Circulation pattern control of wet days and dry days in Free State, South Africa


 Atmospheric circulation is a vital process in the transport of heat, moisture, and pollutants around the globe. The variability of rainfall depends to some extent on the mechanisms of atmospheric circulation. This paper uses the concept of classifying the recurrent large-scale atmospheric circulation patterns in southern Africa, and the linkage of the classified patterns to wet days and dry days in Free State, South Africa, for the analysis of how the probability of wet and dry events in Free State can be associated with specific synoptic situations, in addition to the underlying dynamics. Principal component analysis was applied to the T-mode matrix (column/variable is time series and row is grid points at which the field was observed) of daily mean sea level pressure field from 1979 to 2018 in classifying the recurrent circulation patterns in southern Africa. 18 circulation types (CTs) were classified in the study region. From the linkage of the CTs to the observed rainfall data, from 11 stations in Free State, it was found that dominant austral winter and late austral autumn CTs have a higher probability of bringing dry days to Free State. Dominant austral summer and late austral spring CTs were found to have a higher probability of bringing wet days to Free State. Cyclonic/anti-cyclonic activity over the southwest Indian Ocean, explained to a good extent, the inter-seasonal variability of rainfall in Free State. The synoptic state associated with a stronger anti-cyclonic circulation at the western branch of the South Indian Ocean high-pressure, during austral summer, leading to enhanced moisture transport by southeast winds was found to have the highest probability to bring above-average rainfall in most regions in Free State; while the synoptic state associated with enhanced transport of cold dry air, from the Benguela current, by the extratropical westerlies was found to be associated with the highest probability of (winter) dryness in Free State.


Introduction
The forecast ability of surface variables such as rainfall is of core interest in climatology. According to Vicente-Serrano and López- Moreno (2006), the linkage of large-scale circulation patterns to a surface variable explains in physical terms the intensity and spatial distribution of the surface variable. In the regional context of Free State, southern Africa, this paper examines how speci c synoptic situations can be used to forecast the probability of wet and dry events.  (Maraun and Widmann 2018), which involves the correlation of clustered days with a similar spatial pattern, to a largescale atmospheric variable. Linking atmospheric circulation to local surface variables in the Mediterranean region, Maheras and Kolyva-Machera (1990) noted that zonal recurrent circulation patterns are associated with dry periods whereas meridional recurrent circulation patterns are associated with humid periods. This paper uses the concept of obliquely rotated principal component analysis (PCA), on the T-mode matrix of a climatic variable that explains atmospheric circulation (Richman 1981; Martin-Vide et al. 2008), in obtaining the circulation types in southern Africa. For the characterization of how the mechanism of the individual circulation types could predict rainfall in Free State, the concept of moisture ux convergence (Kuo 1965), will be incorporated in the analysis. Several researchers have found that the parameterization of convective rainfall could be well linked to the concept of moisture convergence (Sylla et al. 2011;Loriaux et al. 2017).
The focus of this paper is thus structured as follows: 1. principal component analysis will be used as an eigenvector based classi cation tool to obtain the recurrent circulation patterns in southern Africa.
2. physically motivated correlation between the mechanism of the recurrent patterns and rainfall variability in Free State will be investigated.

