Evaluating Weather Research and Forecasting Model Sensitivity to Land and Soil Conditions Representative of Karst Landscapes

Abstract

Due to their particular physiographic, geomorphic, soil cover, and complex surface-subsurface hydrologic conditions, karst regions produce distinct land–atmosphere interactions. It has been found that floods and droughts over karst regions can be more pronounced than those in non-karst regions following a given rainfall event. Five convective weather events are simulated using the Weather Research and Forecasting model to explore the potential impacts of land-surface conditions on weather simulations over karst regions. Since no existing weather or climate model has the ability to represent karst landscapes, simulation experiments in this exploratory study consist of a control (default land-cover/soil types) and three land-surface conditions, including barren ground, forest, and sandy soils over the karst areas, which mimic certain karst characteristics. Results from sensitivity experiments are compared with the control simulation, as well as with the National Centers for Environmental Prediction multi-sensor precipitation analysis Stage-IV data, and near-surface atmospheric observations. Mesoscale features of surface energy partition, surface water and energy exchange, the resulting surface-air temperature and humidity, and low-level instability and convective energy are analyzed to investigate the potential land-surface impact on weather over karst regions. We conclude that: (1) barren ground used over karst regions has a pronounced effect on the overall simulation of precipitation. Barren ground provides the overall lowest root-mean-square errors and bias scores in precipitation over the peak-rain periods. Contingency table-based equitable threat and frequency bias scores suggest that the barren and forest experiments are more successful in simulating light to moderate rainfall. Variables dependent on local surface conditions show stronger contrasts between karst and non-karst regions than variables dominated by large-scale synoptic systems; (2) significant sensitivity responses are found over the karst regions, including pronounced warming and cooling effects on the near-surface atmosphere from barren and forested land cover, respectively; (3) the barren ground in the karst regions provides conditions favourable for convective development under certain conditions. Therefore, it is suggested that karst and non-karst landscapes should be distinguished, and their physical processes should be considered for future model development.

1 Introduction

Karst terrain covers approximately 20% of the Earth’s ice-free land surface, with an estimated 40% of the USA east of Tulsa, Oklahoma comprising karst landscapes (White et al. 1995; Ford and Williams 2007) as shown in Fig. 1a. Physical conditions associated with well-developed karst landscapes may affect local and regional weather systems through various processes related to land–atmosphere interactions (Jiang and Yuan 1999; Leeper et al. 2011; Durkee et al. 2012). Karst is defined as a type of terrain, generally underlain by soluble carbonate rocks such as limestone or dolomite, where the topography is primarily formed by the dissolution of rock, and which may be characterized by sinkholes, sinking streams, closed depressions, subterranean drainage, and caves (White 1988; Ford and Williams 2007). Most often, karst landscapes form highly permeable aquifer systems within the carbonate bedrock, which typically have a thin soil cover, if any, and are able to support a variety of surface-land cover ranging from bare, stony rock surfaces to vegetation ranging from cacti to dense tropical forests, depending on the climate and latitude. The water table may be tens to hundreds of metres below the surface, depending on the topography, and the land surface is sometimes rugged and heavily weathered. Soil productivity can be limited by the low nutrient and water availability and the steep, sloping terrain (Li et al. 2003; Ford and Williams 2007; Palmer 2007). Generally, rainfall reaching the ground of most landscapes evaporates, infiltrates, or moves laterally at or near the surface as runoff or interflow. However, on well-developed karst topography, there is often limited surface runoff, since most or all of the precipitation rapidly infiltrates directly into the karst aquifer, either through the soil or sinking streams (Crowther 1987; Hess and White 1989; Groves and Meiman 2005; Groves 2007; Leeper et al. 2011). Groves et al. (2005) were able to capture surface rainfall in a cave within 30–45 min of observed precipitation, showing a clear indication of the rapid transport of meteoric recharge into karst aquifers. Milanovic (1981) observed that karst groundwater tables vary by as much as 100 m after a rain event, which may cause localized flooding and the increase in atmospheric moisture availability within the root zone. Furthermore, gradients in soil moisture may lead to differential heating at the surface through evaporative cooling, thus promoting the development of mesoscale circulations (Milanovic 1981). Karst landscapes and their geomorphic and hydrologic characteristics may well influence the land–atmosphere interface differently when compared with non-karst areas (White et al. 1995; Jiang and Yuan 1999; Bonacci et al. 2009; Heilman et al. 2009; Leeper et al. 2011).

Fig. 1

Study area: a two nested model domains with colour shades representing the areas of karst landscapes; b land-cover types based on data from the 2006 National Land Cover Database; c soil types

Surface and sub-surface karst features, such as sinkholes, underground drainage systems, vertical shafts, and springs, significantly influence localized drainage patterns and hydrological processes. Karst topography, through its effect on local hydrology, can, in turn, significantly alter soil-moisture distributions, which may induce important feedbacks between karst regions and the near-surface atmosphere (Leeper et al. 2011). There is very limited research on the direct impact of karst landscapes on climate, or the attribution of weather/climate events to karst systems. Ji et al. (2015) studied the increasing trend of flood and drought disasters in the past 500 years over a well-developed karst region in south-west China, and found that, under the climate change regimes and human activities investigated, the karst region is susceptible to more frequent flooding and drought due to its land-surface geomorphology. Zhang et al. (2010) analyzed extreme precipitation distributions in another karst region in Guizhou, China, and also noticed an increasing trend of extreme events. However, it is well-known that spatial and temporal heterogeneity in both soil-moisture distributions and wet–dry transitions promote localized mesoscale circulations and subsequent convection (Clark and Arritt 1995; McPherson 2007). Furthermore, Leeper et al. (2011) conducted a sensitivity study for precipitation over karst landscapes in Kentucky and showed that, even under moderate synoptic forcing, adjacent wet/dry land-surface conditions can modify energy balances, the evolution of the planetary boundary layer, mesoscale circulations, and the locations of convection. A study of the 1–2 May 2010 historic mid-south flood suggests that the heaviest localized precipitation fell over the areas located along or adjacent to well-developed karst hydrological boundaries (Durkee et al. 2012).

