Detection of the cloud liquid water path horizontal inhomogeneity in a coastline area by means of ground-based microwave observations: feasibility study

The improvement of cloud modelling for global and regional climate and weather studies requires comprehensive information on many cloud parameters. This information is delivered by remote observations of clouds from ground-based and space-borne platforms using different methods and processing algorithms. Cloud liquid water path (LWP) is one of the 10 main obtained quantities. Previously, the measurements of LWP by the SEVIRI and AVHRR satellite instruments provided the evidences of the systematic differences between LWP values over land and water areas in Northern Europe. An attempt is made to detect such differences by means of ground-based microwave observations performed near the coastline of the Gulf of Finland in the vicinity of St.Petersburg, Russia. The microwave radiometer RPG-HATPRO located 2.5 km from the coastline is functioning in the angular scanning mode and is probing the air portions over land (at elevation angle 90°) and 15 over water area (at 7 elevation angles in the range 4.8°-30°). The problem of the LWP horizontal gradient detection is examined in the measurement domain: the brightness temperatures of the microwave radiation measured at different elevation angles in the 31.4 GHz and 22.24 GHz spectral channels are analysed and compared with the corresponding values which were calculated under the assumption of horizontal homogeneity of the atmosphere. Several specific cases, selected on the basis of the analysis of the satellite observations by the SEVIRI instrument were considered in detail including: clear20 sky conditions, the presence of clouds over the radiometer and at the same time the absence of clouds over the Gulf of Finland, and overcast conditions over the radiometer and over the opposite shore of the Gulf of Finland. The influence of the land-sea LWP difference on the brightness temperature values in the 31.4 GHz spectral channel has been demonstrated and the following features have been detected: (1) an interfering systematic signal is present in the 31.4 GHz channel which can attributed to the humidity horizontal gradient; (2) clouds over the opposite shore of the Gulf of Finland mask the LWP 25 gradient effect. Preliminary results of the retrieval of LWP over water by statistical regression method are presented. These monthly averaged results are compared to the corresponding values derived from the satellite observations by the SEVIRI instrument. The agreement between satellite and ground-based results is very good for warm season in terms of temporal behaviour if systematic difference is neglected. https://doi.org/10.5194/amt-2020-52 Preprint. Discussion started: 27 February 2020 c © Author(s) 2020. CC BY 4.0 License.

InfraRed Imager) and AVHRR (Advanced Very High Resolution Radiometer). The description of the information products delivered by these instruments and relevant to cloud properties can be found in the papers by Stengel et al. (2014Stengel et al. ( , 2017. Previously, the measurements of LWP by the satellite instruments SEVIRI and AVHRR provided the evidences of the differences between LWP values over land and water areas in Northern Europe. The data from the AVHRR instrument were used for compiling regional cloud climatology for the Scandinavian region (Karlsson, 2003). Analysis of this 65 climatology has shown that during spring and summer the cloud amount over land in this region is larger than the cloud amount over the Baltic Sea and major lakes. Karlsson (2003) explained this phenomenon by the stabilization of near-surface layer of the troposphere over water bodies due to air cooling by the cold fresh water from melting snow. This explanation is in a good agreement with the fact revealed later in the study by Kostsov et al. (2018b): the land-sea gradient of the mean LWP values detected by the SEVIRI instrument in the vicinity of St.Petersburg (Russia) for the cold season was noticeably 70 lower than for the warm season. St.Petersburg is located at the estuary of the Neva River which flows in the Gulf of Finland.
The magnitude of the land-sea difference for mean LWP values obtained by SEVIRI in this area for the two-year period of 2013-2014 was about 0.040 kg m -2 , which was about 50 % relative to the mean value over land.
In general, the investigation of cloud properties in the coastal zones is an interesting and important task due to presence of specific atmospheric processes, for example sea breezes, which are able to generate clouds. The climatological 75 study of the impact of sea breezes on cloud types was done by Azorin-Molina et al. (2008) for the area in the southeast of the Iberian Peninsula (province of Alicante, Spain) and for the 6-year period (2000)(2001)(2002)(2003)(2004)(2005) based on cloud observations at synoptic station. The authors of mentioned study emphasize that their findings are site-specific and should be similar to other coastal locations, however, cloud formation associated with sea breezes is also influenced by geographical-physical, meteorological, hydrological and oceanic factors. Therefore there is a need for further research. The sea breeze effects were 80 studied also on the basis of data derived from space-borne observations by AVHRR instrument .
The satellite instruments working in visible and near-infrared ranges are very sensitive to the observational conditions. There are specific requirements to SEVIRI observations: measurements are restricted just after sunrise and before sunset when the solar zenith angle (SZA) is too large. Therefore, all SEVIRI measurements when SZA was greater than 72° were excluded from consideration in the studies by Roebeling et al. (2008) and Kostsov et al. (2018b). As a result, in the 85 latter study devoted to the LWP measurements at high latitudes (60°N) no measurements during winter months December and January could be selected for analysis, and the number of measurements selected in February and suitable for analysis was very small. Besides, the problem of the misinterpretation of measurements in winter over the snow-covered and icecovered surfaces with high reflectance should be mentioned (Musial, 2014;Kostsov et al., 2019). So, the considered satellite observations are impossible in the night time, in winter at Northern latitudes, and there may be problems in winter in the day 90 time over the snow-and ice-covered surfaces. Therefore, in the present study an attempt was made to find a kind of a supplement to satellite measurements in a coastal area in the form of detection of the land-sea LWP gradients by means of https://doi.org/10.5194/amt-2020-52 Preprint. Discussion started: 27 February 2020 c Author(s) 2020. CC BY 4.0 License.
