Diurnal Cycle of Convection over Lake Titicaca Basin based on the Satellite Data from the Climate Prediction Center Morphing (CMORPH)

This paper examines the diurnal cycle of convection (DCC) over Lake Titicaca Basin (LTb) during summertime months based on the high spatial resolution (8 x 8 km2) and hourly temporal resolution, estimates of Climate Prediction Center Morphing technique (CMORPH). Analysis was performed using observed data from rain gauges (Rg-SENAMHI) for the period 2002 to 2013. Graphical comparisons and several statistical metrics such as correlation coefficient, bias, and root mean square error were used to evaluate CMORPH product. Spatial maps and graphic metrics of diurnal cycle were developed to assess CMORPH data, spatial dependency an accuracy over the LTb. Approximately, 43% of the total Rg-SENAMHI variation is explained CMORPH data. The correlation between Rg-SENAMHI and CMORPH is positively over southeast and northern LTb, and negatively in the central and southern LTb. A underestimation bias is observed over most the LTb areas and overestimation bias (e.g., Lagunillas, Isla Suana and Desaguadero stations). In general, spatial patterns of rainfall over the LTb were captured through CMORPH data. Over the surrounding lake area, high mountain, and plateau area, maximum peaks of precipitation occur in the early evening, neverhtheless over low areas such as the lake, surrounding and valleys, maximum precipitation values occur early morning. The results show that DCC its very related by surface exchange processes and local circulation resulting from solar radiation and heterogeneous topography.


Introduction
The precipitation is of great importance in the water cycle. Particulary, understand rainfall spatial-temporal distribution it is going to help a lot in the livelihood of the many Lake Titicaca basin (LTb) communities that predominantly rely on rain fed agriculture [1]. Today, to observe and estimate the amount of surface rain, there are many methods such as rain gauges, satellite sensors and radars. A direct way to measure the rainfall is it through the rain gauges, but the spatial coverage in the LTb is quite deficient and with unequal spatial distribution. In consequence, extrapolation of precipitation leads to inaccuracies in this conditions [2,3].On the other hand, the meteorological radar is an alternative but due to difficult accessibility of the site, the mountain barriers and the financial limitations the installation of radars is not feasible. For these reasons, satellite sensors is a viable option to assess the rainfall in this region [3,7,12,13].
As is known, the LTb topography features and complex land-lake surface processes have influence the spatial-temporal rainfall distribution over this region [28]. During summertime (December-February) approximately 70% of annual rainfall occurs [28,29,30] with a north-south distribution. Varying from 1400 mm in the north-east to 200 mm in the south-west of the basin [28,31]. Inhomogeneous precipitation in this region can easily result in either major droughts [32] or disastrous flooding [33]. Using nine satellite rainfall estimations [12], found a stronger gradient from north to south and weaker from east to west gradient for the present study region. To our area of interest, exist four published works on the performance of satellite rainfall estimations [12,13,34,35], most of the previous studies focused on the evaluation at the annual, monthly and daily time steps showing high accuracy in dry and relatively flat regions [12,36]. However, there are not studies related to the behavior of the diurnal cycle at the hourly level based in satellite estimates in this region. Studies conducted in other regions of the world shows the ability of CMORPH (Climate prediction centre MORPHing) [37,38] in represent the diurnal cycle of precipitation at the hourly temporal resolution [5,10,14,[39][40][41][42][43][44] and good performance in mountainous regions [6,11,12,14,41,44]. Our study analyses the diurnal cycle of convection over Lake Titicaca basin from on high spatio-temporal resolution data from CMORPH for the period from 2002 to 2013. The document is organized as follows: in sections 2 and 3, we presented methods and data used in this study. In section 4, we comparated between CMORPH and observerd data and discuss the results taking into account terrain complex and lake influenced the diurnal cycle of covection. The conclusions are presented in section 5.