The complexity of karst groundwater flow systems is such that, while karst hydrological modelling has progressed, many challenges still exist (e.g., Meng and Wang 2010; Hartmann et al. 2013). While quantitative descriptions of land-surface conditions and processes coupled with atmospheric models also continue to evolve, none have proper representations of karst landscapes (Chen and Dudhia 2001; Dai et al. 2003; Skamarock et al. 2008). Limited research has been completed on the direct impacts of karst landscapes on atmospheric processes and karst–atmosphere coupling. However, with the vast improvement in computational resources and the ability to understand and better simulate these processes at much higher rates and resolutions, studying the impacts of localized karst features has become increasingly feasible. Prior to representing karst-landscape characteristics in land-surface models or the coupling of karst conditions with atmospheric processes, exploratory methods, such as sensitivity experiments, facilitate the investigation of the potential effects of karst landscapes on the atmosphere. Fan (2009) used the Weather Research and Forecasting (WRF) model to study the impacts of changes on regional weather simulations by surface-heating conditions derived from soil-temperature observations. They indicate that incorporation of the observed soil temperatures introduces a persistent soil heating that is favourable to convective development and, consequently, the improved simulation of precipitation. Gao et al. (2013) used the WRF model, which is coupled with the simplified Simple Biosphere Model of Xue et al. (1991), to study the impacts of land degradation over the Guizhou karst plateau on the regional climate. The degraded lands were represented by short shrubs with bare soil for moderately degraded land or bare soil for severely degraded land, with the degraded land over the south-west China karst region shown to have an impact on the regional climate. We use a similar approach to Fan (2009) and Gao et al. (2013) to simulate the responses of the WRF model to different land-cover and soil types over the karst regions of central USA shown in Fig. 1. If the area of a cell is dominated by karst, it is considered as a karst region, which is similar to the treatment of land use and soil types in the WRF modelling system (Chen and Dudhia 2001; Chen et al. 2007; Skamarock et al. 2008).

Our objective is to explore whether weather events are sensitive to the land-surface conditions available in the current WRF model, whether the model can mimic certain characteristics of karst landscapes, and whether the model is able to distinguish between the input conditions defining karst and non-karst conditions. Given that no existing model distinguishes between karst and non-karst conditions, the experiments are designed to determine if any existing land types in the model, along with their physical parameters, result in improved weather simulations in karst regions, and thereby serving as a “proof-of-concept” before investment in additional effort to develop more realistic physical and/or chemical processes of karst regions. As it is an exploratory sensitivity study, the experiments reflect only some of those characteristics representative of a karst landscape.

Additional objectives examine how the proposed land-cover or soil types may mimic karst impacts. As with many karst landscapes, the study area (Fig. 1) is characterized by an uneven soil-bedrock interface buried under a typically shallow layer of soil and/or fully exposed bedrock with no soil cover. In the case of the exposed karst (i.e., exposed bare rock surfaces), there is higher albedo, higher runoff, and less soil moisture than for soil-covered areas. The “barren” land-cover type in existing land-surface models is sparsely vegetated, and thus an approximation of exposed karst areas. This type of land cover typically leads to a higher sensible heat flux, higher air and surface temperatures, and lower soil moisture. Forest land cover is used as a contrasting experiment, where forested land cover over a karst region may reduce albedo, increase evapotranspiration, and, therefore, increase moisture transfer into the atmosphere (Bonan 2008). While not yet investigated for karst areas, deeper root systems of the forest over a karst landscape help preserve soil moisture by penetrating into bedrock fractures, which may lead to possible impacts on atmospheric conditions (e.g., Jackson et al. 1999; Schwinning 2008).

As indicated earlier, an important feature of karst is the existence of highly permeable bedrock, resulting in the rapid drainage of rainwater into the subsurface, whose representation may be the prescription of sandy soils in the existing land-surface model, which have the lowest moisture content and relatively high permeability (Mitchell 2005). The sensitivities of five selected weather events to the karst landscape are tested with each of the representations mentioned above using the Advanced Research WRF model version 3.2.1 (Skamarock et al. 2008). Brief descriptions for the weather events and detailed experimental designs are given in Sect. 2, Sect. 3 presents the analysis and discussion of model simulations, with concluding remarks summarized in Sect 4.

2 Model, Data, and Experimental Design

The national karst map from the U.S. Geological Survey (Davies et al. 1984; Weary and Doctor 2014) was incorporated into the WRF model, which is configured here with two one-way nested domains (Fig. 1a). The model resolution for the outer domain is 18 km (covering 2700 km east to west; north to south) and 6 km for the nested domain (extending 906 km east to west; north to south), with 49 vertical Eta levels extending from the surface to 100 hPa (here, Eta levels refers to a vertical coordinate system based on normalized pressures above mean sea level, Mesinger and Janjic 1974). Model physical parametrizations follow Gaines (2012), where a squall-line event in central USA was simulated with various combinations of parametrizations, including the Lin microphysical parametrization (Lin et al. 1983), the Kain-Fritsch (new Eta) cumulus parametrization over both domains (Kain and Fritsch 1993), the ACM2 (Pleim) planetary boundary-layer parametrization (Skamarock et al. 2008), the Rapid Radiative Transfer Model longwave radiation parametrization (Mlawer et al. 1997), the Goddard shortwave radiation parametrization (Chou et al. 1998), and the Noah land-surface model (Chen and Dudhia 2001). Model simulations are driven by North American Regional Reanalysis data (Mesinger et al. 2006).

As noted previously, five convective weather events over the karst region were selected for the sensitivity study (Table 1), featuring a wide variety of total precipitation from light to moderate rainfall, to a historic flooding event (Fig. 2). The selection of convective events facilitates consideration for any initial feedback from the karst landscape to the atmosphere under various conditions, such as three different seasons, including late spring, early summer, and autumn, and which represent typical atmospheric conditions for the study area.

