1. Introduction
Rainfall in continental regions can be strongly affected by features of the land surface [e.g., Charney (1975)]. Vegetation has been found to modify precipitation in both large-scale and mesoscale modeling studies [e.g., Dirmeyer and Shukla (1996); Chang and Wetzel (1991)]. This modification is due to the coupling of the planetary boundary layer (PBL) with the land cover type through characteristic surface fluxes of heat, moisture, and momentum. In semiarid climates, soil moisture availability controls evaporation and evapotranspiration rates. Through these transfers, antecedent rainfall modifies the PBL. This may affect subsequent precipitation via both dynamical effects, and changes in stability of the lower atmosphere to moist convection. Under appropriate conditions, a feedback on precipitation is possible.
Positive feedbacks between soil moisture and rainfall have been widely studied at the continental scale. Observed rainfall anomalies have been linked to unseasonal soil moisture and antecedent rainfall conditions (Brubaker et al. 1993; Brubaker and Entekhabi 1996; Lare and Nicholson 1994; Findell and Eltahir 1997). Numerical modeling studies illustrate the influence of large-scale evaporation on precipitation [e.g., Walker and Rowntree (1977); Oglesby and Erickson (1989); Rowell and Blondin (1990); Beljaars et al. (1996)]. At the mesoscale, gradients in soil moisture may generate spatial variability in the PBL, producing favored areas for convection (Anthes 1984; Lanicci et al. 1987). Additionally, extreme surface variability induces mesoscale flows in the PBL. These can produce the local convergence required for the development of convection (Sun and Ogura 1979; Chen and Avissar 1994). At spatial scales of a few kilometers however, advection and turbulence effectively mix out surface-induced variability in the PBL [e.g., Raupach and Finnigan (1995)].
The recent Hydrological–Atmospheric Pilot Experiment in the Sahel [HAPEX–Sahel (Goutorbe et al. 1994)] was designed to further our understanding of the links between the land surface and atmosphere in the semiarid climate of southwest Niger. A variety of surface, atmospheric, and remotely sensed measurements were taken during an intensive observation period (IOP) at the end of the 1992 wet season and the beginning of the dry-down. Rainfall was monitored by a high-resolution rain gauge network operated as part of the Estimation des Pluies par Satellite, expérience Niger; [EPSAT-Niger (Lebel et al. 1992)]. Over a seven-week period, an extreme rainfall gradient of 284 mm per 9 km developed across the densely instrumented southern supersite (SSS). This prompted Taylor et al. (1997) to examine the evolution of the accumulated rainfall pattern over successive storms. They observed that heavy rain fell preferentially at certain stations. This kind of convective scale variability is hidden by larger-scale features when looking at the EPSAT–Niger (E–N) dataset.
To explain this anomaly, Taylor et al. (1997) proposed that the rainfall pattern was maintained by a positive surface feedback. Across the area of high rainfall, the PBL was observed to be moister than elsewhere due to increased surface evaporation. It was suggested that the prestorm PBL anomalies were large enough to influence the location of intense convective cells in passing storms. The heaviest rainfall consequently fell in previously wetter areas, thus reinforcing soil moisture patterns.
If a positive feedback was responsible for the rainfall gradient across the SSS in 1992, one would expect to find similar persistent rainfall patterns elsewhere in the region, and during other periods. The aim of this study is to examine the E–N dataset for evidence of more widespread persistence at convective length scales. Two years of data are analyzed here to assess whether there is a positive correlation between daily and antecedent rainfall differences. This will place the SSS case study in a more general context. If the correlation is high, it will imply that the persistence found at the SSS is a manifestation of a more widespread and predictable aspect of Sahelian rainfall. As rainfall is crucial in determining the surface energy balance, the discovery of a feedback would be central to the aims of the HAPEX–Sahel study, and our understanding of land surface–atmosphere interactions in general.