Data And Methodology
Classi cation of circulation patterns was achieved with gridded reanalysis mean sea level pressure (SLP) dataset, from the European Center for Medium-Range Weather Forecasts (ECMWF), ERA-Interim (Dee et al. 2011). The original temporal resolution is 6 hourly data, from 1979 to 2018. Daily averages were computed, for the complete analysis period. The horizontal resolution of the ERA-Interim SLP dataset is. The spatial coordinate for the circulation typing is 5.25°E-55.25°E and 6°S-50.25°S. Daily rainfall data from 11 stations in Free State, obtained from http://www.dwa.gov.za/Hydrology/Veri ed/hymain.aspx, for the 1979-2018 period, was used in characterizing the rainfall characteristics of the recurrent patterns in Free State, South Africa (Fig. 1). The dotted red lines in Fig. 1 are the geographical locations of the selected rainfall stations in Free State.
For the classi cation of the recurrent patterns in southern Africa, obliquely rotated principal component analysis (PCA) was applied to the T-mode matrix of daily z-score standardized SLP eld in southern Africa. The decision to represent the matrix in a T-mode structure is based on the nding that obliquely rotated PCA on the T-mode matrix of a eld that explains atmospheric circulation is an optimal classi cation procedure, for the representation of the basic temporal modes of variability associated with a climatic variable that explains atmospheric circulation, in terms of recurrent patterns (Richman 1986;Compagnucci and Richman 2008). Richman and Lamb (1985) noted that rotated PCA on the T-mode eld results in a simpli ed time-series isolating subgroups of observations with a coherent spatial pattern. In the classi cation process, a correlation matrix was used, which yielded correlation coe cients between pairs of daily time observations in the study period, which constituted 14610 observations. Singular value decomposition was used in factorizing the correlation matrix to obtain the eigenvalues and the eigenvectors. The selection of the optimal number of components to retain was based rst, on scree-test (Cattel 1966;Wilks 2006). This was helpful to have an idea of the range of possible optimal number of components to retain for the analysis -based on cutting the component numbers after a relatively small slope is followed by a noticeable drop. The discarded components have typically low and close eigenvalues in line with the recommendation of North et al. (1982) on ensuring the separability of eigenvalues of the retained components. However, since Preisendorfer et al. (1981) noted that a few of the discarded components might contain meaningful information necessary for the research goal; sensitivity analysis was applied for the optimization of the number of components to retain. The sensitivity analysis ensures that the addition of a further component uncovers a new pattern that has not been already delineated by previous vectors; this was statistically approached by ensuring that the congruence coe cient between the new input pattern (i.e. component score) and the already classi ed input patterns is low (Richman 1981). Richman and Lamb (1985) recommended that multiplying the eigenvectors by the square root of their corresponding eigenvalues makes them more responsive to rotation; hence the retained eigenvectors were further loaded with the square root of their corresponding eigenvalues which makes them longer than a unit length henceforth referred to as loadings. To simplify the structure of the eigenvector loadings, they were rotated obliquely using Promax at a power of 2 ((Richman 1986). The oblique rotation maximizes the number of near-zero loadings so that each retained component clusters a unique number of variables that a general in uence can be attributed to (Richman 1981). Also, the decision of using oblique rotation was to ensure that orthogonality constraint does not lead to arti cial physical features in the classi cation (Richman 1981;Wilks 2006). The component scores present the input spatial patterns localized in time by the eigenvector loadings, and loadings (time-steps) that are near zero do not contribute to the PC sores (Compagnucci and Richman 2008). The absolute value of the loadings represent a vital signal, and for a given retained component, further clustering of the component loadings into negative high loadings and positive high loadings using a speci ed threshold will decrease the internal distances among classes so that there is greater similarity between days grouped under a given class (Richman and Gong 1999). Thus each component yields two classes and the SLP composite of the days grouped under a class is the circulation type (CT). Richman and Gong (1999) recommended that threshold values within the range of 0.2-0.35 will be su cient to separate the PCs, here was used. precipitation less than 1mm. In this work, dry days were characterized, as the count of days with rainfall less than 1mm at the complete 11 selected stations.
The rainfall characteristics of each CT, concerning the probability of being associated with dry days and wet days, were calculated using Eq. 1 and 2, respectively.

Study Regions
Southern Africa is located between three oceans -the Southern Ocean, the South Atlantic Ocean, and the South Indian Ocean. The western subtropical regions of Southern Africa are relatively drier than the eastern regions due to the in uence of the cold Benguela current. Rainfall is mostly in austral summer (DJF), except for the southernmost regions of South Africa that are characterized by the Mediterranean climate. The local study region, Free State ( Fig. 1), is a province in South Africa. Its attitude is about 1600m above sea level. The escarpment at the eastern regions of Free State is steeper relative to the western regions. Free State is characterized by hot summers and cold winters; also, rainfall is much common in the summer months.  The anti-cyclonic circulation at the South Indian Ocean high-pressure strengthens southeast winds, and thus enhances moisture advection into southern Africa from the southwest Indian Ocean. Low-level convergence of the moisture from the southwest Indian Ocean advected by easterly winds and the moisture advected from the tropical South Atlantic Ocean (warm pool) by the circulation at the Angola low, create the foundation zone of the SICZ (Cook 2000). Also, moisture convergence in the SICZ can be supported by the moisture advected as a result of the migratory mid-latitude cyclones. According to (Cook 2000) the Agulhas current equally in uences the SICZ through the enhanced evaporation in the region, moreover, rainfall variability in South Africa is also modulated by sea surface temperature (SST) anomalies at the Agulhas current (Walker 1990).