Table 1 Simulation and analysis time periods of the five chosen cases with analysis and rainy periods

Considered are a stationary front due to downstream blocking near the eastern Atlantic Ocean (case 1), a cold front becoming stationary over the Ohio Valley region (case 2), a weakly forced summertime cold front (case 3), a mesoscale convective system (case 4), and a strong cold front that produced record rainfall across the Ohio and Tennessee Valley regions (case 5), for a total of 20 simulations (five weather events and four land-cover scenarios as described below). Light to moderate rainfall amounts were recorded during the stationary front (case 1) and the weak cold front (case 3), with larger amounts produced from the two cold fronts (cases 2 and 5) and the mesoscale convective system (case 4). We have previously investigated these precipitation events, for which we have developed comprehensive knowledge (e.g., Quintanar et al. 2008, 2009; Durkee et al. 2012; Quintanar and Mahmood 2012; Suarez et al. 2014).

Fig. 2

The 24-h accumulated Stage-IV precipitation (mm) ending at: a case 1: 0000 UTC 12-06-2006; b case 2: 0000 UTC 19-06-2006; c case 3: 0000 UTC 24-06-2006; d case 4: 1200 UTC 30-09-2008; e case 5: day 1 0000 UTC 02-05-2010; and f case 5: day 2 0000 UTC 03-05-2010

The land cover of the outer domain shown in Fig. 1b is based on the 2006 National Land Cover Dataset (Fry et al. 2011), and depicts a small band of the dryland crop and pasture located over the Ohio and Tennessee Valley regions, with a small area extending through central Kentucky, Tennessee, and southwards. Largely deciduous broadleaf forest surrounds the small area of dryland crop and pasture within the nested domain. Areas along the Mississippi River and northwards near the Ohio River mainly consist of mixed dryland/irrigated crop and pasture.

The experiments consist of control, barren-land, forest, and sandy-soil simulations for each event, with specific land and soil types used in the corresponding model experiment to best represent a karst landscape over the karst areas (Fig. 1a), and to study the potential atmospheric impacts. The control run uses the WRF model with the default land cover and soil types as shown in Fig. 1b, c. The barren experiment is conducted by changing all land-cover types over the karst areas (Fig. 1a) to a barren-land type, with little or no vegetation cover to better simulate karst landscapes of this variety. For the forest experiment, all land-cover types over the karst areas are changed to forest. Another change introduced to both the barren and forest experiments, is to the vegetation fraction over karst areas, which is changed to 0 and 100%, respectively, corresponding to the land-cover types. The last experiment places sandy soils over the karst areas (Fig. 1a), but with the same land-cover types as the control experiment. This simulates the rapid drainage of water, which is associated with dry sands and may reflect karst hydrological characteristics with high bedrock permeability. As sand has the least water content among all of the soil types in the current Noah land-surface model (Mitchell 2005), it was chosen for this experiment.

The numerical experiments are initiated with a 3-h spin-up, which allows the model to adjust to its background forcing, and are followed by a simulation of 48-h duration (see Table 1). The results of 24-h simulation periods (the hatched grey areas in Table 1) are analyzed and verified, corresponding to the rainy period for each case, and allowing sufficient time for changes in land cover and soils to take effect. The rainy period was set immediately after model spin-up in cases 1, 3 and 5, case 4 allowed for a further 12 h, and case 2 allowed for 24 h between spin-up and the rainy period. Case 5 is analyzed for a longer period of time (two 24-h analysis periods) to more accurately reflect the longevity of the convective event, which produced periods of heavy rain over the Tennessee and Ohio Valley regions.

The model-simulated precipitation is compared with the National Centers for Environmental Prediction (NCEP) multi-sensor precipitation analysis Stage-IV dataset, which is based on a combination of quality controlled radar and gauge observations (Lin 2011). Each of the experiments is also compared with the control run for the sensitivity analysis. Model evaluations are performed using statistical scores, including the root-mean-square error (RMSE) and bias (BIAS) using the NCEP Automated Data Processing Global Upper Air and Surface Weather Observations (May 1997—continuing, available at http://rda.ucar.edu/datasets/ds337.0/, accessed October 2015). While the RMSE measures the overall error of a simulated variable compared with its observations, the bias assesses the systematic underestimation (BIAS < 0) or overestimation (BIAS > 0), with BIAS = 0 being perfect. For precipitation, the 2 $\times$ 2 contingency table-based equitable threat score (ETS) and frequency bias score (fBIAS) are calculated for a variety of thresholds for comparison (Wilks 2010), with ETS values considered in assessing the model skill of precipitation simulations. Higher ETS values represent more accurate results (termed more “skilful”, with ETS = 1 being perfect) and lower values represent the opposite. The related fBIAS score represents the bias of frequency of a particular rain amount (used as a threshold) or greater, where fBIAS = 1 represents a perfect skill, while fBIAS $> 1$ (or $< 1$) indicates overestimation (or underestimation) of the frequency of the given precipitation threshold or greater. Other model-simulated and derived variables, such as the convective available potential energy (CAPE, energy available to an ascending air parcel), convective inhibition (CIN, energy needed to lift an air parcel to its level of free convection), temperature, dew point temperature, equivalent potential temperature, and surface heat fluxes are used in analyzing the mesoscale convective development.

3 Model Simulation Analysis

The results of model simulations are compared with observations, (1) to evaluate their performance; and (2) to investigate the impacts of the different land-cover and soil conditions over karst regions during the five chosen precipitation events. Case 4 is presented here in detail with a focus on the nested domain, with general results presented from the other cases. Case 4 is a mesoscale convective system, where moderate lift, moisture, instability, and favourable vertical wind shear contribute to its substantial growth.

3.1 Model Verification

3.1.1 Precipitation

The 24-h accumulated precipitation of case 4 from the control simulation during the rainy period (1200 UTC 29-09-2008 to 1200 UTC 30-09-2008) is shown in Fig. 3a for the nested domain, where the major precipitation areas are simulated well, with light to moderate amounts of rainfall of 0.2–51.2 mm over the domain. Larger amounts of rainfall are found over the western portions of Kentucky and into south Illinois and Indiana. Figure 3b shows the difference in 24-h accumulated precipitation between the control simulation and Stage-IV data. For most areas receiving precipitation, especially locations along west Kentucky and south Indiana and Illinois, a large area of positive difference (control minus Stage-IV data) in precipitation is detected, which is particularly noticeable over areas with the heaviest rainfall, indicating a positive bias in the simulation. In contrast, the model produces a negative bias over areas of lighter precipitation.

