‐up table method for optimising coupling ratio in broadband sequential power amplifiers

This study reappraises the optimum design parameters for the sequential power amplifier (SPA) when taking relative phase difference into account. By including the phase relationship between the main and peaking amplifiers, a modified efficiency formulation is derived that reveals the impacts of the key design parameters on the SPA efficiency at output power back-off. To optimise a wideband high-efficiency SPA design, a look-up table method is used to predict the required coupling ratio for a wideband directional coupler. To validate the design approach, a 1.5–2.4GHz SPA is designed and measured, showing drain efficiency higher than 40% at 6dB back-off across the band. When characterised using a 20MHz long term evolution (LTE) signal and digital predistortion, the SPA shows good linearity with error vector magnitude <1.3%, and adjacent channel leakage ratio levels better than −45 dBc across the band.

A Non-Linear Temperature Compensation Model for Improving the Measurement Accuracy of an Inductive Proximity Sensor and Its Application-Specific Integrated Circuit Implementation.

The non-linear characteristic of a non-contacting Inductive Proximity Sensor (IPS) with the temperature affects the computation accuracy when measuring the target distance in real time. The linear model based method for distance estimation shows a large deviation at a low temperature. Accordingly, this paper presents a non-linear measurement model, which computes the target distance accurately in real time within a wide temperature range from to . By revisiting the temperature effect on the IPS system, this paper considers the non-linear characteristic of the IPS measurement system due to the change of temperature. The proposed model adopts a non-linear polynomial algorithm rather than the simple linear Look-Up Table (LUT) method, which provides more accurate distance estimation compared to the previous work. The introduced model is fabricated in a 0.18 m Complementary Metal Oxide Semiconductor (CMOS) process and packaged in a CQFN40. For the most commonly used sensing distance of 4 mm, the computed distance deviation of the Application-Specific Integrated Circuit (ASIC) chips falls within the range of mm. According to the test results of the ASIC chips, this non-linear temperature compensation model successfully achieves real-time and high-accuracy computation within a wide temperature range with low hardware resource consumption.

High-Linearized and Fast-Convergent RmI Look-up Table Control Method for Space Solar Array Simulator

Space solar array simulator (SSAS) is a key power input device for spacecraft power supply testing. SSASs are also required to simulate the steady-state I-V curve with a high tangent slope of the aerospace solar panel output and to have the dynamic response performance of the fast convergence to switching working point under a spacecraft power supply test environment. This paper proposes a high-linearized and fast-convergent R m I (HLFC-R m I) look-up table control method, which is aimed at solving these problems. This study converts the conventional voltage-current UI data table into the corresponding impedance-current R m I data table without adding any auxiliary hardware circuit. The R m I data table is used as a target form for I-V outer loop control, by using the proposed equivalent impedance R m linearization formula, thereby achieving the simulation of a high tangent slope I-V curve. In the process of looking up table control, the optimized equivalent impedance R m_real-time linearization formula is used to approximate the high-speed convergence characteristics of the UI look-up table method under constant-voltage load switching conditions. The new I-V outer loop control method is applied to a 1 kW hardware power platform of SSAS. The SSAS can not only simulate an arbitrary I-V curve with a high tangent slope but also has the characteristics of high-speed convergence of the switching working point.