Circulation types in southern Africa
The application of the scree-test for the decision of the optimal number of components to retain, as shown in Fig. 3, suggests retaining 6 to 8 components. However, in line with the ndings of Preisendorfer et al. (1981), the sensitivity analysis led to retaining 9 (optimal) components. Fig. 4 shows the SLP composites (i.e. CTs) classi ed in the study region. Each retained component yields two CTs; hence there is a total number of 18 CTs. Fig. 5 shows the relative monthly frequency of occurrence for each CT in Fig. 4. In as much as it is common for any of the CTs to occur at any time of the year, the CTs can be further classi ed with respect to their dominance in either austral winter/autumn season or austral summer/spring season. CT1, CT6, CT7, CT9, CT11, CT14, and CT16 can be grouped as winter/autumn recurrent patterns, with CT9 and CT11 extending dominance into early austral spring (September/October); generally, they can be analogous to CTs associated with cold seasons. Similarly, CT2, CT3, CT5, CT8, CT10, CT12, CT13, CT15 and CT18 can be grouped as austral summer/spring recurrent patterns; their dominant periods are within the range of October (late austral spring) to February (late austral summer), with CT5, CT2, and CT3 extending dominance into early austral autumn (March/April). The occurrence of CT4 was a bit mixed up; it has a high probability to occur, almost homogenously, at any time of the year. CT17 is speci cally an austral spring dominant pattern. In general, CT2, CT5, CT8, CT10, CT12, CT13, CT15, CT18 can be grouped as warm-season recurrent patterns.
The probability of occurrence of the CTs (Fig. 6) was calculated as the ratio of the number of days clustered under the CT to the total number of days in the study period (i.e. 14610 days). CT1 is the most occurred cold season CT in the study period, followed by CT9. CT5 similarly, is the most occurred warmseason CT, followed by CT8. CT5 is the austral summer climatology of atmospheric circulation in the study region. CT12 and CT18 are relatively rare CTs. CT1 is close to the climatological mean state of SLP eld variability in the study region (Molteni et al. 1990).
The oblique rotation allows inter-correlation between the component scores, and also a day might have high loadings (>0.2) under more than one retained component so that the classi cation procedure allows for the grouping of a day under more than one CT, which logically implies the CTs that reoccurred on the day in question. Since the classi ed data is continuous it is justi ed that more than one day is assigned to a CT. As a result, the sum of the percentages in Fig. 6 does not add up to 100%. Atmospheric circulation is a continuum and this justi es the relaxation of a rigid grouping (e.g. K-means clustering), which allows a day to be classi ed under only one CT. CT1, CT4, CT5, and CT8 were found to relatively have a higher probability to occur; Harr and Elsberry (1995) explained such CTs as nearly constant recurrent patterns that have slowly varying features; the external distances among the classes were satisfactorily large except with aforementioned CTs.