Fig. 3

The 24-h accumulated precipitation (mm) and differences (mm) for case 4 over the nested domain, and ending at 1200 UTC 30-09-2008: a control run; b difference between control and Stage-IV data as shown in Fig. 2d; c difference between barren and control simulations; d difference between forest and control simulations; e difference between sandy-soil and control simulations

Barren – control (i.e. subtracting control results from the barren results) simulations show a negative bias of precipitation over areas with the heaviest amounts of rainfall (Fig. 3c), suggesting the barren experiment corrects some of the overestimation of the control run for heavy rainfall. This finding also somewhat concurs with Leeper et al. (2011), where a lowering of the soil moisture in the model (thereby simulating the lower karst soil moisture) produces precipitation in better agreement with the observations. The barren experiment shows large positive differences (6.4–25.6 mm) in light to moderate precipitation areas along the western Kentucky region where the control simulation underestimates the precipitation. Hence, using the barren-land type to simulate a karst landscape improves the precipitation estimates, which also holds true for the other cases, as discussed below.

For the forest experiment (Fig. 3d), differences in 24-h rainfall compared with the control experiment are more spatially intermittent than, for example, the control differences with the Stage-IV data (Fig. 3b). Larger areas of positive differences are evident across Kentucky and into south Indiana/Illinois. Results from the west Kentucky and Missouri karst regions reveal areas of positive total precipitation differences where the precipitation is light to moderate (Fig. 3a, d). While the precipitation differences between the sandy-soil and control runs (Fig. 3e) are broadly similar to those from the forest experiment, the sandy-soil-control comparison shows smaller magnitudes in the total rainfall differences, especially with smaller positive differences, than for the forest-control comparison.

To better understand the model performance, a further quantitative analysis of precipitation is conducted to numerically differentiate among the land-cover and soil types, where the analysis of RMSE and BIAS values provides a better assessment of the accuracy of the simulations.

The RMSE and BIAS values of model-simulated 6-h precipitation for case 4 are compared with the Stage-IV precipitation for the eight 6-h periods after the 3-h spin-up time in Fig. 4, where the barren simulation performs better than the other experiments. Of the eight 6-h periods, the barren experiment shows the largest improvements over the four time periods according to RMSE and BIAS values (Fig. 4), all of which correspond to the rainy period, while the remaining four time periods (ending at 0600, 1200 UTC 29-09-2008, 1800 UTC 30-09-2008 and 0000 UTC on 01-10-2008) show minimal differences from the other two experiments. Furthermore, the averaged RMSE and BIAS values over all eight time periods indicate that the barren simulation has the lowest RMSE (2.69 mm) and the least absolute BIAS (0.24 mm). The forest simulation has the highest average RMSE (3.14 mm) and BIAS (0.51 mm) values. The sandy-soil RMSE (2.95 mm) and BIAS (0.41 mm) values show no notable change from the control run (RMSE = 2.98 mm; BIAS = 0.40 mm), as both remain in between the estimates for the barren and forest simulations. These results suggest that the approximation of karst landscapes as barren land produces the best simulation of precipitation. The change from the original land-cover types (the control run) to forest is less dramatic and produces more uncertainty in the simulation. The smaller differences between the sandy-soil and control runs than those between the barren and control runs imply that the soil type plays a lesser role than the land-cover type on the simulation of precipitation (the soil types in the barren experiment and the land-cover types in sandy-soil experiment are the same as for the control experiment).

Fig. 4

Values of RMSE and BIAS of 6-h accumulated precipitation from the control, barren, forest, and sandy-soil experiments for case 4, verified with Stage-IV precipitation data. The dates shown represent the ending point of each 6-h period

Fig. 5

Equitable threat score for eight precipitation levels (0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6 mm) during the 1800 UTC 29 September 2008–1200 UTC 30 September 2008 rainy period for the control, barren, forest and sandy-soil experiments of case 4

Fig. 6

Frequency bias score for eight precipitation levels (0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6 mm) during the 1800 UTC 29 September 2008–1200 UTC 30 September 2008 rainy period for the control, barren, forest and sandy-soil experiments of case 4

After evaluating both the RMSE and BIAS values, which show overall differences of model-simulated precipitation from the observations, the evaluation of ETS and fBIAS values is also performed to clarify the extent to which each simulation experiment accurately simulates the precipitation amount. The ETS and fBIAS values are calculated for eight precipitation thresholds (i.e. 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8 and 25.6 mm). Further evaluation focuses on the four 6-h periods during the rainy period (1200 UTC 29 September 2008–1200 UTC 30 September 2008) for case 4 as suggested by the RMSE and BIAS values. The ETS values give the highest magnitudes during these four time periods (Fig. 5, other times with lower ETS values not shown) along with the overall lowest fBIAS values, which are also closest to unity (Fig. 6, other times with worse fBIAS values not shown). These results suggest that the model performs well for smaller precipitation levels of 0.2–1.6 mm (Figs. 5, 6). It is important to note that during these time intervals for case 4, the ETS values increase during the middle of the rainy period, while the fBIAS values are more dramatically reduced. The lower fBIAS values are considered an improvement among the model simulations, suggesting the model satisfactorily simulates the precipitation during this period.

Among the experiments for all the cases, the average ETS and fBIAS values are calculated to further examine model skill and accuracy. Figure 7 presents the averaged ETS and fBIAS values for cases 1, 2, 3 and 5 for the eight precipitation thresholds through each rainy period as defined in Table 1, revealing model simulations with improved skill and accuracy for all cases among the smaller precipitation thresholds of 0.2–1.6 mm, with the opposite for the larger precipitation thresholds (i.e., 6.4–25.6 mm). Moreover, the ETS values are higher (better skill) for each experiment through the first four thresholds, while the fBIAS values (frequency bias) are the lowest during this period. The opposite occurs for the larger precipitation thresholds, as the ETS values are relatively low, with the highest fBIAS values for these thresholds (Fig. 7). Overall, while results suggest the model tends to overestimate precipitation (all fBIAS $> 1$), an improved skill and accuracy in all five cases for the lighter precipitation thresholds is evident. Regarding the three sensitivity experiments, the overall conclusion is consistent with case 4 whereby the barren experiment has the highest skill for precipitation thresholds of 0.2–3.2 mm, with fBIAS values closer to one. The forest and sandy-soil experiments have a similar skill (lower than the barren experiment), which is also close to that of the control experiment.