A fast and accurate radiative transfer model for aerosol remote sensing

After several decades’ development of retrieval techniques in aerosol remote sensing, no fast and accurate analytical Radiative Transfer Model (RTM) has been developed and applied to create global aerosol products for non-polarimetric instruments such as Ocean and Land Colour Instrument/Sentinel-3 (OLCI/Sentinel-3) and Meteosat Second Generation/Spinning Enhanced Visible and Infrared Imager (MSG/SEVIRI). Global aerosol retrieval algorithms are typically based on a Look-Up–Table (LUT) technique, requiring high-performance computers. The current eXtensible Bremen Aerosol/cloud and surfacE parameters Retrieval (XBAER) algorithm also utilizes the LUT method. In order to have a near-real time retrieval and achieve a quick and accurate “FIRST-LOOK” aerosol product without high-demand of computing resource, we have developed a Fast and Accurate Semi-analytical Model of Atmosphere-surface Reflectance (FASMAR) for aerosol remote sensing. The FASMAR is developed based on a successive order of scattering technique. In FASMAR, the first three orders of scattering are calculated exactly. The contribution of higher orders of scattering is estimated using an extrapolation technique and an additional correction function. The evaluation of FASMAR has been performed by comparing with radiative transfer model SCIATRAN for all typical observation/illumination geometries, surface/aerosol conditions, and wavelengths 412, 550, 670, 870, 1600, 2100 nm used for aerosol remote sensing. The selected observation/illumination conditions are based on the observations from both geostationary satellite (e.g. MSG/SEVIRI) and polar-orbit satellite (e.g. OLCI/Sentinel-3). The percentage error of the top of atmosphere reflectance calculated by FASMAR is within ± 3% for typical polar-orbit/geostationary satellites’ observation/illumination geometries. The accuracy decreases for solar and viewing zenith angles larger than 70∘. However, even in such cases, the error is within the range ± 5%. The evaluation of model performance also shows that FASMAR can be used for all typical surfaces with albedo in the interval [0−1]and aerosol with optical thickness in the range [0.01−1].

High-Precision Soil Moisture Mapping Based on Multi-Model Coupling and Background Knowledge, Over Vegetated Areas Using Chinese GF-3 and GF-1 Satellite Data

This paper proposes a combined approach comprising a set of methods for the high-precision mapping of soil moisture in a study area located in Jiangsu Province of China, based on the Chinese C-band synthetic aperture radar data of GF-3 and high spatial-resolution optical data of GF-1, in situ experimental datasets and background knowledge. The study was conducted in three stages: First, in the process of eliminating the effect of vegetation canopy, an empirical vegetation water content model and a water cloud model with localized parameters were developed to obtain the bare soil backscattering coefficient. Second, four commonly used models (advanced integral equation model (AIEM), look-up table (LUT) method, Oh model, and the Dubois model) were coupled to acquire nine soil moisture retrieval maps and algorithms. Finally, a simple and effective optimal solution method was proposed to select and combine the nine algorithms based on classification strategies devised using three types of background knowledge. A comprehensive evaluation was carried out on each soil moisture map in terms of the root-mean-square-error (RMSE), Pearson correlation coefficient (PCC), mean absolute error (MAE), and mean bias (bias). The results show that for the nine individual algorithms, the estimated model constructed using the AIEM (mv1) was significantly more accurate than those constructed using the other models (RMSE = 0.0321 cm³/cm³, MAE = 0.0260 cm³/cm³, and PCC = 0.9115), followed by the Oh model (m_v5) and LUT inversion method under HH polarization (mv2). Compared with the independent algorithms, the optimal solution methods have significant advantages; the soil moisture map obtained using the classification strategy based on the percentage content of clay was the most satisfactory (RMSE = 0.0271 cm³/cm³, MAE = 0.0225 cm³/cm³, and PCC = 0.9364). This combined method could not only effectively integrate the optical and radar satellite data but also couple a variety of commonly used inversion models, and at the same time, background knowledge was introduced into the optimal solution method. Thus, we provide a new method for the high-precision mapping of soil moisture in areas with a complex underlying surface.

Bipercentile parameter estimators of bias reduction for generalised Pareto clutter model

The generalised Pareto distribution is an efficient model to characterise the high-resolution sea clutter. Robust and precise estimation of the model's parameters is a precondition of effective target detection in sea clutter. It is known that the explicit bipercentile (BiP) estimators are efficient in computation and robust to outliers. In this study, it is proved that the explicit BiP estimators are also consistent with respect to sample size. In practical applications, only limited samples are available and the bias of the BiP estimators degrades the estimation precision. The properties of the biases are analysed and BiP estimators of bias reduction are constructed by the look-up table method. The BiP estimators of bias reduction are verified by simulated data and measured sea clutter data.