Study area
Titicaca Lake is located quite high in the Andes (15°45'56''S and 69°31'34''W), in a geographical area of high plateau morphology, with maximum altitude about 6500 m asl, the total area of the lake is close to 8,400.00 km 2 and storing a volume of 932 km 3 (~3810 m asl). It is surrounded by the eastern and western ranges in the Andes, and the drainage is part of a great fluvial system (TDPS), integrated with the basins Poopó, Coipasa, and Uyuni, all of which have acommon collector in Lake Titicaca [45]. The ratio between the basin area and lake surface is nearly 7:1. The maximum depth of Late Titicaca is 280 m and, its average depth ranges from 140 m to 180 m . Titicaca is known as the largest and highest navigatin lake in South America, with a few commercial boats running from southeastern to northwestern parts of the lake, between cities of Puno (Peru) and to the direction of La Paz city (Bolivia). The tributaries rivers to Lake Titicaca contribute between 201 m 3 s -1 to 270 m 3 s -1 of the total annual flow and, its main contribution is mostly from rainfall of convective origin on the lake. Desaguadero River during its course receives water from several tributaries has a mean annual flow of 89 m 3 s -1 and continues its trajectory to the south until reaching Lake Poopó [46]. The lake is supplied by rainfall (47%) and river water (35%), mainly by the river Ramis and loses water by evaporation (91%) and at the control point in the Desaguadero River (9%), the average annual temperature in the lake basin fluctuates between 7 and 10 ° C [47]. We are mainly interested in the area between 14-18°S and 69-71°W with has an average elevation of 4000 m ( Fig. 1)

Data set
The rain gauges data sets and satellite used for this study are presented in Table 1, they include rainfall gauge data sets derived from the National Meteorological and Hydrological Service of Peru (Rg-SENAMHI) and CMORPH respectively. We used the period between 2002 and 2013 to do the analysis.

1. Gauge precipitation data
The dataset used is result DECADE project (Data on climate and Extreme weather for the Central AnDEs), based in [48] and includes daily precipitation (mm), maximum and minimum temperature (°C ) measurements, data that previously received statistical control. A total of 34 conventional weather stations and two automatic weather stations were available for this study (Fig.  1). We selected 34 stations with available daily precipitation data (period 2002-2013) of Rg-SENAMHI. Figure 2 shows the monthly precipitation values at the stations located in the Lake Titicaca basin. Annual precipitation average to long-term varies range to 530 mm year -1 and 980 mm year -1 for the period analysed 2002 to 2013. Almost 82% rainfall annual occurs between November and March months.

2. CMORPH
CMORPH is a precipitation dataset analyses technique described by [35] that uses microwave observation data from several satellites combined with geostationary infrared data, and developed by NOAA's that provides high spatial-temporal resolution (8-km in the equatorial zone and 30-minute) this will allow in-depth understand the diurnal cycle of convection in LTb.

Methods
Spatial-temporal CMORPH rainfall estimation is will be linked to the Rg-SENAMHI rainfall observed as follows: In the firts way (point-to-grid comparison) CMORPH and Rg-SENAMHI dataset are compared within the satellite grid box. This first test establishes that locally observerd are compared with Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 23 February 2020 doi:10.20944/preprints202002.0333.v1 5 CMORPH satellite data. CMORPH data are extracted using the coordinates location of the rain gauges.
In the second way (areal comparison) CMORPH rainfall estimation is compared with the interpolated Rg-SENAMHI rainfall stations. The Rg-SENAMHI rainfall observations are interpolated adopting method [49] and compared with the respective CMORPH rainfall estimation for LTb.

Statistical measures
To compare the point observed Rg-SENAMHI with CMORPH data were used following statistical indices: the linear correlation coefficient (CORR), root mean square error (RMSE) ratio, and bias.
The coefficient of determination ( ) was adopted as a main evaluation index to evaluate quantitatively the degrre of correlation between the observed and estimated precipitaton and, is a mesuare of the degree of association between two variables.; see Eq. (1).
Where is Rg-SENAMHI measurements, is the coefficient of determination, is CMORPH satellite estimated values, and is number of items analyzed.
Bias is a measure tendency of how CMORPH rainfall magnitude compares Rg-SENAMHI rainfall and know if over-or under-estimated. This measure establishes the ratio of the mean CMORPH rainfall estimated value to mean Rg-SENAMHI observed value; see Eq. (2). wher is the rainfall value from Rg-SENAMHI and is the rainfall value from the CMORPH.
RMSE measures residuals (prediction errors) between Rg-SENAMHI and CMORPH data, and through the standard deviation calculates a weighted average error. The lower the RMSE score, the closer the CMORPH represents the Rg-SENAMHI measurements; see Eq. (3).
where is the rainfall value from Rg-SENAMHI, is rainfall value obtained from the CMORPH, and is the total data pairs analysed.