Fig. 7

Averaged ETS and fBIAS values for eight precipitation levels (0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6 mm) during rainy periods for the control, barren, forest and sandy-soil experiments of cases 1, 2, 3 and 5

3.1.2 Surface Air Temperature, Humidity, and Wind Speed

In addition to the verification of model-simulated precipitation, near-surface atmospheric variables at the land–atmosphere interface reflect changes of land-surface conditions on the atmosphere. The observed 2-m air temperature ($T_2, {^{\circ }}\hbox {C}$), the 2-m specific humidity ($Q_{2}$, g $\hbox {kg}^{-1})$, and the westerly and southerly velocity components at 10-m height (U and V, respectively, m $\hbox {s}^{-1})$ are available in the NCEP observational dataset, and are used to verify all four model simulations in terms of RMSE and BIAS values, which are calculated for all grid points in the nested domain for karst and non-karst grid points. For ease in counting the karst grid points, the observational data are interpolated to the model grid, where changes in the simulations are generally notable for the karst regions and marginal for the surrounding non-karst regions. Figure 8 shows, for example, the results for the karst regions from case 4 at 3-h intervals during the two-day simulation (0000 UTC 29-09-2008–0000 UTC 01-10-2008), with results from all five cases shown in Table 2. Note that the control results are indiscernible from the sandy-soil results in Fig. 8 for the case 4 variables analyzed.

Fig. 8

Root-mean-square error and BIAS between model simulations and the NCEP observations over karst-only regions for: a surface air specific humidity $Q_{2}$ (g $\hbox {kg}^{-1})$, b surface air temperature $T_2$ (${^{\circ }}\hbox {C}$), c surface west-east velocity component U (m $\hbox {s}^{-1})$, and d surface south-north velocity component V (m $\hbox {s}^{-1})$. Results correspond to the control, barren, forest and sandy-soil experiments of case 4 from 0000 UTC 29 September 2008 to 0000 UTC 1 October 2008 at 3-h intervals. Grey shading indicates the night time. The control and sandy-soil experiments are indistinguishable

Table 2 Average values of RMSE and BIAS of model-simulated surface air specific humidity ($Q_{2}$, g $\hbox {kg}^{-1})$, 2-m surface air temperature ($T_2, {^{\circ }}\hbox {C}$), and 10-m wind speed (U, V, $\hbox {m s}^{-1})$ over karst areas from the control, barren, forest and sandy-soil experiments of all five cases, as calculated separately for day and night (for five cases, there is a total of 45 3-h day points and 40 3-h night points)

For the surface atmospheric humidity (Fig. 8a), the WRF model normally (the control experiment) generates a positive bias throughout the day, and is further enhanced during the daytime by changes in land cover to forest. In contrast, the barren experiment largely corrects the daytime moist bias in the karst region, which, as shown in Table 2, is in agreement among all five cases.

For the 2-m air temperature, the control experiment displays a strong cold bias at night (Fig. 8b and Table 2). For the forest experiment, the bias worsens with increasing values of RMSE, while the barren experiment shows a noticeable improvement by correcting the cold bias at night, and thus reducing the magnitude of the RMSE value. For the surface wind speeds (Fig. 8c, d, and Table 2), while the barren experiment produces larger errors than both the control and forest experiments, for case 4, the differences in wind speed are more likely the result of the large-scale synoptic variations. In addition, the overall results for the wind speeds shown in Table 2 may be dominated by the severe weather of case 5.

3.2 Model Sensitivity Analysis

Each model sensitivity to different land-cover and soil types in karst regions is compared with the control experiment. When different land and soil conditions are assumed for the karst landscape, complex model responses are expected, through which the performance of each model experiment may be explained by examining the near-surface atmosphere (e.g., latent and sensible heat fluxes, surface air temperature, humidity and wind speed), convective development and precipitation (e.g., CAPE, CIN), as well as a cross-sectional analysis of the equivalent potential temperature and atmospheric instability.

3.2.1 Surface Air Temperature and Dew Point

The surface air temperature ($T_2$) and dew point temperature ($T_{d2})$ from each of the three experiments are compared with those of the control simulation within the nested domain during the rainy period for each case, as these times are well into the model simulation period. To further emphasize the influence of karst areas, these variables are analyzed over both karst and non-karst areas, in addition to the entire nested domain, with the motivation to separate the localized impacts from those extending downstream, since only modifications to the karst areas are performed. To better understand the $T_2$ and $T_{d2}$ differences among the entire domain versus the karst and non-karst areas, the root-mean-square difference (RMSD) and BIAS values for $T_2$ and $T_{d2}$ are calculated for each particular consideration and for each of the three experiments with respect to the control experiment. The calculation of RMSD and BIAS values for the entire nested domain uses all grid points, while only the karst and non-karst grid points are used for the calculation of karst and non-karst areal RMSD and BIAS values, respectively. These are illustrated in Fig. 9 for each of the three experiments for $T_2$ and $T_{d2}$, which are averaged over all 6-h time periods and all five cases. While the values of RMSD indicate the extent to which the modelling result of an experiment deviates from the control experiment, a positive (negative) BIAS value implies a warmer (cooler) or more (less) humid surface air than the control experiment.

Fig. 9

Root-mean-square difference (${^{\circ }}\hbox {C}$) and BIAS (${^{\circ }}\hbox {C}$) between the barren, forest, sandy-soil and control experiments for the surface air temperature ($T_2$, a–c) and dew point temperature ($T_{d2}$, d–f) evaluated over the entire nested domain (a, d), karst areas (b, e), and non-karst areas (c, f). Results are averages over all 6-h time periods for all five cases

With regard to $T_2$ for the entire nested domain (including both karst and non-karst regions), the RMSD value for the barren experiment increases by $1.3\,{^{\circ }}\hbox {C}$ compared with the control experiment (Fig. 9a), while the forest and sandy-soil experiments result in reduced values of 0.75 and $0.67\,{^{\circ }}\hbox {C}$, respectively (Fig. 9a). When only karst areas are considered, all three experiments (barren, forest and sandy soil) respond similarly with larger magnitudes (compare Fig. 9a with b), with the barren experiment providing the greatest increase of $1.8\,{^{\circ }}\hbox {C}$ throughout (Fig. 9b). Both the forest and sandy-soil experiments show reduced temperatures of 1 and $0.8\,{^{\circ }}\hbox {C}$ over the karst areas, respectively, implying stronger cooling than over the entire nested domain (Fig. 9b). In non-karst areas where all experimental settings are the same as the control experiment (i.e. no changes made), the smallest impacts from each experiment are found (Fig. 9c), with the barren and sandy-soil experiments resulting in a small cooling and warming effect, respectively, which are opposite to the responses seen in karst areas (Fig. 9b). Thus, the overall impacts over the entire nested domain are dominated by the results shown for karst areas, implying a more localized impact from the karst regions.