Fine Doppler shift acquisition algorithm for BeiDou software receiver by a look-up table

The BeiDou software receiver uses the fast Fourier transform (FFT) to perform the acquisition. The Doppler shift estimation accuracy should be less than 500 Hz to ensure satellite signals to enter a locked state in the tracking loop. Since the frequency step is usually 500 Hz or larger, the Doppler shift estimation accuracy cannot guarantee that satellite signals are brought into a stable tracking state. The straightforward solutions consist in increasing the sampling time and using zero-padding to improve the frequency resolution of the FFT. However, these solutions intensify the complexity and amount of computation. The contradiction between the acquisition accuracy and the computational load leads us to research for a more simple and effective algorithm, which achieves fine acquisition by a look-up table. After coarse acquisition using the parallel frequency acquisition (PFA) algorithm, the proposed algorithm optimizes the Doppler shift estimation through the look-up table method based on the FFT results to improve the acquisition accuracy of the Doppler shift with a minimal additional computing load. When the Doppler shift is within the queryable range of the table, the proposed algorithm can improve the Doppler shift estimation accuracy to 50 Hz for the BeiDou B1I signal.

An ultrafast and high accuracy calculation method for gas radiation characteristics using artificial neural network

In this work, a new approach to efficient gas radiation characteristics calculating is proposed to satisfy the demand for high accuracy and efficient calculation in many applications. This approach establishes a mapping relationship between gas condition parameters and radiation characteristics using a back-propagation neural network (BPNN). The line by line (LBL) model is utilized for the generation of training samples in the BPNN model. The values of pressure, temperature and component concentration are taken as input, and absorption coefficient values are taken as output. A case study of CO2 transmittance at 2250–2350 cm− 1 band is presented. The comparison and analysis of the results indicated that the BPNN model has a high accuracy of LBL fitting and is insensitive to the input. Although the training time of BPNN is long, once the training is completed, the computational efficiency is very high. Compared to the look-up table method or other accelerated methods using parameter pre-calculation, the BPNN method occupies much less storage space. It can replace the LBL model to a certain extent when dealing with the needs of high precision and high-speed computing.

Column Integrated Water Vapor and Aerosol Load Characterization with the New ZEN-R52 Radiometer

The study shows the first results of the column-integrated water vapor retrieved by the new ZEN-R52 radiometer. This new radiometer has been specifically designed to monitor aerosols and atmospheric water vapor with a high degree of autonomy and robustness in order to allow the expansion of the observations of these parameters to remote desert areas from ground-based platforms. The ZEN-R52 device shows substantial improvements compared to the previous ZEN-R41 prototype: a smaller field of view, an increased signal-to-noise ratio, better stray light rejection, and an additional channel (940 nm) for precipitable water vapor (PWV) retrieval. PWV is inferred from the ZEN-R52 Zenith Sky Radiance (ZSR) measurements using a lookup table (LUT) methodology. The improvement of the new ZEN-R52 in terms of ZSR was verified by means of a comparison with the ZEN-R41, and with the Aerosol Robotic Network (AERONET) Cimel CE318 (CE318-AERONET) at Izaña Observatory, a Global Atmosphere Watch (GAW) high mountain station (Tenerife, Canary Islands, Spain), over a 10-month period (August 2017 to June 2018). ZEN-R52 aerosol optical depth (AOD) was extracted by means of the ZEN–AOD–LUT method with an uncertainty of ±0.01 ± 0.13*AOD. ZEN-R52 PWV extracted using a new LUT technique was compared with quasi-simultaneous (±30 s) Fourier Transform Infrared (FTIR) spectrometer measurements as reference. A good agreement was found between the two instruments (PWV means a relative difference of 9.1% and an uncertainty of ±0.089 cm or ±0.036 + 0.061*PWV for PWV &lt;1 cm). This comparison analysis was extended using two PWV datasets from the same CE318 reference instrument at Izaña Observatory: one obtained from AERONET (CE318-AERONET), and another one using a specific calibration of the 940-nm channel performed in this work at Izaña Atmospheric Research Center Observatory (CE318-IARC), which improves the PWV product.

Estimation of Multi-Species Leaf Area Index Based on Chinese GF-1 Satellite Data Using Look-Up Table and Gaussian Process Regression Methods

Leaf area index (LAI) is an important biophysical parameter, which can be effectively applied in the estimation of vegetation growth status. At present, amounts of studies just focused on the LAI estimation of a single plant type, while plant types are usually mixed rather than single distribution. In this study, the suitability of GF-1 data for multi-species LAI estimation was evaluated by using Gaussian process regression (GPR), and a look-up table (LUT) combined with a PROSAIL radiative transfer model. Then, the performance of the LUT and GPR for multi-species LAI estimation was analyzed in term of 15 different band combinations and 10 published vegetation indices (VIs). Lastly, the effect of the different band combinations and published VIs on the accuracy of LAI estimation was discussed. The results indicated that GF-1 data exhibited a good potential for multi-species LAI retrieval. Then, GPR exhibited better performance than that of LUT for multi-species LAI estimation. What is more, modified soil adjusted vegetation index (MSAVI) was selected based on the GPR algorithm for multi-species LAI estimation with a lower root mean squared error (RMSE = 0.6448 m2/m2) compared to other band combinations and VIs. Then, this study can provide guidance for multi-species LAI estimation.