2. Observational data and methodology
a. Characteristics of the observational domain
The daily rainfall data used for this study come from the network of over 100 gauges operated by EPSAT–Niger in southwest Niger. In 1991 and 1992, these gauges were located typically every 12.5 km across an area encompassing the HAPEX–Sahel 1° square. Topographic features of the region included the Niger River in the southwest of the domain, and the Dallol Bosso sunken river valley in the east (Fig. 1a). Elsewhere, a number of laterite plateaus rise about 30–50 m above sandy cultivated soils. Marked gradients in seasonal rainfall are observed at a range of spatial scales (Figs. 1b,c). The climatic latitudinal gradient characteristic of the Sahel is masked by mesoscale variability over a single year (Lebel et al. 1997). Maxima found at scales of approximately 10–20 km do not have any clear relationship with either topographic features, or rainfall gradients in other years.
b. Sensitivities of feedback model
The proposed surface feedback mechanism should be sensitive to a number of surface and atmospheric factors. These factors need to be considered in designing and interpreting a statistical test for rainfall persistence. In a simple one-dimensional sense, the feedback relies upon two key factors.
1) The sensitivity of evaporation to antecedent rainfall
This is determined by properties of the soil and vegetation. Evaporation in a sparsely vegetated semiarid region such as the Sahel is most sensitive to rainfall in the day or two following an event. This timescale is determined by the drying of the top soil layer, typically 10 cm. Bare soil evaporation rates of about 3–4 mm day−1 may be maintained for this period (Wallace and Holwill 1997), ensuring that total evaporation from the sparsely vegetated surface is typically double that of a surface with a dried top layer (Gash et al. 1997). On timescales of several weeks, rainfall affects evapotranspiration via deeper soil moisture reservoirs and leaf development. Total evaporation will be more sensitive to rainfall accumulated over the preceding weeks when the top soil layer is dry.
2) The sensitivity of rainfall to surface evaporation
The effect of evaporation on rainfall will depend on various meteorological features. The rainfall must be convective for surface evaporation to influence precipitation directly. The convective available potential energy (CAPE) will generally be more sensitive to PBL moisture when the atmosphere is conditionally unstable to greater heights. A positive feedback is therefore more likely in deeper, more intense storms. In addition, in the presence of organized low-level convergence, PBL air will be forcibly carried to the level of free convection. This will increase the sensitivity of the feedback to anomalies of CAPE and evaporation (Barnston and Schickedanz 1984). Thus, one might expect persistence to be more pronounced in mature organized storms such as squall lines. However, the extent to which surface fluxes influence deep convection will depend upon the phase of the diurnal cycle, and in the absence of well-organized storm systems, details of the structure of the PBL (Ek and Mahrt 1994).
Of course, the convective rainfall patterns under investigation are not simple one-dimensional systems. At this scale, advection in the PBL degrades surface-induced atmospheric features, while convective-scale dynamics of tropical squall lines are complex [e.g., Houze (1977)]. The most surprising aspect of finding a surface feedback on convective rainfall variability would be that a simple one-dimensional model has any utility in describing the effects of these three-dimensional processes.
c. Statistical test for persistent patterns
In this study, we are not interested in the absolute values of event rainfall as these are determined primarily by larger-scale features of the atmosphere. Here we focus on local variability within storms, and therefore must examine differences in rainfall between pairs of gauges. The adopted hypothesis is that there is a positive correlation between daily and antecedent rainfall differences at the convective scale. The alternative null hypothesis is that no such relationship exists. For this study, convective scale is taken to be between 7.5 and 15 km. This range is chosen to ensure a large sample of pairs of gauges from the network: 242 in 1991, and 349 in 1992. Antecedent rainfall differences are accumulated over a range of timescales linked to the surface processes discussed above.