The dew point temperature yields different results for the entire nested domain. The BIAS values in Fig. 9d indicate a drying effect for the barren experiment with a $0.7\,{^{\circ }}\hbox {C}$ reduction in $T_{d2}$, while the forest and sandy-soil experiments both yield increases of $0.2\,{^{\circ }}\hbox {C}$. The RMSD values are further changed when only karst areas are considered, with results suggesting additional lowering (i.e., drier) of $T_{d2}$ for the barren land ($-\,1.5\,{^{\circ }}\hbox {C}$) with slightly moister responses for the forest ($0.3\,{^{\circ }}\hbox {C}$) and sandy-soil ($0.4\,{^{\circ }}\hbox {C}$) experiments compared with the control simulation. With non-karst areas having the same experimental settings as the control experiment, significantly smaller responses are detected than for karst areas. Over non-karst areas, the barren experiment gives a slight drying, while both the forest and sandy-soil experiments result in a minor moistening effect.

In summary, clear differences in sensitivity responses between the karst and non-karst regions are detected, with varying responses for both $T_2$ and $T_{d2}$, and differences for the barren experiment showing a noticeable $T_2$ increece and $T_{d2}$ decrease across the karst areas (Figs. 9b, e). Interestingly, both the forest and sandy-soil experiments show a reduced $T_2$ across the karst areas (Fig. 9b), with an increased $T_{d2}$. The magnitude of $T_2$ across non-karst areas is much smaller with nearly negligible changes, as barren and sandy-soil experiments result in a slight cooling effect, while the forest has a minor warming effect (Fig. 9c). Similar results are found for $T_{d2}$, as non-karst areas with the barren experiment result in a drier atmosphere, while the forest and sandy-soil experiments both give a slightly moister atmosphere. Overall, $T_2$ and $T_{d2}$ give clear changes linked to karst area simulations (Fig. 9a, d).

Figure 10 shows the spatial distributions of differences in $T_2$ and $T_{d2}$ for the barren–control, forest–control, and sandy-soil–control experiments at 0000 UTC 30 September 2008, which is 1800 local standard time and 12 h into the rainy period of case 4 (Table 1). Here, $T_2$ has large positive differences of 3–8$\,{^{\circ }}\hbox {C}$ for the barren experiment, and thus a warming of the karst areas (Figs. 1a, 10a). The vegetation in the control experiment consists of a large area of deciduous broadleaf within the nested domain (Fig. 1b), resulting in larger latent heat fluxes as discussed in detail in the following section. For the barren experiment, the sparse or total lack of vegetation cover results in more energy partitioned into the sensible heat flux, leading to the positive differences in $T_2$ (Fig. 10a).

The magnitudes of $T_{d2}$ differences are unlike those of $T_2$, as larger negative differences of − 2 to $-\,7\,{^{\circ }}\hbox {C}$ occur along the karst areas (Figs. 1a, compare 10b with a). While $T_2$ differences are positive across karst areas, $T_{d2}$ differences are large and negative, indicating drier conditions (Figs. 1a, 10a, b). It is worth noting that this time (0000 UTC 30 September 2008), is halfway through the rainy period (12 h into the 24-h period observed) (Table 1, Fig. 10b). Once the precipitation from the mesoscale convective system affects these areas, moderate rain continues to fall across the nested domain, resulting in larger negative differences due to the cooler, drier air behind the leading edge of precipitation (see Figs. 2b, 10b).

The forest experiment produces larger negative differences in $T_2$ of − 1 to $-\,4\,{^{\circ }}\hbox {C}$ across the karst areas (Figs. 1a, 10c) as the forest cover provokes cooler conditions (Figs. 1a, 10c). Although $T_2$ in the forest simulation is slightly lower than that of the control experiment, larger positive differences in $T_{d2}$ of 1–$4\,{^{\circ }}\hbox {C}$ are found (Figs. 1a, 10d). Throughout the nested domain, much wetter conditions are found for the karst areas covered by a forest canopy (Figs. 1a, 10d), which increases evapotranspiration and thus leads to increased atmospheric moisture (Fig. 10d).

Fig. 10

Differences between barren-control (a, b), forest-control (c, d), and sandy-soil–control (e, f) experiments for case 4, over the nested domain at 0000 UTC 30 September 2008: a, c, e surface air temperature ($T_2, {^{\circ }}\hbox {C}$); b, d, f dew point temperature ($T_{d2}$ ${^{\circ }}\hbox {C}$). The line XYZ in a marks the location for cross-sectional analysis with non-karst (Y) and karst (X, Z) areas

Interestingly, $T_2$ and $T_{d2}$ from the sandy-soil experiment show negligible differences compared with the control simulation within the nested $\hbox {domain}$ (Figs. 1a, 10e, f). Sandy soil is the most porous of all soil types, becoming drier more quickly than any other type (Oke 1987). Since the land-cover type is kept the same as the control simulation, the negligible changes to $T_2$ and $T_{d2}$ suggest that the land-cover type dominates the land–atmosphere feedback, which may suppress impacts from different soil types.