Analysis of diurnal cycle of convection
To better understand the dayli rainfall distribution in LTb. Concept of phase will be defined and thus study the characteristics of the diurnal cycle of convection during austral summer precipitation. The period of time during which the peaks of precipitation appear, due to fluctuations in global radiation, it know as diurnal cycle phase. These events are evident, usually low latitudes, in areas where solar forcing its reached maximum values. In addition, in subtropical and polar regions is influenced by topography and frontal systems, just as it is influenced during austral winter and summer. CMORPH precipitation estimate rates is in UTC (Coordinated Universal Time) and were converted for the LTS (Local Solar Time).
To better analyze CMORPH, averages were made and accumulated for the austral summer of the period from 2002 to 2013, plotting graphs and analyzing the time of occurrence of the convective events and the peak hours of precipitation along the diurnal cycle.
Seven sub-regions were selected using criteria of similarity in the seasonal rainfall regime to better understand and explain the DCC in the LTb, due to the complexity of the study area which includes islands, mountains, basins, Peruvian altiplano and the lake Titicaca. These seven sub-regions are presented in Figure 1; four of them are in the continent and three over the lake. Maps of precipitation estimates were generated for 24 hours (at a time level), to observe the diurnal cycle of precipitation for the rainy season.

Comparison point-to-grid
The CMORPH rainfall estimates were accumulate in annual and monthly time intervals. Rg-SENAMHI data and CMORPH values extracted for the 34 stations are represented for the three standard statistical tecnhiques (Fig. 3a-c). Figure 3a shows an strong and weak correlations between CMORPH and Rg-SENAMHI. For CMORPH, the 2 ranges from a minimum value of -0.39 (Lagunillas-LS ws) to a maximum of 0.75 (Chuquibambilla-CH ws). Approximately 43% total Rg-SENAMHI variation is explained CMORPH data. In figure 4, we show the relationships of CMORPH with Rg-SENAMHI in the LTb. Over southeast and northern LTb, time series of CMORPH they are positively correlated with Rg-SENAMHI data, and negatively correlated in the central and southern of LTb. For some regions (e.g., Lagunillas), the correlation coefficients were statistically insignificant .  The bias calculated (Fig. 3b) for CMORPH and Rg-SENAMHI ranges from 0.28 to 0.86. The CMORPH underestimated Rg-SENAMHI observed data; approximately, underestimate values was 60%. CMORPH overestimate 3 stations (Lagunillas-LS, Isla Suana-IA and Desaguadero-DO, marked in green circles in Fig. 5b). This stations registered average values of 150 mm of rainfall during dry season months (June, July and August), that increased the annual cumulative average (Fig. 5a). The RMSE shown in Fig. 3c present similar trends as in Fig. 3a. The RMSE shows high values (150.5 mm month -1 , 200.2 mm month -1 and 249.1 mm month -1 ) for Lagunillas-LS, Isla Suana-IA and Desaguadero-DO stations, respectively, and a RMSE below average (95 mm month -1 ) for others stations.  9 other hand, 23 weather station (blue circles shows in figure 5b) probably affected by a combination rains fo convective and orographic origin. In consequence, stations probably affected by both orographic and convective rainfall will have a higher bias than the stations probably affected by convective precipitation only. These results agree with the findings of [50] where, 16 stations registered a higher bias, concluding that, stations located in mountain hillslope would be affected because of orographic lifting of moist air that generate rainfall, while the other stations located in the plain would be affected by convective rainfall.