ground-based microwave observations. The concept of these measurements is straightforward: a radiometer which is located close to a coastline can probe the air portions over land and water surface if it works in the angular scanning mode at appropriate direction. Microwave measurements can be carried out during all seasons, day and night, excluding rain and 95 strong snowfall conditions. Ground-based MW measurements characterise only the local scale LWP distributions in the close vicinity of the observational point, and this is their disadvantage if compared to satellite measurements. However they can provide the important information on the diurnal cycle of LWP over land and water surface with high temporal resolution, and also they can be used for validation of satellite data on LWP obtained for the coastline area near the groundbased validation point. The RPG-HATPRO microwave radiometer, which is functioning at the observational site of the 100 Faculty of Physics, St.Petersburg State University (Russia), perfectly suits the requirements to the experiment aimed at the LWP gradient detection. It is located at a distance of 2.5 km from the coastline of the Gulf of Finland and performs angular scanning towards the Gulf of Finland every 20 minutes while doing routine observations. The idea to use ground-based microwave radiometers in the angular (elevation and azimuth) scanning mode for detecting horizontal gradients and for plotting maps of atmospheric parameters is not new. The 22-channel radiometer 105 MICCY (Microwave Radiometer for Cloud Carthography) with high temporal (1 s) and spatial (antenna beam 1°) resolution and scanning possibilities in horizontal (0-360°) and vertical (0-90°) planes was designed for mapping clouds (Crewell et al., 2001). It should be noted that this radiometer is transportable and can be used for mobile measurements. Another instrument is a 10-channel ASMUWARA, the All-Sky MUlti WAvelength Radiometer. It is a system designed for tropospheric monitoring and it is able to observe the sky in all directions with an angular resolution of 9° (Martin et al., 2006a). 110 Retrieving maps of integrated water vapour and liquid water is one of the purposes of this instrument. The examples of these maps can be found at http://www.iapmw.unibe.ch/research/projects/ASMUWARA/online/, last access: 15 May, 2019. A description of the LWP retrieval algorithm, LWP sky maps and corresponding photographs of the sky are presented in the article by Martin et al. (2006b). A short overview of angular scanning observations of cloud liquid water by ground-based MW radiometers can be found in the article by Westwater et al. (2004). Also, the tomographic approach to the retrieval of 115 LWP should be mentioned which is based on MW observations in angular scanning mode from moving platforms -airborne and ground-based. This approach was first proposed in the 1980s. Huang et al. (2010) demonstrated the feasibility of tomographically retrieving the spatial structure of cloud liquid water using current microwave radiometric technology and provided several general guidelines to improve future field-based studies of cloud tomography.
It should be mentioned that microwave radiometers are capable to provide the information on the spatial 120 inhomogeneity not only of LWP but also of air humidity. Schween et al. (2011) have shown the potential of a single fullscanning MW radiometer RPG-HATPRO for detecting horizontal water-vapour variability. They demonstrated that applying a simple linear-gradient model together with an assumed vertical profile derived from the closest radiosonde ascent, the strength and direction of the horizontal-humidity gradient can be determined with a temporal resolution about 15-20 min. https://doi.org/10.5194/amt-2020-52 Preprint. Discussion started: 27 February 2020 c Author(s) 2020. CC BY 4.0 License. Meunier et al. (2015) performed simulated experiments for retrieving two-dimensional water vapor fields using a 125 tomographic approach and multiple ground-based MW radiometers. The goal of the mentioned study was to investigate how the various aspects of the instrument setup (number and spacing of elevation angles and of instruments, number of frequencies, etc.) affected the quality of the retrieved field. Stahli et al. (2011) have proposed an imaging method for both water vapour and liquid clouds which used ground-based observations by the SPIRA ground-based MW radiometer operating at 91 GHz by continuously scanning the sky over a range of elevation angles in a fixed azimuth direction. Marke et 130 al. (2020) studied the influence of a heterogeneous land surface on the spatial distribution of atmospheric water vapor: they used ground-based remote sensing measurements of integrated water vapour (IWV) by a microwave radiometer HATPRO during clear sky conditions at 30° elevation angle (full azimuth scans with 10° step).
While the above mentioned studies considered the general problem of LWP mapping by means of MW observations, the present study deals with the specific task: to assess feasibility of detecting LWP horizontal gradients in the coastline area. 135 We emphasize that the retrieval of LWP over land and water surface in the vicinity of the radiometer and the analysis of an error budget is not the primary goal of our study. In order to get insight into typical qualitative features of the LWP land-sea gradient in the vicinity of the radiometer and to identify the main problems relevant to quantitative analysis of measurements and to the solution of the inverse problem of the LWP retrieval over water area using MW angular scans, we start the investigations by focusing the research on the measurement domain. We examine the results of brightness temperature 140 measurements in several spectral channels of the radiometer and at several elevation angles in order to identify the evidences of the land-sea LWP gradient just in the measured quantity, i.e. MW radiation. The analysis is done for different seasons. To our opinion, such an approach, while being relatively simple, is an efficient way to highlight the main points which require thorough investigation. Nevertheless, we also present some preliminary results of the LWP retrievals over water surface.
2 Description of the instrument, measurement geometry and data processing algorithm 145 The 14-channel RPG-HATPRO radiometer (Radiometer Physics GmbH -Humidity And Temperature PROfiler, https://www.radiometer-physics.de/; last access 30 May 2019) is mounted on the top of the metal tower on the roof of the building of the Institute of Physics, St.Petersburg State University, 59.88107°N, 29.82597°E, 56 m a.s.l. The integration time of an instantaneous measurement of atmospheric signal is 1 s. The sampling interval depends on operation mode. In the zenith viewing mode, which is the main observational mode, the sampling interval is about 1-2 s. Every 20 min zenith 150 measurements are interrupted and the angular scanning is done in the North-East direction with the azimuth of 24.7°.