Linkage of wet and dry days in Free State to the circulation types
The probability of dry days and wet days in each CT was calculated using Eq. 1 and 2 respectively. The probability of dry days in each of the 18 CTs can be visualized in Fig. 7. Recall that CT1, CT6, CT7, CT9, CT11, CT14, and CT16 were categorized as cold season CTs. Fig. 7 shows that these recurrent patterns have, relatively, the higher chances of bringing dry days to Free State, when they occur. Generally, the inference is that cold season dominant CTs are associated with a higher possibility of dry days in Free State. According to Reason and Mulenga (1999), the reason is that SST anomalies at the southwest Indian Ocean in uences the inter-seasonal rainfall variability in most regions of South Africa; they linked dry days in South Africa to the cooling of SST at the southwest Indian Ocean -which is a common phenomenon in the cold season CTs. From Fig. 4, for the aforementioned cold season CTs, anti-cyclonic circulation dominates over the southwest Indian Ocean. Anti-cyclonic circulation is normally associated with the less convective activity (Harr and Elsberry 1995). CT6 and CT14 have the highest probability to bring dry days in Free State; Fig. 8 also shows that relatively, there is generally a low possibility of wet days when either of these CTs occurs; supporting the fact they are truly dry synoptic situations in Free State. Fig. 10 shows the SLP eld, moisture ux, and convergence eld during CT6 and CT14. Under CT14 a high-pressure system and associating divergence are evident over Free-state and the Greater Agulhas region, leading to subsidence (rainfall suppression), and reduction of convective activity at the Agulhas current which is a principal source of moisture to South Africa, respectively. Under CT6, the mid-latitude cyclone strengthens and tracks further north so that westerly wind is enhanced in the advection of cold drier to Free State. Hence at the synoptic scale, enhanced dryness in Free State can be attributed to largescale subsidence, suppression of convection at the Greater Agulhas region, and advection of cold dry air by extratropical westerly winds, from the Benguela region.
From Fig. 7, for the warm season CTs, i.e. CT2, CT3, CT5, CT8, CT10, CT12, CT13, CT15, and CT18, the probability of dry days in these CTs are generally less, relative to the cold season CTs. Fig. 8 shows the probability of each CT to bring wet days across all the eleven selected stations. The distribution portrayed by the box-plots also helps in understanding the strength of each CT to bring a homogeneous or heterogeneous number of wet days across the 11 stations (jointly considered). Take for example; the exceptional skewness of CT15 indicates that its mechanism makes it bring (enhanced) rainfall in speci c regions only.
For the eleven selected stations in Free State, Fig. 9 shows the regions under the dominant in uence of a given CT, based on having the highest probability of bringing wet days (Fig. 9a) and the probability of bringing extreme rainfall (Fig. 9b). An extreme rainfall day for each CT was characterized as the count of days with daily rainfall amount greater than the 99 percentile rainfall value, per station. Fig. 8 and Fig. 9 show that CT12 has the highest chances of bringing widespread extreme rainfall to most regions in Free State when it occurs. Southwestern regions in Free State are more likely to be in uenced by the dynamics of CT15. Some regions are under the in uence of CT13. However, the application of the classi cation scheme to other SLP gridded data set (not shown) reproduced all the CTs with the exception of CT13, suggesting that it might be an artifact of ERA-Interim. Hence more focus will be placed on CT15.
From Fig.10, at the synoptic scale, extreme rainfall in most regions in Free State under CT12 can be attributed to the strengthening of the South Indian Ocean high-pressure leading to enhanced advection of moisture by the southeast wind. Also, the offshore movement of the thermal low into the South Atlantic Coast implies moistening of the western subtropical boundary layer, weakening of the South Atlantic Ocean high-pressure, and enhanced convergence in the region, so that more moisture is available to be advected into Free State by westerly winds. On the other hand, CT15 re ects enhanced convergence of moist winds from the Angola warm current and cross-equatorial trade wind into the Angola low. The western branch of the South Indian Ocean high-pressure is equally weakened so that fewer southeast winds penetrate Free State compared to CT12; however, the continental tropical low evident in this synoptic situation, coupled with the enhanced cyclonic activity at the Agulhas region, and the enhanced convergence at the Angola low are generally favourable for the enhancement of deep convection at preferred regions in Free State. In general, extreme rainfall in Free State can be attributed to enhanced transport of moisture by southeast and southwest winds into the local study region; the formation of continental tropical lows at the western regions of southern African, coupled with enhanced cyclonic activity at the Agulhas current.

Conclusions
In this study, the CTs in southern Africa were classi ed and linked to rainfall variability in Free State, South Africa. The CTs associated with the higher probability of bringing wet days and dry days to Free State were noted. The mechanisms, in the light of moisture ux and convergence, through which the selected CTs can in uence the intensity and spatial variability of rainfall across 11 stations in Free State were equally analyzed.
Using obliquely rotated PCA on the T-mode matrix of SLP data set (Richman 1981), 18 CTs were classi ed and each CT was found to be related to the probability of a speci c weather event. CTs dominant in austral summer and austral late spring -when SST is high at the southwest Indian Oceanwere found to be associated with a higher possibility of bringing wet days to Free State; whereas austral winter and austral late autumn dominant CTs -when SST is low at the southwest Indian Ocean -were found to be associated with a higher possibility of bringing dry days to Free State, in line with the nding of Reason and Mulenga (1999) that SST anomalies at the southwest Indian Ocean explain to a good extent the inter-seasonal variability of rainfall in South Africa.
The synoptic situation associated with the highest probability of wet days and extreme wet days in Free State is characterized by stronger circulation at the South Indian Ocean high-pressure leading to the enhanced transport of moisture from the southwest Indian Ocean by southeast winds; it equally features moistening of the Benguela current. According to Lazenby et al. (2016), stronger circulation at the South Indian Ocean high-pressure during austral summer correlates with the strengthening of the SICZ and enhanced rainfall in southern Africa. On the other hand, the occurrence of continental tropical lows and enhanced cyclonic activity at the Agulhas region was equally found to cause enhanced rainfall in some regions in Free State.
Finally, enhanced dry conditions in Free State can be attributed to large-scale subsidence (Dedekind et al. 2016), suppression of convection at the Greater Agulhas region (Reason 2001), and advection of cold dry air from the Benguela region to Free State, by the extratropical westerly wind.       Analysis of the CT with the highest probability of wet days (a) and extreme rainfall days (b) at each of the selected stations Physical mechanism associated with the CTs with the highest probability of wet days and dry days in Free State. Color bar is the composite of the divergence eld for each CT with the unit in 10^6/s ; the green vector is moisture ux in gm/kgs. Vector scale is written on top of the maps