Areal comparison
To make a more realistic comparison, areal Rg-SENAMHI is compared with the areal CMORPH for the LTb, through the methodology of linear multiple regression, where topography variable has been included in rainfall spatial distribution (Fig. 6a-d). Initially average annual accumulated rate of precipitation was compared. Precipitation rates distribuitions shown in figure 5a-b (period 2002-2013), derived from CMORPH and Rg-SENAMHI, respectively. CMORPH stations with values recorded in dry season shows precipitation maxima over three regions: the south, western and southwestern of LTb (Fig. 6a).
We can see that both the extend and magnitude of maximum rainfall from Rg-SENAMHI data exist mainly over Titicaca Lake (Fig. 6b). Note that over Lake Titicaca basin precipitation characteristics is non-uniform well, this is likely due to the influence of both convective and orographic precipitation, showing notable accordance with major precipitation patterns exist in these regions due to presence over Andean slopes. During the summers (December, January and February) of 2002-2013 the distributions of mean precipitation rates derived from CMORPH and Rg-SENAMHI indicate decreases from the northwest to the southeast (Fig. 6c) and from the north to the south (Fig.6d). CMORPH high temporal-spatial resolution shows Foehn effect existence over northeastern region of LTb (Fig. 6c), this was corroborated with observed data of the stations located on Chaupi Orco hillslope (Fig. 6d). Masses of moist air transporte by SALLJ (South American Low-Level jet east of the Andes), fall as precipitation on the hillslope due to mountain presence (cf. Figure 3a in Garreaud et al 2003 [28]). In this region Andean slopes acts as a natural barrier restricting the entry of moisture from Amazon basin, and consequence, there is water vapor deficiency on the other side (leeward) . These results were also obtained by Zhang et. al [51], who used satellite data from CMORPH and TRMM on the South and East Asia region. Precipitation pattern over LTb, obtained with Rg-SENAMHI data, was entire represented form CMORPH data. The southeastern and northeastern regions, precipitation patterns, were well respresented.
The areal bias computed ( Fig. 7a-b), which represents the difference between CMORPH and Rg-SENMAHI, presented a high underestimation percentage of annual cumulative average rainfall (300% on average), while that for summer precipitation the areal bias underestimates by an average of 78%. The bias for CMORPH both for the annual cycle of precipitation and austra summer is not constant; it overestimates for Lagunillas by 930% and underestimates for Isla Soto by 700% (Fig. 7a). The summer precipitation bias map (Fig. 7b) indicated that the CMORPH consistently underestimates the Rg-SENAMHI; for Isla Soto and Lagunillas by 156 and 38 %, respectively.