In analyzing the rainfall dataset described above, we must determine which pairs of observations should be used in the statistical analysis. First of all, we note that according to the feedback model, storm patterns are likely to be more sensitive to antecedent conditions during intense events. We thus adopt the criterion C1, that rainfall at both gauges exceeds a threshold value T on the day in question. In this study we adopt values of T = 1, 10, 20, and 30 mm to assess the validity of this assertion. Second, we wish to diminish the effect of larger-scale gradients on the sample, as found for example, near the edge of a storm track. To this end, pairs of observations must also satisfy criterion C2, that rainfall at all other stations within a search radius λT/2 of either gauges exceeds half the threshold value, T/2. A value of λT/2 = 30 km is chosen here. Finally, care must be taken in areas with dense observations (i.e., around the “supersites”) to ensure that the same convective scale patterns are not sampled more than once. Thus, if there is a pair of gauges with a larger antecedent rainfall difference than that of the pair under consideration, the distance between these two pairs must exceed a radius, λmin (criterion C3). From analysis of daily isohyets around the super sites, a value of λmin = 5 km is adopted to avoid this oversampling.
3. Persistence over a range of timescales
a. Short-lived persistence (1–2 days)
As discusssed above, bare soil evaporation has a pronounced effect on the surface energy balance for several days after rain. During this period, the contrast in evaporation between wet and dry areas is marked. Isolated showers can therefore induce strong surface and PBL gradients over the following 1–2 days. To test whether subsequent rainfall patterns are modified in this scenario, we examine the relationship between rainfall differences for one day and accumulated over the previous two days for the pairs of observations available. Two further criteria are adopted in this section to ensure that the differences in antecedent rainfall are representative of local contrasts in bare soil evaporation. First, pairs of observations are chosen for events when antecedent rain has fallen at one gauge but not the other within a period of 2 days, but with an intervening dry period of at least 6 h (C4). In addition, apart from the event 1–2 days previous, neither gauge has recorded any other rainfall within the previous 2–3 days (C5).
The data is presented in a scatterplot in Fig. 2, with a value of the threshold rainfall T = 10 mm. A large range of daily rainfall gradients of up to 55 mm per 10 km is shown. However, when the antecedent rainfall difference exceeds a few millimeters, there is a clear positive correlation between the two variables over successive events.
A linear relationship can be usefully applied to the data. The results of this test are shown in Table 1. Taking all 93 event pairs, a line intercepting the origin with gradient of 0.59 explains 12.1% of the variance. The null hypothesis that there is no positive correlation between the variables is rejected at the 99.94% significance level according to a single-tailed Student’s t-test. When examining antecedent contrasts of at least 5 mm, the value of r2 increases to 0.314. Similar features are found for rainfall thresholds of 1 and 20 mm. Both the values of r2 and the gradient increase with increasing T. The correlation coefficient increases for all three thresholds by restricting the sample to only those points with larger antecedent differences. In these cases, the gauges are more likely to be associated with prestorm PBL humidity gradients. However, it should be noted that in restricting the sample to those antecedent differences larger than say, 5 mm, the parent distribution of the correlated variates can no longer be assumed to be gaussian. As a result, the t test on r2 is no longer strictly valid. As the resultant distribution remains symmetrical though, the significance test is not too far out of the domain of validity.
Of the 30 points highlighted in Fig. 2, there are eight event pairs (circled) arising from rainfall on 20–22 July 1992. The isohyets for these events (Fig. 3) illustrate the spatial features of the correlated rainfall variables more clearly, and are typical of the other points in the regression. Rainfall in the storm on the afternoon of 22 July (Fig. 3b) is highly variable. Maxima result from locally intense convection embedded within the larger-scale disturbance. These convective-scale features are only partially resolved by the observations. However, what is striking about the patterns is that in the central region affected by the prior storm (Fig. 3a), the “bull’s-eyes” are well correlated with the previously wet areas.
The pairs of gauges sampled in this test are found throughout the E–N domain and are not related to annual gradients in rainfall (Fig. 1). So while the analysis shows that patterns persist over 1–2 days, on the seasonal timescale they are a transient feature. This appears to exclude both orography and land cover patterns as a primary forcing mechanism for persistence. The test thus provides strong evidence that a hydrological feedback can influence convective rainfall. Even the simple one-dimensional model offers useful predictive ability of rainfall variability over the short timescales studied here.
b. Long-lived persistence (10 days)
The bare soil component of evaporation over sparsely vegetated surfaces decreases rapidly as the top soil layer dries. After several days of dry conditions, total evaporation is more closely linked to transpiration and deeper soil moisture, due to rainfall accumulated over several weeks. To assess the possibility of persistence over these longer timescales, differences between gauges in antecedent rainfall are accumulated over 10 days. The influence on the selected sample of recent rainfall is reduced by the introduction of a further criterion in addition to C1, C2, and C3. Pairs of gauges are only selected when both sites have remained dry for at least Ndry days prior to the event under consideration (C6). Setting Ndry = 2 diminishes the effect of bare soil evaporation on the observations, and ensures that the sample is independent of the data used in the preceding section.