Seven spectral channels located in the 0.5 cm oxygen absorption band (51.26, 52.28, 53.86, 54.94, 56.66, 57.30, 58.00 GHz) provide the information on atmospheric temperature profile, and seven channels located in the centre and the wing of the 1.35 cm water vapour line (22.24, 23.04, 23.84, 25.44, 26.24, 27.84, 31.40 GHz) provide the information on atmospheric humidity profile and cloud liquid water path. Zenith measurements are processed by the multi-parameter retrieval algorithm based on the optimal estimation method (Kostsov, 2015). Previously, the results of LWP retrievals were validated and the error analysis was made (Kostsov et al., 2018a). Zenith and angular measurements in combination are also processed by the built-in quadratic regression retrieval algorithm developed by the instrument manufacturer. Both optimal estimation and regression algorithm independently provide the vertical profiles of temperature, absolute and relative humidity, integrated water vapour, and the cloud liquid water path. It is important to emphasize that the angular scans are 160 used only for temperature retrievals in order to improve the results at the boundary layer altitudes. This is a common procedure for radiometers of this type. The "temperature channels" are optically thick and, as a result, the angular measurements are not affected by horizontal inhomogeneities of atmospheric parameters.
The location of the radiometer with respect to the coastline of the Gulf of Finland (the river Neva bay) is shown in The set of elevation angles of the line of sight of the microwave measurements is the following: 90°, 30°, 19.2°, 14.4°, 11.4°, 8.4°, 6.6°, and 4.8°. The viewing geometry in the vertical plane is shown in Fig. 2. The radiometer is remotely 170 probing the air portions over land at elevation angle 90° and over water areas at 7 elevation angles in the range 4.8°-30°. Different spectral channels have different response to the spatial distributions of temperature, humidity and cloud liquid water. The channels in the water vapour line and oxygen band (at 22-28 and 51-58 GHz) are mainly influenced by humidity and temperature distributions while the channel in the so-called "transparency window" (31.40 GHz) provides the information on LWP. In order to demonstrate that the "LWP channel" is transparent enough in the entire atmospheric region 175 of interest, we calculated optical depth for this channel along lines of sight corresponding to different elevation angles. The results are plotted in Fig. 3 as a 2D-map. In order to model maximal absorption, as an input for the calculations we took the profiles of temperature and humidity which are typical for warm and humid days in July in St.Petersburg region. The integrated water vapour was 31 kg m -2 . The LWP of the modelled cloud was equal to 0.4 kg m -2 which is the maximal value for non-rainy clouds. Overcast conditions were modelled; the cloud base and top were selected at 1 km and 2 km 180 correspondingly. One can see that even for this extreme case the optical depth at 31.4 GHz does not exceed 1.8 for the smallest elevation angle at a horizontal distance of 28 km from the radiometer which is the opposite shore of the Gulf of Finland and about 10 km inland. At the opposite coastline which is 18 km from the radiometer, the optical depth reaches a value of about 1 in its maximum. The obtained results lead to the important conclusion: clouds in the layer 2-4 km over the opposite shore of the Gulf of Finland at about 20 km from the radiometer are detectable at small elevation angles (4.8° -185 8.4°). In case such clouds are present, the detection of LWP land-sea gradient for clouds in the lower layers will become rather complicated task. https://doi.org/10.5194/amt-2020-52 Preprint. Discussion started: 27 February 2020 c Author(s) 2020. CC BY 4.0 License.
The measured atmospheric microwave radiation is registered as a set of brightness temperature values T b corresponding to observations at spectral channels with central frequencies  and elevation angles  and will be designated as T bm . Brightness temperature values which are calculated for any given set of atmospheric parameters will be designated 190 below as T bc . Data processing was done according to the algorithm which is shown in Fig. 4. The set of T bm is the basic input to the processing and analysis but zenith and angular observations are treated separately. Zenith observations at all 14 spectral channels are processed by the multi-parameter retrieval algorithm based on the optimal estimation approach. The obtained profiles of atmospheric parameters are then used for calculation of brightness temperature values corresponding to elevation angles of angular scans under the assumption of horizontal homogeneity of the atmosphere. At the next step these 195 calculated values are compared to corresponding measured values. The difference between measured and calculated brightness temperatures is taken as a main quantity for analysis: This quantity can be considered as a sum of several terms: where D grad is the brightness temperature difference which is directly caused by the difference between LWP of a cloud above the radiometer and LWP of a cloud observed at the elevation angle . For simplicity, this term will be referred below as the LWP gradient signal. D Tq is the brightness temperature difference caused by the horizontal inhomogeneity of temperature and humidity. The term D err is the interfering signal stipulated by errors and uncertainties of different kind. First, we point at the errors in retrieved profiles of atmospheric parameters which are used for calculation of T bc under the 205 assumption of horizontal homogeneity. The contribution of these errors to D err needs more detailed explanation. In order to make this explanation more evident, let us consider the example case with a humidity profile error. Let us imagine the situation when the error (the difference between the true and the retrieved humidity profile) is positive in the lower layers of the troposphere and we know the true profile. If we calculate T bc for zenith direction using the true and the retrieved profile the difference between the obtained T bc values will be small and comparable to the random error of microwave 210 measurements and the T bc value will be very close to T bm value. However, if we calculate T bc for small elevation angles using the "erroneous" profile and compare it to the corresponding T bm value, this difference can be noticeably higher due to the considerable increase of optical path through the layers where the retrieved profile has errors. In our example case, the result would be the overestimation of T bm by T bc . Here, one important note should be made: the retrieval errors for profiles have random and systematic components (the latter is caused mainly by a priori information used for retrievals). As a result, the 215 term D err might consist of both components also. The pointing error (elevation angle error) can be another source of D err , which is important for small elevation angles. Also, for small elevation angles, the surface emission interference can take place through side lobes of the antenna pattern. When considering small elevation angles, one should keep in mind the uncertainty of refraction calculations stipulated by the uncertainty in the vertical and horizontal distribution of atmospheric humidity.
In order to give an impression of the origin of the LWP gradient signal, in Fig. 5a we present a simplified schematic picture of the MW radiation transfer from the atmosphere to an instrument which makes an observation at some elevation angle. We consider two cases: a cloudy atmosphere and a cloud-free atmosphere (temperature and humidity are assumed to be the same). In the cloudy case, the radiation from cold upper atmospheric layers is considerably absorbed by a cloud, at the same time a cloud itself is a strong emitter of a radiation. As a result, an instrument registers the radiation which is formed 225 mainly in warm atmospheric layers within and below a cloud. In the clear sky case an instrument can "see" upper tropospheric layers which are cold and less dense than the lower layers. Hence in a clear sky case the measured brightness temperature is lower than it is in a cloudy case. This reasoning is valid also in case when clouds over a radiometer and over a water body have different LWP: the lower LWP is, the weaker the emission by cloud and absorption of downwelling radiation are. So the measured brightness temperature for clouds with low LWP will be smaller than for clouds with high 230 LWP.