A review of the estimation of downward surface shortwave radiation based on satellite data: Methods, progress and problems

The estimation of downward surface shortwave radiation (DSSR) is important for the Earth’s energy budget and climate change studies. This review was organised from the perspectives of satellite sensors, algorithms and future trends, retrospects and summaries of the satellite-based retrieval methods of DSSR that have been developed over the past 10 years. The shortwave radiation reaching the Earth’s surface is affected by both atmospheric and land surface parameters. In recent years, studies have given detailed considerations to the factors which affect DSSR. It is important to improve the retrieval accuracy of cloud microphysical parameters and aerosols and to reduce the uncertainties caused by complex topographies and high-albedo surfaces (such as snow-covered areas) on DSSR estimation. This review classified DSSR retrieval methods into four categories: empirical, parameterisation, look-up table and machine-learning methods, and evaluated their advantages, disadvantages and accuracy. Further efforts are needed to improve the calculation accuracy of atmospheric parameters such as cloud, haze, water vapor and other land surface parameters such as albedo of complex terrain and bright surface, organically combine machine learning and other methods, use the new-generation geostationary satellite and polar orbit satellite data to produce high-resolution DSSR products, and promote the application of radiation products in hydrological and climate models.

A multi-axis differential optical absorption spectroscopy aerosol profile retrieval algorithm for high-altitude measurements: application to measurements at Schneefernerhaus (UFS), Germany

Abstract. We present a new aerosol extinction profile retrieval algorithm for multi-axis differential optical absorption spectrometer (MAX-DOAS) measurements at high-altitude sites. The algorithm is based on the lookup table method. It is applied to retrieve aerosol extinction profiles from the long-term MAX-DOAS measurements (February 2012 to February 2016) at the Environmental Research Station Schneefernerhaus (UFS), Germany (47.417∘ N, 10.980∘ E), which is located near the summit of Zugspitze at an altitude of 2650 m. The lookup table consists of simulated O4 differential slant column densities (DSCDs) corresponding to numerous possible aerosol extinction profiles. The sensitivities of O4 absorption to several parameters were investigated for the design and parameterization of the lookup table. In the retrieval, simulated O4 DSCDs for each possible profile are derived by interpolating the lookup table to the observation geometries. The cost functions are calculated for each aerosol profile in the lookup table based on the simulated O4 DSCDs, the O4 DSCD observations, and the measurement uncertainties. Valid profiles are selected from all the possible profiles according to the cost function, and the optimal solution is defined as the weighted mean of all the valid profiles. A comprehensive error analysis is performed to better estimate the total uncertainty. Based on the assumption that the lookup table covers all possible profiles under clear-sky conditions, we determined a set of O4 DSCD scaling factors for different elevation angles and wavelengths. The profiles retrieved from synthetic measurement data can reproduce the synthetic profile. The results also show that the retrieval is insensitive to measurement noise, indicating the retrieval is robust and stable. The aerosol optical depths (AODs) retrieved from the long-term measurements were compared to coinciding and co-located sun photometer observations. High correlation coefficients (R) of 0.733 and 0.798 are found for measurements at 360 and 477 nm, respectively. However, especially in summer, the sun photometer AODs are systematically higher than the MAX-DOAS retrievals by a factor of ∼2. The discrepancy might be related to the limited measurement range of the MAX-DOAS and is probably also related to the decreased sensitivity of the MAX-DOAS measurements at higher altitudes. The MAX-DOAS measurements indicate the aerosol extinction decreases with increasing altitude during all seasons, which agrees with the co-located ceilometer measurements. Our results also show maximum AOD and maximum Ångström exponent in summer, which is consistent with observations at an AERONET station located ∼43 km from the UFS.