Diurnal cycle of convection using CMORPH data
We examine the characteristics of the summer precipitation diurnal cycle in detail using the high resolution CMORPH data. Spatial distribution of DCC intensity (Fig. 8a-v) and phase of wet period rainfall (December -February) over the Titicaca Lake and its peripheral areas (period 2002 -2013), derived from CMORPH estimates. As shown in Fig. 8, over continental areas, the precipitation peaks in the afternoon. Over the surrounding lake area, high mountain, and plateau area, maximum peaks of precipitation occur in the early evening, neverhtheless over low areas such as the lake, Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 23 February 2020 doi:10.20944/preprints202002.0333.v1 surrounding and valleys, maximum precipitation values occur early morning. This is due to the Altiplano region receive greater amounts radiation during the day [52,53,54], and heterogeneous tropography play a decisive role in the convective rainfall dynamics, generating moist convection and maximum low level atmospheric instability that manifests through maximum values (peaks) of precipitation in the afternoon. The predominant southeast LTb winds propagate the thermal convection activities to northwest LTb, leading to a precipitation maximum during 16:00-17:00 LST over the surrounding terrain northwest Titicaca Lake (Fig. 8m). Over the Titicaca Lake, precipitation peaks generally occurs between midnight and sunrise. The maximum precipitation usually occurs during 04:00-06:00 LTS (Fig. 8d), especially over northwest Titicaca Lake. WRF model results were compared rather favorably with observations in the SALLJEX simulations [55], that showed that the regions of preferred convergence and vertical motion are consistent with distribution pattern derived from CMORPH data. Both results are consequent with studies cited to in Section 1.
During nighttime (Fig. 8a,s,v), there is internal gravity waves propagation, due to radiative cooling over complex orography causing drainage flows, which can produce low-level convergence over the lake. With the air coming from the continent to the lake, of terrestrial breeze front is formed with upward motion on the lake. In some cases it is possible to observe clouds formation and precipitation cores estimates. Figure 9 shows DCC average for seven selected regions in the Lake Titicaca basin (See Fig. 1 for the locations on a map) derived from CMORPH. Region 1 -Puno; Reg. 2 -Santa Rosa; Reg. 3 -Crucero; Reg. 4 -Cabanillas; Reg. 5 -Isla Suana; Reg. 6 -Arapa; and Reg. 7 -Isla Soto. In particular, in the regions 3, 5 and 7 we observed an obvious semi diurnal cycle. On the other hand, in the 1,2,4 and 6 regions, the diurnal cycle of convection is similar and the peaks occur in the afternoon period which is consistent with the previos results [5,42]. When we compared figure 9a with figure 10 (observed data) the results suggests that CMORPH can represented the diurnal phase of convective rainfall. The time of maximum peak is about 1-2 h earlier that Rg-SENAMHI-puno. It is around 18:00 LST.
This results suggests that, the main pattern of the diurnal cycle of convection is consistent with previous studies [5,14,42,43]. On the other hand, the high resolution of the CMORPH data used here, show more significant regional differences when compared to previous studies, such as a less coherent phase pattern over certain regions (Reg. 3, 5 and 7). This results suggest that, DCC main pattern is regulated by surface exchange processes over heteogeneous topography, valley breezes Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 23 February 2020 doi:10.20944/preprints202002.0333.v1 12 and slope who play a important role on convective and orographyc processes near to the mountains [56][57][58]. The diurnal cycle configuration over Titicaca lake and its surroundings can may result by local circulation influenced for the surface energy balance (SEB) and the complex terrain. The slope mountain effects on the available radiant energy [53,54,57,58], orographic moisture blockage over the LTb, and the corresponding local advection processes impact the DCC. In this matter, regional water vapor conditions from Titicaca lake and other factors could affect the regional characteristics of DCC. Understand how this mechanism influence the DCC over the surrounding terrain remains to be further investigated.

Conclusions
Currently, the accuracy of rainfall estimates is very import for the expansion and maintenance of the agricultural frontier, water security of LTb communities, and to reduce natural desasters directly related to droughts and floods [1,34,56,59]. In this study, our objective was to evaluate CMORPH rainfall estimates over Lake Titicaca basin. The river Desaguadero is the main beneficiary with the waters collected by this basin. The evaluation is carried out on several time scales (annual, seasonal and hourly) and with resolution (8 x 8 km 2 ) for the period between January 2002 and December 2013 obtained from CMORPH, and the evaluation was carred out based on 34 rain gauges distributed in our study area. To examine CMORPH data accuracy, graphic techniques and statistical measures were used. When interpreting rain maps generated with surface station data, special care was taken in the regions that have few or no rain gauges , especially over Southwestern LTb. The main conclusions will be made based on the results presented as follows: 1. CMORPH estimates exhibit remarkable agreement with regard precipitation patterns observed with Rg-SENAMHI, and achieved to capture daily rainfall frequency better that rainfall amounts over the LTb. Maximum precipitation peaks can be appreciated in two well-marked regions: Over Titicaca Lake and surrounding terrain. It should be noted that, both extend and magnitude of maximum precipitation form CMORPH data underestimate Rg-SENAMHI precipitation data. On the other hand, CMORPH precipitation estimates underestimate in most LTb regions, except in some regions (e.g., Lagunillas, Isla Suana and Desaguaderos stations) were rainfall is overestimated.
2. Rainfall distribution over our interest area shown regional differences that are seen in the convective diurnal cycles. Over low regions such as the valleys (near to lake) and Titicac lake, it maximum peaks rainfall around midnight and ends to early morning. The results show that DCC its very related by surface exchange processes and local circulation resulting from solar radiation and heterogeneous topography.
3. The bias underestimation is observed over most the LTb areas and overerestimation (e.g., Lagunillas, Isla Suana and Desaguadero stations). The total bias increases/decreases near mountais and attaining maximum value when approaching to lake respectively [4,5]. In addition, high spatial and temporal resolution CMORPH data can captured regional details (e.g., Isla Suana) which show a less coherent phase pattern that the others stations.