For characterisation of a magnitude of the LWP gradient signal D grad we present Fig. 5b where we modelled the atmospheric situation with the LWP land-sea difference. According to LWP measurements by the SEVIRI instrument in 2013-2014 in the vicinity of St.Petersburg, the mean LWP over the HATPRO radiometer site was 0.080 kg m -2 , and the mean LWP over the river Neva bay was 0.040 kg m -2 (Kostsov et al., 2018b). We modelled 2D radiative transfer for ground-235 based measurements using these values and disposing clouds within 1-2 km and 3-4 km altitude layers. The artificial cloud with LWP=0.080 kg m -2 was placed over the radiometer location and the artificial cloud with LWP=0.040 kg m -2 was placed over the entire water area and over the opposite shore of the Gulf of Finland. Annual mean profiles of pressure, temperature and humidity for St.Petersburg region were taken as a necessary input for calculations and and the assumption of horizontal homogeneity of these parameters was used. Fig. 5b shows that, as expected, the 31.4 GHz channel has the largest LWP 240 gradient signal which reaches 14-16 K for the smallest elevation angle. The signals in the 22.24 GHz and 51.26 GHz channels, which are shown for comparison, do not exceed 6 K. The signal at 51.26 GHz is nearly zero for smallest elevation angle because of its high opacity if compared to other considered channels. For 31.4 GHz and 22.24 GHz channels, the signal is higher when the cloud is located within 3-4 km layer than in case of lower cloud, but this difference is not large There is an emerging question: to what extent the signal relevant to horizontal inhomogeneity of LWP D grad interferes with signals D Tq and D err . In order to obtain the most realistic assessment of the magnitude of the latter signals we decided to analyse the results of angular scans which have been made during several cloud-free days, instead of compiling computer models of inhomogeneous temperature and humidity fields suitable for the considered experiment. The obtained estimates are presented in the next section. 250

Case study
In order to perform a kind of "testing and calibration" of the algorithm for detection of horizontal gradient of LWP, we analysed measurements which were made during different atmospheric situations. These situations were selected on the basis of space-borne measurements of LWP in the vicinity of St.Petersburg by the SEVIRI instrument which had been analysed earlier in the article by Kostsov et al. (2018b). In order to study the parallax effect of the space-borne measurements, 255 Kostsov et al. (2018b) compared the results of LWP measurements made by SEVIRI for two ground pixels: the one which is the nearest to the position of the HATPRO radiometer and the other which is the neighbouring pixel but located over the Gulf of Finland just to the North of the radiometer. Measurements during four days were analysed (6 May 2013, 6 June 2013, 5 October 2014 and 11 October 2014) when large differences between LWP over land and sea were detected. In the present study, the consideration of only two mentioned pixels is not sufficient. When the atmosphere is observed by the 260 radiometer at small elevation angles, the air portions over the opposite shore of the Gulf of Finland will make a contribution to measured radiance. Therefore, the distributions of clouds in pixels 241 and 219 (as shown in Fig. 1) should be taken into account as well as in pixels 243 (the radiometer location) and 242 (the Gulf of Finland). Analysing the SEVIRI LWP data in four pixels, we tried to find the following long lasting atmospheric situations: A) LWP is equal to zero in all four pixels; a cloud-free atmosphere is everywhere. This situation is best for assessing the 265 D Tq and D err terms in the expression (2). B) A cloud-free atmosphere is in all pixels except one at the radiometer location. This situation is best for assessing the D grad term in the expression (2) during the most favourable observational conditions (without background signal formed by the clouds over the opposite shore of the Gulf of Finland). C) A cloud-free atmosphere over water area and clouds over both shores of the Gulf of Finland. This is the worst case for 270 detection of the land-sea LWP gradient since the effect can be masked by the background emission from clouds over the opposite shore.
In Fig. 6 the LWP values detected by SEVIRI in four measurement pixels are displayed as a function of time for the date 25 August 2013 (warm and humid season). Accordingly, the values of brightness temperature difference D TB for the set of elevation angles are plotted in the form of 2D time charts for two spectral channels. The colour scale contains 3 parts. The 275 pure yellow part corresponds to the brightness temperature difference in the interval [-1 K; 1 K]. An appearance of yellow colour in a 2D plot means that the difference between measurement and model calculation is negligibly small for corresponding combination time/elevation angle. The red hue describes positive values of D TB , the blue hue describes negative values. Fig. 6 refers to a cloud-free atmospheric situation as detected by SEVIRI instrument: the LWP values are all equal to zero except for pixel 219 after 267.7 fractional day, however those values are less than 0.008 kg m -2 and can be 280 considered as negligibly small. Here and below we use the UTC for time scales and fractional days. The day count starts on negative and its absolute value increases. The map has only one specific signature: at about 267.2 fractional day the absolute value of negative D TB is the largest reaching 14 K and 26 K for 31 GHZ and 22 GHz channels correspondingly. In general, 285 the brightness temperature difference for the 22 GHz channel is noticeably larger than for the 31 GHz channel. The reason for that is the larger optical thickness of the 22 GHz channel and higher sensitivity of this channel to water vapour variations. Let us consider the most interesting case which is described by Fig. 9. This is the case with heavy cloudiness (LWP is reaching 0.3 kg m -2 ) over both shores of the Gulf of Finland and clear conditions over water area (25 July 2013). We stress, 310 that we have the information on the spatial distribution of clouds only from the SEVIRI observations. Unfortunately, the ground-based measurements for 25 July 2013 are available starting only from 236.34 fractional day, nevertheless the observational period is long enough for analysis. First, we point at the large amplitude of the brightness temperature difference: from -18 K to 24 K. The reason for that is the presence of clouds with high LWP. Second, we point at the mixture of positive and negative D TB values for 31 GHz channel within the time period 236.34-236.6 fractional day. As it was already noted, the ground-based measurements are very local, instantaneous and not averaged. Therefore, if the cloud distribution is fragmented, the disposition of separate clouds over the radiometer, over water area and over the opposite shore of the Gulf of Finland may be considered to a certain extent random. This fact manifests itself as a mixture of positive and negative D TB . As a result, the LWP land-sea gradient, which obviously existed during the considered day according to SEVIRI observations, is completely masked due to presence of cloudiness over the opposite shore of the Gulf of Finland. 320 Starting from 236.6 fractional day, clouds disappeared everywhere and for this period the D TB 2D map is more homogeneous. Similar to cloud-free situations during warm and humid season described by Figs. 6 and 8, the D TB values are predominantly negative for this period and the absolute difference of brightness temperatures is larger for small elevation angles. Concluding this section, we can formulate the following statements: 1) As predicted, the LWP land-sea gradient (higher LWP over land, lower LWP over water) shows up as positive values of 335 the difference between modelled and measured brightness temperatures of the MW radiation. These positive values can be detected in the whole considered range of elevation angles (4.8°-30°).