Fig. 11

Root-mean-square difference (W $\hbox {m}^{-2})$ and BIAS (W $\hbox {m}^{-2})$ between the barren, forest and sandy-soil experiments and the control experiment for the latent heat flux (a–c) and sensible heat flux (d–f) evaluated over the entire nested domain (a, d), karst areas (b, e), and non-karst areas (c, f). Results are averages over all 6-h time periods of all five cases

3.2.2 Latent and Sensible Heat Fluxes

As land–atmosphere interactions involve exchanges of mass and heat, and, therefore, latent ($Q_{E})$ and sensible ($Q_{H})$ heat fluxes as illustrated in Fig. 11, where the RMSD and BIAS values between each of the three experiments and the control experiment for $Q_{E}$ and $Q_{H}$, are averaged over all five cases. For the entire nested domain, the RMSD and BIAS of $Q_{E}$ for the barren experiment indicates a large decrease of 32 W $\hbox {m}^{-2}$ when compared with the control experiment (Fig. 11a), while the forest and sandy-soil experiments result in small increases of 9 W $\hbox {m}^{-2}$ and 2 W $\hbox {m}^{-2}$, respectively (Fig. 11a). Responses are very distinct when only the karst areas are considered, as the barren experiment shows an even larger decrease than the entire nested domain of 55 W $\hbox {m}^{-2}$ (compare Fig. 11b with a). It should be noted that, compared with the entire nested domain, the forest and sandy-soil experiments give larger $Q_{E}$ increases of 24 W $\hbox {m}^{-2}$ and 4 W $\hbox {m}^{-2}$ in the karst areas, respectively (compare Fig. 11b with a). As non-karst areas show the smallest, but opposite, effect from each experiment (Fig. 11c), the overall impacts over the nested domain are dominated by the results related to the karst area, again implying a localized impact from karst regions.

In comparison with the $T_{d2}$ responses shown in Fig. 10b, d, f, it is clear that the moisture transferred from the land surface to the atmosphere is associated with $Q_{E}$, which results in a change in atmospheric humidity. In comparison with the control experiment, the $Q_{E}$ partitioning for the barren experiment decreases, causing drier near-surface atmospheric conditions with reduced $T_{d2}$ over the karst areas. The forest and sandy-soil experiments produce a higher upwards $Q_{E}$, resulting in moister near-surface atmospheric air over the karst areas. In addition, the impacts of land-type changes on $Q_{E}$ and near-surface humidity are primarily local as shown by the minimal responses over the non-karst areas.

Furthermore, the values of $Q_{H}$ for the entire nested domain are less distinct (compare Fig. 11d with a). However, the RMSD and BIAS values for both the barren and forest experiments indicate a slight increase in $Q_{H}$ of 2 and 4 W $\hbox {m}^{-2}$, respectively, across the entire nested domain (Fig. 11d). While both the barren and forest experiments provide slight increases for the entire nested domain, the sandy-soil experiment produces a decrease of 3 W $\hbox {m}^{-2}$ (compare Fig. 11d with a). When karst areas are considered, the values of $Q_{H}$ increase by 9 W $\hbox {m}^{-2}$ for the barren experiment, with larger decreases of 3 and 9 W $\hbox {m}^{-2}$ for forest and sandy-soil experiments, respectively. For the non-karst areas, opposite but negligible changes are found when compared with the karst areas and the entire nested domain (compare Fig. 11f with d, e).

In comparison with the $T_2$ responses in Fig. 10a, c, e, we find that $Q_{H}$ is a significant factor for the surface air temperature, resulting in changes dependent on the particular experiment. When compared with the control experiment, the barren experiment gives an increased sensible heat flux, causing warmer surface conditions with an increased $T_2$ over karst areas. However, both the forest and sandy-soil experiments produce a smaller $Q_{H}$, leading to a cooler surface temperature over the karst areas. Similar to $Q_{E}$ and the surface humidity, impacts on $Q_{H}$ and air temperature are also local, with marginal responses over non-karst areas.

As an example, Fig. 12 presents the spatial distributions in both latent and sensible heat fluxes for the barren-control, forest-control, and sandy-soil-control experiments for case 4 at 1800 UTC 29 September 2008, which is noon local standard time and 6 h into the rainy period. Note that the timestamps are different than that of $T_2$ as $Q_{H}$ typically shows the smallest changes around sunset or sunrise, but larger during the middle of day or at night. Moreover, Fan (2009) found that the heat flux converges and produces the temperature change.

Fig. 12

Spatial distribution for the barren-control (a, b), forest-control (c, d) and sandy-soil-control (e, f) experiments for case 4 over the nested domain at 1800 UTC 29 September 2008: a, c, e latent heat flux (W $\hbox {m}^{-2})$; b, d, f sensible heat flux (W $\hbox {m}^{-2})$

The barren experiment for case 4 generates negative $Q_{E}$ differences of $-\,160$ to $-\,200$ W $\hbox {m}^{-2}$ from the control experiment across the karst areas in the entire nested domain (Figs. 1a, 12a). Areas including central Illinois and Indiana provide positive differences of 40–100 W $\hbox {m}^{-2}$ outside of the karst areas where the land cover consists of mostly cropland and deciduous broadleaf forests (Figs. 1a, b, 12a). These noisy, but localized, distributions, with some horizontal patterns, indicate that the differences are mostly likely caused by the weather system (i.e., changes within the atmosphere), which moved to the south-east from the north-west of the domain. However, the barren land (for karst areas) results in positive $Q_{H}$ differences in the spatial distribution across the nested domain (Figs. 1a, 12b). Note that this time is 6 h into the rainy period and $T_2$ is still high (Fig. 10a). Thus, it is possible that several karst areas show a negative difference in $Q_{H}$. More detailed examination shows that $Q_{H}$ is more intermittent over the karst areas, with positive differences occurring along the karst and non-karst boundaries (Figs. 1a, 12b). The negative and positive differences along these boundaries may be attributed to the sharp transition from barren land to vegetation (Fig. 12b).

Unlike the barren experiment, the forest experiment provides large positive $Q_{E}$ differences of 100–200 W $\hbox {m}^{-2}$ over the karst areas, which is expected (Fig. 12c). In contrast, $Q_{H}$ over the karst areas gives positive differences of 40–120 W $\hbox {m}^{-2}$, with a slight increase over central and west Kentucky when compared with the barren experiment (compare Fig. 12d with b). Figure 12d also shows even stronger positive differences of 40–160 W $\hbox {m}^{-2 }$ across central Tennessee. Overall, modelling results show that forests have a cooling effect through the increased $Q_{E}$. The sandy-soil experiment provides overall minimal differences in $Q_{E}, Q_{H}, T_2$ and $T_{d2}$ across the nested domain (Figs. 1a, 12e, f).

