###### Abstract
Early developments of mono-window algorithms were undertaken by [9], also [10] suggests in his review paper a single channel algorithm. Further work was presented by [11; 12]. A more recent overview is given by [1] who address the mono-window algorithms as single-channel methods. The work of [8] complements the overview with an additional statistical mono-window algorithm. All these methods are based on precomputed coefficients and functions, which can vary for different states of the atmosphere. In the literature, numerous split-window algorithms have been published, starting as early as 1970, when first studies were published about the estimation of Sea Surface Temperatures [13]. The studies were based on modelled and on measured data. A good overview is given in [1]. The authors divide the split-window algorithms into linear and non-linear split-window algorithms. Both these algorithms use the information of one of the two brightness temperatures as a general offset, as well as the difference between the two brightness temperatures to express the magnitude of absorption in the atmosphere. All algorithms come with a range of coefficients, which are determined empirically and reflect the influence of the emissivity, the difference of the emissivities of the two bands, the water vapour in the atmosphere and the sensor view angle. As such, expressions have been developed to empirically deduct the coefficients from these variables in a linear or also non-linear way (e.g., [9; 14; 15; 16; 17; 18]). Another way of incorporating the influence of water vapour, the longer atmospheric path determined by the view angle, and also temperature itself to the expression, is to use different sets of coefficients for subranges of each variable. This approach was followed for example by [16; 19], who simulated band brightness temperatures using a radiative transfer model for a variety of atmospheric conditions and a range of sensor view angles. The atmospheric conditions thereby covered given ranges of atmospheric water vapour, and initial guess LST or T\({}_{\text{air}}\) broad enough, to reflect the most possible atmospheric conditions. The coefficients are then derived for subranges of atmospheric water vapour and initial guess LST or T\({}_{\text{air}}\) from the modelled brightness temperatures and the input LST into the radiative transfer runs. As the band brightness temperatures usually are modelled using the sensors spectral response, the resulting coefficients are sensor-specific and cannot be transferred from one to another sensor without loss of accuracy. There have been studies comparing different split-window algorithms ([3; 20; 21; 22]), highlighting the advances and drawbacks of single algorithms and their implementation at that time. As pointed out by [8], the approach of creating sets of coefficients does also apply for mono-window algorithms. Nowadays, the availability of long term time series of medium resolution data of sensors such as AVHRR enables researchers to investigate climate relevant trends in this multi-decadal Earth Observation data. This study therefore investigates the suitability of a variety of selected algorithms to long time series processing in the framework of the TIMELINE project at the Earth Observation Center (EOC) of the German Aerospace Center (DLR). The project aims in creating long and homogeneous time series from AVHRR/1, AVHRR/2 and AVHRR/3 starting in the early 80s. Most of the proposed split-window algorithms have been developed a few years back. This is why the accompanying coefficient sets are usually given only for one or more of the older AVHRR sensors. These coefficient sets might match perfectly to the one AVHRR sensor or to the set of sensors, but fail to give similar accuracies using the coefficients on all available AVHRR data, as each sensor features its unique spectral response curve. As such, the generation of a longer time series with coefficients from literature are prone to larger errors, which might introduce artificial anomalies like sudden steps in the time series.