2) The effect of LWP land-sea gradient can be masked by the signal from clouds over the opposite shore of the Gulf of Finland.
3) There is a systematic negative component of the brightness temperature difference D TB which is clearly revealed under 340 cloud-free conditions and can reach in the warm and humid season 20K by its absolute value at small elevation angles. are not very pronounced.

Statistical characteristics: seasonal features 350
The main idea of this statistical analysis is to compare the monthly mean values of two quantities: D LWP and D TB . Here, D LWP is the difference between LWP obtained by SEVIRI in pixels 243 (land, radiometer location) and 242 (sea, Gulf of Finland) and this quantity in our study is the reference measure of the LWP land-sea gradient. D TB is the brightness temperature difference in the 31.4 GHz channel which has been defined in section 2 and contains the component reflecting the LWP land-sea gradient. In order to minimise the influence of the interfering systematic negative component of D TB attributed to 355 the humidity horizontal gradient, in statistical analysis we consider only the elevation angles larger than 10°. The other advantage of this limitation is the missing of most clouds over the opposite shore of the Gulf of Finland, over second small water area (Sestroretsky Razliv) and the land at about 28 km distance, because the atmospheric layers below approximately 4 km are not scanned. For the sake of correct comparison of the ground-based and space-borne measurements we omitted all HATPRO and SEVIRI measurements made for solar zenith angle (SZA) larger than 72° since the retrieval errors of the LWP 360 measurements by SEVIRI strongly increase for the large SZA. The SEVIRI and HATPRO data sets used for calculations of monthly mean values contained all available high quality measurements. The elements of these data sets were not synchronised, which means for example that when HATPRO did not produce the data because of rain or snow, the SEVIRI data set might have had no gaps. It should be reiterated that both water vapour and cloud liquid water affect the brightness temperature values which are registered in the so-called "humidity channels" (22 -31 GHz, K-band). When we analyse Fig. 11, we keep in mind the interfering influence of atmospheric humidity on the values of D TB . In order to perform a separation of variables in our problem, we need to abandon the analysis of the quantities in the measurement domain (brightness temperatures) and to start the analysis in the domain of sought parameters which in our case are LWP and IWV (integrated water vapour). The 385 simplest and commonly used method to solve the inverse problem of the LWP and IWV retrieval from microwave observations in the K-band of microwave spectra is the application of regression algorithms -linear or quadratic. Both algorithms have advantages and disadvantages; therefore we decided to apply both of them and to compare the results. The regression formulae for the LWP value are as follows: where Eq. (3) refers to linear regression, Eq. (4) refers to quadratic regression; n identifies the elevation angle of observations, in our case n=0,…,7 (zero refers to zenith viewing); a and b are the regression coefficients, index k identifies the spectral channel, L is the total number of spectral channels which are considered in the regression scheme; T is the brightness temperature. In the present study, we used for retrievals only two of seven spectral channels in the K-band: 395 22.24 GHz and 31.40 GHz, so L=2 in Eqs. (3) and (4).
Since we treat measurements at each elevation angle separately, the regression algorithm can be trained using the ensemble of atmospheric states based on simple model of the horizontally homogeneous atmosphere. The only one requirement to this ensemble is the sufficiently wide range of atmospheric parameters which are included in a dataset.
Obviously, if we solved the problem of detecting horizontal gradients without knowing their nature at all, we would 400 definitely use the horizontally homogeneous model. It should be noted that in our specific case the attempt could be made to train the algorithm using the statistical ensemble which contains more sophisticated model with proper geometry of land/water surfaces, randomly generated separate clouds, assigned LWP gradient, and then we could expect higher accuracy of training. However such investigations are beyond the scope of the present study. Below we describe the process of training in detail. 405 Training of the regression algorithms was performed separately for each of the considered seasons and years. At the first step, for every single measurement which was performed within the selected time period, the set of retrieved profiles of atmospheric parameters was used for calculation of brightness temperature values T c (,) under the approximation of https://doi.org/10.5194/amt-2020-52 Preprint. Discussion started: 27 February 2020 c Author(s) 2020. CC BY 4.0 License. horizontally homogeneous atmosphere. Thus, the complete training dataset included the retrieved values of LWP during the selected season of the selected year and the corresponding calculated brightness temperatures in two spectral channels and at 410 eight elevation angles. This training dataset was used for derivation of the regression coefficients. As a result, for each of the regression algorithms (linear or quadratic) of the LWP retrieval we had at our disposal 32 sets of regression coefficients: 4 seasonal periods (2013WH, 2014WH, 2013CD, 2014CD)  8 elevation angles. In order to estimate the bias of the regression algorithms and to eliminate it, we need the reference LWP values. As the reference, we used LWP derived from zenith measurements by the multiparameter retrieval algorithm based on the inversion of the radiative transfer equation. 415 These values were compared with the values of LWP obtained by regression algorithm which was applied to the same zenith measurements. This comparison helped to assess the bias of the regression algorithm. We assumed that the bias for all elevation angles was equal to the bias for zenith observations, so we could correct all regression formulae. Table 1  After applying the regression algorithms to the brightness temperature values measured at different elevation angles we could estimate the land-sea LWP difference as obtained from ground-based MW observations using the formula: This plot is organised similar to Fig. 11, but contains only one vertical axis (D LWP ). The results obtained by linear and quadratic algorithms appeared to be very similar, so we present the results of the linear algorithm only. 435 Prior to analysis of Fig. 12, several preliminary remarks should be made. First of all, if we compare the mean LWP values in Table 1 obtained from ground-based and satellite observations over land, we can notice that for the warm season there is a large positive bias of SEVIRI data. We can attribute this bias to the possible influence of rainy clouds on statistics.