The results of a linear regression based on this sample are presented in Table 2. Once again, the null hypothesis can be rejected at a very high significance level for all values of threshold rainfall, T. As in Table 1, both the variance explained and the gradient increase with increasing T. The data points satisfying the T = 20 mm criteria are shown in Fig. 4. This figure illustrates the considerable scatter around the regression line for small antecedent rainfall differences, also found for the other values of T. However, a linear fit accounts for 50% of the variance when considering only the 30 largest antecedent differences within the sample.
c. Sensitivity analysis
In this section we assess the sensitivity of the statistical test to the sampling criteria adopted. First, it can be seen from Tables 1 and 2 that the correlation coefficient increases with threshold rainfall, which corresponds to a decrease in sample size. The question is thus raised, “how significant is this increase?” Providing a statistically rigorous answer to that question is nontrivial. Instead, we adopt an alternative test, taking observations which satisfy C1 with T = 1 mm, but omit those that also satisfy the higher threshold level of T = 10 mm. In the resulting regression, the gradient is only slightly positive (0.01) as compared to 0.14 for the sample where T = 10 mm. As a result, the null hypothesis cannot be rejected at the 50% level of significance. This absence of correlation for the variables during light precipitation events suggests that the feedback is sensitive to rainfall intensity. The results are therefore in accord with the feedback model proposed in section 2.
For the remaining sensitivity analyses, we adopt a value of T = 20 mm, and examine the regressions only for those antecedent rainfall differences exceeding 30 mm. This gives a large enough sample size to address the sensitivity of the test to other sampling parameters. We now assess the sensitivity of the regression to the length scale of the passing storm. In the sampling strategy, a minimum length scale is provided by the search radius λT/2 within which all gauges should receive at least half the threshold rainfall for the event under consideration (C2). Here the effects of alternative values of λT/2 of 0.1 and 50 km are evaluated. Relaxing C2 by setting λT/2 = 0.1 km, a linear regression gives a lower value of r2 (18.1% from 72 observations), while restricting the observations to only the largest-scale storms (λT/2 = 50 km) produces a value of r2 = 72.1% from the remaining 14 observations. Again, the significance of this sensitivity is unclear given the changing nature of the sample distribution. The test with λT/2 = 0.1 km is therefore repeated, this time excluding those events that also satisfy C2 with λT/2 = 30 km. From this reduced sample of 43 pairs of observations, the gradient of the linear fit is only 0.01, and the null hypothesis cannot be rejected at the 50% level. The sensitivity of the test to λT/2 therefore suggests that persistence is more marked in larger-scale storms, as expected from the feedback model. Beneath isolated storms, and near the edge of larger-scale storm tracks, other atmospheric factors may obscure the influence of antecedent rainfall conditions on convection.
The regressions between daily and 10-day antecedent rainfall differences have all been performed on observations where there has been no rain for at least 2 days prior to the event in question (Ndry = 2 in C6). This criterion was introduced to try to distinguish feedbacks via deep soil moisture stores from the rapid evaporation at the soil surface in the day or two following rain. Increasing Ndry to 4 (where neither station has received any rain for at least 4 days), the correlation between daily and 10-day antecedent rainfall is high (Table 3, Fig. 5a). Of this sample of 66 event pairs, 36 result from the squall-line event on the evening of 21 August 1992. The isohyets of daily and antecedent rainfall (Fig. 6) for this event illustrate similar spatial characteristics to those shown in Fig. 3. Convective-scale maxima within the squall line are well correlated with strong gradients in antecedent rainfall both around the SSS and in the east of the observation area.