In order to exclude these possible rainy conditions from the satellite data we removed all LWP greater than 0.4 kg m -2 from the SEVIRI dataset before plotting Fig. 12. The second remark concerns possible influence of the clouds over the opposite shore of the Gulf of Finland on the results of the estimation of the land-sea LWP difference from ground-based observations.
In order to make a proper comparison of ground-based and satellite data for such a situation, we have calculated the land-sea LWP difference from the SEVIRI data using three different formulae: Eq. 6 corresponds to pure land-sea LWP gradient which is estimated as the difference between LWP for the land and sea pixels. Eq. 7 models the situation when the HATPRO instrument is probing air portions over sea and over the opposite coastline of the Gulf of Finland for medium elevation angles. The "sea value" of LWP in this case is combined from the equal contributions by pixels 242 (sea) and 241 (opposite coastline are). And Eq. 8 is intended for modelling the HATPRO 450 observations at small elevation angles. In this case there can be an additional contribution from clouds inland relatively far from the opposite coastline, i.e. over pixel 219. Again, as for the previous case, the contributions of pixels to the "sea value" of LWP are equal.
Taking into account the remarks made above, we can analyse Fig. 12. First of all, we pay attention to the fact that after removing the LWP values greater than 0.4 kg m -2 from the SEVIRI datasets the D LWP derived from satellite 455 observations became much smaller than shown in Fig. 11 for the complete datasets. However the temporal behaviour remains the same as in Fig. 11 for all seasons if we look at D S1 . If we look at D S2 and D S3 we can notice the increase of values from February to March 2013 instead of decrease as shown in Fig. 11. The agreement between satellite and groundbased results is very good for warm season if we compare temporal behaviour only. Analysing the values we see that there are only positive ones for SEVIRI while the differences for HATPRO can be positive and negative as well. So even after 460 applying the regression method the negative differences for HATPRO corresponding to the abnormal LWP gradient still remain. This fact should be discussed. In our case we consider the satellite data on the LWP gradient as the reference due to complexity of the problem of detecting LWP gradient from the ground-based observations. So we can say that the HATPRO results are negatively biased with respect to the SEVIRI results for both warm seasons of 2013 and 2014 by about 0.015 kg m -2 . Our first guess was that the reason for that was the systematic component in signal which we attributed to the 465 humidity gradient. If it were so, after applying the regression algorithm to the measurements in two channels one of which is sensitive mainly to humidity variations, we could expect compensation of the effect. However it did not happen in our case. Therefore the conclusion can be made that the origin of the systematic component is more complicated. This problem is discussed in Section 5.
For cold seasons, the situation is not as clear as for warm seasons. The satellite and the ground-based results are very possible to notice and to estimate any kind of bias for cold seasons. Considering all seasons and years and comparing Fig. 11 and Fig. 12, there is not so much improvement from the regression method, for the CD season results are actually worse than before (considering the temporal behaviour). In this respect it should be noted that the possible reason for that is the very small number of satellite measurements during cold season, so the comparison can not be very reliable. 475

Data sampling
Data sampling issue seems to be of primary importance for the solution of the problem of detecting the land-sea LWP gradient. In our case, the angular scan is performed every 20 min. This time interval is very large for cloud studies. Rose et al. (2005) has noted that the integration time (or sampling interval) should not be greater than 20 s in order to register the 480 short-period variations of tropospheric humidity and cloud liquid water. Kostsov et al. (2016) have estimated the optimal value of sampling interval of ground-based microwave observations by HATPRO using the information approach: the values of the information volume calculated for measurement sequences with different sampling intervals have been compared. The integration time was always the same and equal to 1 s, the lower sampling rates were obtained by sparsely sampling the data.
The sampling interval that corresponded to the maximum of the information volume was considered as optimal. Kostsov et 485 al. (2016) have made the conclusion that even for stable atmospheric situation the sampling interval should not be greater than 100-200 s. In this case maximum information could be extracted form MW measurements.
For detection of land surface induced atmospheric water vapor patterns, Marke et al. (2020) used passive MW measurements by the HATPRO radiometer in zenith direction and in azimuth scanning mode at the elevation angle of 30°.
The interval between scans varied from 10 to 30 min. This interval is similar to the interval in our study. However, it should 490 be specially noted that Marke et al. (2020) investigated only clear sky cases without any considerable advection.
Taking into account the above mentioned findings relevant to the sampling interval studies we can conclude that the shortest possible sampling interval would be the best solution. The clouds are a highly variable atmospheric object. The problem of detection of the LWP gradient can be considered as an estimation of a small difference of two large quantities.
These quantities are the LWP values over land surface and water body. The solution of the problem requires simultaneous 495 and frequent measurements of these quantities which are variable in space and time. Obviously, the problem can not be solved without averaging of measurements over specific time periods. The long averaging periods and the short sampling intervals are preferable for obtaining accurate estimates of the LWP gradient. The value of 10 s for sampling interval seems to be the optimal trade-off: the short-period variations can be registered keeping the amount of data not very large. However, the angular scanning procedure itself consumes some time: for HATPRO, one angular scan takes 4.5 min. Thus, several 500 practical suggestions can be made, for example: https://doi.org/10.5194/amt-2020-52 Preprint. Discussion started: 27 February 2020 c Author(s) 2020. CC BY 4.0 License.
-to implement scan-by-scan observational mode with small number of elevation angles in order to increase the sampling rate, in this case the sampling interval could be shortened to 1-2 min; -to alternate 20 min period of zenith observations with 20 min period of observations at one selected elevation angle and to use the sampling rate of 10 s within these periods. 505 These suggestions could be helpful also with respect to the problem of comparison of the ground-based and satellite data.
Such a comparison requires time averaging of the ground-based data. Different studies recommend different time periods and weighting functions for averaging. Our experience (Kostsov et al., 2018b(Kostsov et al., , 2019 has shown that the period of 20 min is a good choice for comparisons with the data delivered by satellite instruments SEVIRI and AVHRR.

Orientation of the instrument 510
It has been shown by the case study (see section 3) that clouds over the opposite shore of the Gulf of Finland can play an interfering role and mask the effect of the LWP land-sea gradient in angular observations. Fig. 2 demonstrates geometrically that clouds located over the opposite shore in the altitude layer 2-4 km can be detected by observations at three smallest elevation angles. The lake Sestroretsky Razliv located not far from the opposite coastline is a small water body (see Fig. 1).
Therefore one can not expect strong influence of this water body on cloud properties, and the entire area within 18-28 km 515 distance along horizontal projection of the line of sight can be assumed as "land".
If we look at both Figures 1 and 2 we can come to the conclusion that the optimal orientation of the horizontal projection of the line of sight could be strictly to the North. In this case the line of site would pass the long distance (up to about 30 km) over the Gulf of Finland which is the main water body in our research. The interfering influence of clouds over the opposite shore of the Gulf of Finland would be minimized. At the same time the line of sight would not pass over the 520 island Kotlin which can be a source of heat as a land surface and as an urban area (the city of Kronstadt occupies part of the island territory). However it should be noted that the HATPRO instrument operating at St.Petersburg University is firmly attached to the metal tower and has no appliance for rotation azimuthally, so changing its orientation requires special actions.

Data processing algorithm
In the present study we considered only one algorithm of the derivation of LWP from microwave observations which was 525 based on regression relationships linking measured brightness temperature values and LWP. The regression algorithm (linear or quadratic) is widely used for processing the microwave observation data. Simplicity and computational efficiency are its main advantages. The other algorithm is called "physical" or "physical-iterative" and it is based on the inversion of the radiative transfer equation, usually by optimal estimation method (Rodgers, 2000). The detailed analysis of the applicability of both algorithms and of their combination to the problem of derivation of LWP and integrated water vapour (IWV) from 530 two-channel microwave observations was done by Turner et al. (2007). In general, the superiority of the physical algorithm over regression algorithm originates from the fact that this method accounts for the spatial distribution of all parameters which influence the radiative transfer in the considered spectral channels. In particular, the information about temperature in cloud layers helps to reduce the LWP retrieval errors. The applicability of the physical method to the problem of the LWP and IWV retrieval by two-channel radiometers implies that the a priori profiles of pressure, temperature and humidity are 535 available from external data sources and the cloud liquid water profile is assigned in a model form. In the process of solving the inverse problem by the physical method, cloud liquid water and humidity profiles are modified in one way or another to deliver minimum to the residual between measured and simulated brightness temperatures. For multi-channel radiometers, all mentioned profiles, including temperature and pressure ones can be derived from microwave observations simultaneously. Also, the microwave measurements can be combined with other measurement data and constraints. Such 540 approach is called IPT (integrated profiling technique) or general approach to solution of multi-parameter inverse problems (Loehnert et al., 2008;Kostsov, 2015ab).
Since the physical approach is more accurate than the regression approach its application to the considered problem of the detection of LWP land-sea gradient seems to be a promising direction of a further research. One should keep in mind that measurements at different elevation angles are treated separately due to horizontal inhomogeneity of atmospheric 545 parameters. Therefore the considered inverse problem in its general formulation through the radiative transfer equation will be the classical strongly underdetermined ill-posed problem which will require a system of constraints.

Systematic component of signal
Last but not least we discuss the systematic component which was detected in measured brightness temperature. First of all, we note that when azimuth scans at different elevation angles are performed the directional dependent interference can be 550 present in measured signal. For example, Marke et al. (2020) registered such interference in the unprotected 26.24 GHz channel at four specific azimuth directions. Corresponding measurements were filtered out and missing values were filled with linear interpolation. In our case, we can not determine whether the systematic component is directionally dependent or not, since there is no possibility to perform azimuthal scanning (the radiometer is firmly attached to the stand and has no appliance for the azimuthal rotation). In Section 3 we have made the statement that so far we do not have enough 555 information for accurate identification of the origin of the negative component of brightness temperature in the water vapour channel and the LWP channel of the radiometer. However, there is a high probability that this component reflects the horizontal gradient of the air absolute humidity. If this hypothesis is accepted, then we have to explain the origin of high absolute humidity over the Gulf of Finland and/or over the territory located between the radiometer and the Gulf of Finland.
High content of water vapour over the water body can be explained either by the evaporation or by the advection of humid 560 air. Considering the problem of the quantification of evaporation from lakes Finch and Calver (2008) note, in particular, that:  There are a number of factors that can affect the evaporation rates; first of all, one can mention the climate and physiography of the water body and its surroundings. Also the stored heat can be transported within the water body itself and into and out of it.  Seasonal variations in the evaporation rate depend on the heat storage capacity of the water body which is greatly 565 determined by its depth.  Seasonal variations of the evaporation rate are not necessarily synchronised with seasonal variations of the net solar radiation; as the water depth increases, the maximum evaporation can be observed within the period from one to four months after the summer solstice.  The significant factor influencing the evaporation rate is the heat which is transferred into a water body by inflows and 570 outflows. The variety of inflows includes seepage from groundwater bodies, changes in bank storage, rivers flowing into the water body and land surface run off. Enumerating outflows, one can mention rivers, controlled withdrawals (reservoirs) and leakage to groundwater.