The sensitivity of the test to the value of Ndry can be seen by comparing the values of r2 in Table 3. Examining observations where rain fell either 3 or 4 days previously (Ndry = 2, but excluding observations that also satisfy Ndry = 4), the variance explained is somewhat lower than for Ndry = 4. A third independent sample of observations is also analyzed with Ndry set to 0, but excluding observations which also satisfy Ndry = 1. In this sample of pairs, prior to the event in question, rain must have fallen at both gauges on the previous day, although successive events with an interval of less than 6 h are removed. From the resulting 38 event pairs, there is no correlation between daily and antecedent rainfall.
The sensitivity of the statistical test to the value of Ndry appears to support the physical interpretation of the feedback hypothesis. When rain has fallen at both gauges on the previous day, for example, following the passage of a squall line, high bare soil evaporation rates are likely to dominate the surface energy balance everywhere. In this case, prestorm contrasts in low-level humidity are likely to be small. Only when the top soil has dried for several days will deeper soil moisture reservoirs affect surface fluxes. Under such conditions, large differences in 10-day antecedent rainfall totals are linked to subsequent rainfall variability.
Up until now, the accumulation period for antecedent rainfall has been set at 10 days. To examine how rainfall contrasts remain correlated over alternative periods of time, antecedent rainfall differences are accumulated over a range of days from 4 to 50. The resulting samples are then correlated with daily rainfall differences, with test parameters T = 20 mm and Ndry = 2 days. Taking the 30 largest antecedent rainfall differences for each sample, values of r2 exceeding 30% are maintained from 6 to 36 days. The null hypothesis is rejected at significance levels of 99.85% throughout this range.
Of the 30 event pairs taken for this series of regressions, typically 6 or 7 are associated with the rainfall anomaly at the SSS previously identified by Taylor et al. (1997). To ensure that this single feature is not wholly responsible for the persistence signal, the tests are repeated having removed all observations within 15 km of the SSS. The null hypothesis is again rejected over a similar range of accumulating days at a significance level of generally greater than 95%, and values of r2 greater than 10%. The weakening of the regression in this case appears to be due to the removal of the strongest antecedent contrasts in the sample. However, the test still indicates that persistence of up to one month occurs elsewhere in the study area. Examples of this persistence are highlighted in the next section.
4. Persistent rainfall patterns
It has been shown that convective-scale rainfall persistence occurs at a range of time scales in the E–N dataset. Here we identify some common features of long-lived patterns. Figure 7 shows the four most marked patterns over a period of 30 days. The gradients all exceed 13 mm km−1 over the 30 days shown, as compared to an annual climatic gradient of 1 mm km−1 across the Sahel (Lebel et al. 1992). The gradient observed across the SSS in 1992 was the most pronounced feature, with 27.3 mm km−1 accumulating over 30 days (Fig. 7c). During the 1992 season, this ensured that the three wettest gauges in the network were all associated with the persistence pattern around the SSS.
In all four of the cases shown, latitudinal gradients are larger than longitudinal ones. This is typical of many of the persistent patterns in the dataset, and may be linked with the preferred easterly direction of storm travel in the Sahel (Taylor et al. 1997). The rain gauge network is not of sufficient spatial resolution to determine characteristic length scales of the patterns. However, the marked gradients appear to be associated with rainfall maxima less than 20 km across north–south.
Also shown in Fig. 7 are the time series of daily rainfall at the wet and dry gauges indicative of the strong gradients. The differences arise from a number of storms with local contrasts in rainfall of up to 50 mm. The largest persistent 30-day features occur between mid-July and the end of August in 1992. This coincides with the passage of rain events typically every 2–3 days.
From the perspective of the simple feedback model, several criteria may be crucial in sustaining rainfall persistence over several weeks. Deep convective events must pass over the area regularly, a condition met during the wettest months of July and August in Niger. If the time interval between large-scale events is shorter than the characteristic timescale over which the top soil dries (∼1–2 days), prestorm evaporation rates will be uniformly high. In this case, persistence is not favored. On the other hand, if the event timescale is 3–4 days, heterogeneity in deeper soil moisture may influence the PBL through transpiration rates. If soil moisture deficits differ markedly, variability in vegetation growth will reinforce surface contrasts further. In such conditions, persistence over several weeks is more likely.