The Neva bay, the part of the Gulf of Finland over which the line of sight of the radiometer passes, is very shallow, its depth does not exceed several meters. The Neva bay is separated from the main part of the Gulf of Finland by the dam. Therefore, 575 to a first approximation, the Neva bay may be considered as a big lake with the Neva River as the major inflow. The exchange of water between the Neva bay and the main part of the Gulf of Finland goes on through several special passages in the dam. Taking into account all factors presented above, one can suggest that investigation of the seasonal behaviour of the systematic component would be reasonable action in order to attribute it to the evaporation from the Neva bay.
The land surface territory between the radiometer and the nearest coastline of the Gulf of Finland can be also a source 580 of evaporation. This territory is covered by the forest (park). In the study by Marke et al. (2020) devoted to land surface induced atmospheric water vapor patterns, it has been shown that less water vapour seems to be present at elevated deciduous forest. In our case the forest is not elevated, however one can not expect a pattern of extra humidity over the forest.
The systematic component of the brightness temperature can be caused not only by high absolute humidity along the 585 line of sight but also by the larger air temperature than expected under the approximation of the temperature horizontal homogeneity. The measured signal is affected by air temperature directly through the emission of radiation and indirectly through the temperature dependence of the absorption by water vapour and liquid water. The line of sight at elevation angles other than 90° passes in its horizontal projection about 150 m over the roof of the building of the Institute of Physics which can be a kind of heat source, especially during sunny days when the roof is warmed up. In addition, there should be an air 590 temperature gradient over the coastline itself. These factors can also contribute to systematic component of signal.

Measurement geometry and data quality control
When the HATPRO measurements in the zenith direction are processed routinely, the data quality control procedure includes several steps. The first step is filtering out the data obtained during rain events (as detected by the rain sensor) and during a certain period after a rain event. The duration of this period is taken equal to 4 hours as recommended in the special 595 study (Kostsov et al., 2018a). At the next step the convergence of the iterative process of the inversion of the radiative transfer equation is analysed. The convergence limit is set to 12 iterations. All data corresponding to unconverged processes are filtered out. It should be noted that normally the number of iterations before successful convergence varies from 5 to 9.
The last check refers to the analysis of the residual between measured brightness temperature values and the corresponding values calculated on the basis of the retrieved atmospheric parameters. In case the RMS residual exceeds 1 K, the results are 600 considered erroneous. This 3-step procedure helps to keep only the good quality data.
Measurement geometry which is used and analysed in the present study is based on angular scanning. Such geometry gives the possibility to probe remotely the air portions which are located very far from the radiometer in the horizontal direction. In this case a situation may occur when the line of sight passes through a rain event (a shower) while there is no rain at the radiometer location and the rain sensor detects no rain. When the regression algorithm is used for the LWP 605 retrieval, it is difficult to ensure the sufficient data quality control. However, the application of the physical method (already discussed in section 5.3) would allow implementing the described above second and third steps of quality control procedure similar to the case with zenith observations. There is another aspect relevant to the measurement geometry which should be mentioned. The solution of the problem of the detection of the LWP land-sea gradient implies the combination of zenith and angular microwave 610 observations. While zenith observations deliver the absolutely local "spot" data over the radiometer (the horizontal dimension is determined by the beam width), the data obtained at angular observations may be considered as averaged over a certain horizontal distance. For small elevation angles this distance can reach dozen of kilometres. If we take into account the high temporal and spatial variability of clouds, the direct comparison of the results of zenith and angular observations made during one scan can be erroneous. Probably, more rigorous way of comparison would require temporal averaging of 615 the results of zenith observations over a certain period of time as it is done, for example, when ground-based measurements of LWP are compared to the satellite data. The satellite data are spatially averaged over a ground pixel area and in order to perform proper comparison the ground-based data are time averaged over a period approximately equal to a time of an air parcel movement at a given wind speed through a ground pixel of a satellite measurement. For the problem which is considered in the present study, one could suggest performing zenith measurements with high sampling rate and the 620 subsequent averaging of them just before making an angular scan. https://doi.org/10.5194/amt-2020-52 Preprint. Discussion started: 27 February 2020 c Author(s) 2020. CC BY 4.0 License.

Summary and conclusions
Previously, the measurements of the cloud liquid water path (LWP) by the SEVIRI and AVHRR satellite instruments provided the evidences of the systematic differences between LWP values over land and water areas in Northern Europe. In the present study an attempt is made to detect such differences by means of ground-based microwave observations 625 performed near the coastline of the Gulf of Finland in the vicinity of St.Petersburg, Russia. The microwave radiometer RPG-HATPRO located 2.5 km from the coastline is functioning in the angular scanning mode and is probing the air portions over land (at elevation angle 90°) and over water area (at 7 elevation angles in the range 4.8°-30°). The data obtained within The main conclusion of the study is the following: the approach to detection of the land-sea LWP gradient from microwave measurements by the HATPRO radiometer operating at the observational site of St.Petersburg State University 655 has been successfully tested and the results confirmed the presence of the horizontal land-sea LWP gradient in the vicinity of the radiometer. It has been shown that further research is needed in order to increase the accuracy of the applied method. The study has identified several problems: sparse data sampling in angular scanning mode, not optimal azimuthal orientation of the instrument, the necessity to improve the data processing algorithm and the need to find the origin of the systematic component in signal measured in angular scanning mode. 660

Data availability
The LWP data derived from the RPG-HATPRO observations at the measurement site of Saint Petersburg State University are available upon request (please write to Vladimir Kostsov at v.kostsov@spbu.ru). The LWP data derived from the SEVIRI observations are available at https://www.cmsaf.eu, last access: 15 May 2019 (EUMETSAT CM SAF, 2019).