However, this simple model is complicated by a number of factors. Reinforcement of surface moisture patterns appears to be less favored by the passage of weaker and smaller-scale events. Furthermore, storms may pass over affected areas when horizontal gradients in the PBL are weak, for example in early morning or when wind speeds are high (Taylor et al. 1997). Together, these processes will act to dissipate persistence.
5. Conclusions
This study has demonstrated that Sahelian rainfall patterns exhibit persistence at convective length scales of approximately 10 km. The influence of antecedent rainfall on storm development is clearest when intense, large-scale storms pass over marked contrasts in surface evaporation. Patchy rainfall events in the previous few days can generate this heterogeneity through near-surface moisture. Evaporation is more sensitive to weekly and monthly rainfall when the top soil has been drying for several days. A persistence signal emerges from the observations for both these scenarios.
The clearest example of persistence over a number of weeks occurs around the SSS in 1992. However, other monthly patterns can be identified elsewhere. Although only partially resolved by the rain gauge network, these patterns have similar characteristic length scales. By demonstrating that persistence occurs throughout the observation area, the study provides additional evidence to support the proposed surface feedback mechanism (Taylor et al. 1997). Given the complexity of the PBL and storm dynamics at this length scale, it is surprising that a simple one-dimensional model has any utility in predicting convective rainfall patterns.
These findings have implications for our understanding of land surface–atmosphere interactions. Even in the absence of significant topographic features, successive rainfall patterns are not independent at convective length scales. This feature may need to be incorporated in future hydrological models. The feedback raises issues in the parameterization of convection and surface hydrology in large-scale atmospheric models. It also demonstrates that even over 10 km, surface features can have a profound influence on the hydrological cycle.
When rainfall patterns persist over several weeks, the effects on local communities can be dramatic. For example, during July and early August 1992, low rainfall in the north of the study area was exacerbated by a persistent local minimum around several villages. As a result, the millet crop failed, and all the adult males within a 10–15-km radius were forced to travel hundreds of miles to the coast in order to make enough money to survive through the dry season.
At this local scale, persistence could prove to be a useful short-term forecasting tool under semiarid conditions provided high-resolution rainfall observations were available. On the larger scale, it is unclear how the positive feedback mechanism affects precipitation. Antecedent rainfall gradients may, for example, influence the organization of isolated convection into squall lines. The use of a cloud-resolving model in conjunction with a realistic surface description will shed light on these questions.
Acknowledgments
This research was funded by the NERC through its TIGER (Terrestrial Initiatives in Global Environmental Research) programme, Award GST/91/III.2/2A. Funding of the EPSAT–Niger experiment by the TOA department of ORSTOM and from INSU (Institut National des Sciences de l’Univers) is gratefully acknowledged. The authors would also like to thank Chris Huntingford, Richard Harding, and the reviewers for their comments on the manuscript.
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(a) The 40-m height contours across the E–N area. Total rainfall (mm) for the periods (b) 1 June–4 October 1991 and (c) 1 May–1 October 1992.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
(a) The 40-m height contours across the E–N area. Total rainfall (mm) for the periods (b) 1 June–4 October 1991 and (c) 1 May–1 October 1992.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
(a) The 40-m height contours across the E–N area. Total rainfall (mm) for the periods (b) 1 June–4 October 1991 and (c) 1 May–1 October 1992.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Scatterplot of daily against antecedent rainfall differences accumulated over 2–3 days (T = 10 mm). The triangles indicate the 30 points with antecedent differences exceeding 5 mm used to calculate the linear regression shown. Data from the 20–22 July 1992 events are circled.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Scatterplot of daily against antecedent rainfall differences accumulated over 2–3 days (T = 10 mm). The triangles indicate the 30 points with antecedent differences exceeding 5 mm used to calculate the linear regression shown. Data from the 20–22 July 1992 events are circled.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Scatterplot of daily against antecedent rainfall differences accumulated over 2–3 days (T = 10 mm). The triangles indicate the 30 points with antecedent differences exceeding 5 mm used to calculate the linear regression shown. Data from the 20–22 July 1992 events are circled.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Daily rainfall (mm) on (a) 20 and (b) 22 July 1992. Pairs of gauges used in the regression in Fig. 2 are joined by dotted lines.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Daily rainfall (mm) on (a) 20 and (b) 22 July 1992. Pairs of gauges used in the regression in Fig. 2 are joined by dotted lines.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Daily rainfall (mm) on (a) 20 and (b) 22 July 1992. Pairs of gauges used in the regression in Fig. 2 are joined by dotted lines.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Daily and antecedent rainfall differences accumulated over 10 days with T = 20 mm. Triangles indicate the subset of data with antecedent differences exceeding 30 mm used to calculate the linear regression shown.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Daily and antecedent rainfall differences accumulated over 10 days with T = 20 mm. Triangles indicate the subset of data with antecedent differences exceeding 30 mm used to calculate the linear regression shown.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Daily and antecedent rainfall differences accumulated over 10 days with T = 20 mm. Triangles indicate the subset of data with antecedent differences exceeding 30 mm used to calculate the linear regression shown.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Scatterplots of daily against antecedent rainfall differences accumulated over 10 days (T = 20 mm) for (a) dry surface conditions (Ndry = 4), and (b) surfaces wetted on the previous day (Ndry = 0).
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Scatterplots of daily against antecedent rainfall differences accumulated over 10 days (T = 20 mm) for (a) dry surface conditions (Ndry = 4), and (b) surfaces wetted on the previous day (Ndry = 0).
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Scatterplots of daily against antecedent rainfall differences accumulated over 10 days (T = 20 mm) for (a) dry surface conditions (Ndry = 4), and (b) surfaces wetted on the previous day (Ndry = 0).
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Rainfall (mm) (a) accumulated over the period 11–20 August 1992 and (b) 21 August 1992. Pairs of gauges used in the regression in Fig. 5 are joined by dotted lines.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Rainfall (mm) (a) accumulated over the period 11–20 August 1992 and (b) 21 August 1992. Pairs of gauges used in the regression in Fig. 5 are joined by dotted lines.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Rainfall (mm) (a) accumulated over the period 11–20 August 1992 and (b) 21 August 1992. Pairs of gauges used in the regression in Fig. 5 are joined by dotted lines.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Accumulated 30-day rainfall from (a) and (b) 14 July to 12 August 1992, and (c) and (d) 27 July to 25 August 1992, (a) around the east-central site, (b) 40 km east of the SSS, (c) the SSS, and (d) in the east of the observational area.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Accumulated 30-day rainfall from (a) and (b) 14 July to 12 August 1992, and (c) and (d) 27 July to 25 August 1992, (a) around the east-central site, (b) 40 km east of the SSS, (c) the SSS, and (d) in the east of the observational area.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Accumulated 30-day rainfall from (a) and (b) 14 July to 12 August 1992, and (c) and (d) 27 July to 25 August 1992, (a) around the east-central site, (b) 40 km east of the SSS, (c) the SSS, and (d) in the east of the observational area.
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
(Continued)
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
(Continued)
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
(Continued)
Citation: Monthly Weather Review 126, 6; 10.1175/1520-0493(1998)126<1597:OEOPCS>2.0.CO;2
Results of linear regression of data satisfying criteria C1–C5, accumulating antecedent rainfall over 1–2 days.
Results of linear regression of data satisfying criteria C1–C3 and C6, with Ndry = 2, and accumulating antecedent rainfall over 10 days.
Results of linear regression of daily and antecedent rainfall differences over 10 days for threshold rainfall T = 20 mm. No rain has fallen at either gauge for at least Ndry days, but in the case of Ndry = 2 and Ndry = 0 days, the sample excludes observations which also satisfy Ndry = 4 days and Ndry = 1 day, respectively.