3.2.3 Convective Available Potential Energy and Convective Inhibition

The values of CAPE and CIN help assess the evolution and development of precipitation, with differences in maximum CAPE and CIN of an atmospheric column between the barren and control experiment for case 4 shown in Fig. 13. As case 4 features a mesoscale convective system, which propagates from the north-west of the nested domain to the south-east during the experiment (see Fig. 2d), strong negative CAPE differences of − 400 to − 800 J $\hbox {kg}^{-1}$ across sections of Missouri and Illinois and intermittent positive differences of 400–800 J $\hbox {kg}^{-1}$ in central Indiana, south Illinois, and west Kentucky are detected (Fig. 13a, b). The strongest positive CAPE differences of 600–800 J $\hbox {kg}^{-1}$ occur along west Kentucky and into west Tennessee during the middle of the rainy period (Table 1, Fig. 13c). The larger positive and negative values of CAPE move to the south-east into central Tennessee and north Alabama through the rainy period (Table 1, Fig. 13d, e). The CAPE estimates are reasonable and represent the leading edge of the mesoscale convective system while propagating to the south-east (Fig. 13d, e). Figure 13b shows the onset of larger positive CAPE differences from central Indiana and southwards along the Ohio River, indicating the leading line of the convective storm maximizes all the atmospheric energy for storm initiation, and, consequently, the south-east progression of enhanced values of CAPE and precipitation (Figs.2d, 13a–e).

Fig. 13

Differences between the barren and control simulations for case 4 over the nested domain at 6-h intervals from 1800 UTC 29 September 2008 to 1800 UTC 30 September 2008: a–e CAPE (J $\hbox {kg}^{-1})$; f–j CIN (J $\hbox {kg}^{-1})$

The CIN values are less distinct across the nested domain for this event. Throughout much of the rainy period, intermittent CIN values are present over west Kentucky and Tennessee (see Fig. 13f, g and Table 1), and continue propagating across Tennessee and eventually into north Alabama towards the end of the rainy period (see Table 1, Fig. 13h–j). Along areas of large negative differences in CAPE, some positive CIN differences also occur, which indicates suppression of the convection (Fig. 13a–c, f–h), while the opposite is found for larger positive CAPE values, with negative CIN values indicating potentially enhanced convection (see Fig. 13b, c, g, h). A similar observation and assessment applies to the CIN values has intermittent positive and negative differences occur along the leading edge of the precipitation system (Fig. 13g–i). As both CAPE and CIN values coincide well with one another, the most noticeable differences occur along the frontal line of precipitation (compare Fig. 13a–e with f–i). Overall, it appears that the barren experiment for both the column maximum CAPE and CIN values has no real influence across the near-surface atmosphere as they follow the leading edge of the precipitation from the mesoscale convective system closely throughout the rainy period (see Figs. 2d, 13). This implies that both convective parameters are largely controlled by larger, synoptic conditions. The analysis along a vertical cross-section in the next section further reveals the responses of the magnitude of CAPE to the land-cover changes in both the barren and forest experiments.

3.2.4 Vertical Cross-Section Analysis

The investigation of vertical cross-sections aids in understanding possible near-surface land–atmosphere feedbacks. The location of the cross-section is marked in Fig. 10a, with X, Y and Z representing karst, non-karst, and karst sections, respectively, along the propagation of the system from the north to the south. Therefore, the effects across both karst and non-karst areas for the barren and forest experiments may be examined.

Figure 14 shows vertical cross-sections from the comparison of barren and forest experiments with the control experiment for the analysis of the near-surface conditions for temperature ($T_{air}, {^{\circ }}\hbox {C}$), moisture (water vapour mixing ratio $Q_{V}$, g $\hbox {kg}^{-1})$, equivalent potential temperature ($\theta _{\mathrm{e}}, {^{\circ }}\hbox {C}$), vertical circulation, and CAPE values at 0600 UTC 29 September 2008, which is 9 h after model initialization and 6 h before the rainy period, so that the changes in land-cover types have taken effect during the first 9 h of integration, and yet have not been notably affected by the more intense precipitation.

• (a) Air Temperature and Specific Humidity

For the cross-section of air temperature $T_{air}$ shown in Fig. 14a, the first kilometre of the atmosphere at point X shows mostly positive differences between the barren and control experiments. Relatively small differences are shown across point Y, which features mainly non-karst areas, and hence the land cover is the same as for the control run (Figs. 10a, 14a). However, relatively large negative differences of − 0.2 to $-\,0.4\,{^{\circ }}\hbox {C}$ are present close to the boundary of X and Y, which is indicative of the leading edge of the precipitation system resulting in rain-cooled air. At location Z, results correspond well with the previous analysis for the barren experiment as large positive differences of $0.6{-}1\,{^{\circ }}\hbox {C}$ are noted over the karst areas (Figs. 10a, 14a), with an intense warming effect for the barren experiment over the karst areas resulting in warmer surface conditions (Fig. 14a). The forest cross-sectional analysis features the exact opposite results compared with the barren experiment, with a large cooling of − 0.2 to $-1\,{^{\circ }}\hbox {C}$ near the surface over karst areas (Figs. 10a, 14b; points X and Z), which are represented well across both locations over karst areas, while small differences are once again seen over the non-karst areas (point Y; Figs. 10a, 14b).

Fig. 14

Differences between the barren and control experiments (a, c, e), and the forest and control experiments (b, d, f) for case 4 along the vertical cross-section XYZ marked in Fig. 10a at 0600 UTC 29 September 2008: a, b air temperature ($T_{air}, {^{\circ }}\hbox {C}$); c, d water vapour mixing ratio ($Q_{v}$, g $\hbox {kg}^{-1})$; e, f equivalent potential temperature ($\theta _{e}, {^{\circ }}\hbox {C}$) and vertical circulation (reference vectors shown at upper-right corners); g, h CAPE (J $\hbox {kg}^{-1})$ at each grid point. The line XYZ in Fig. 10a marks the location of the cross-sectional analysis where non-karst (Y) and karst (X, Z) areas begin and end

Differences in $Q_{v}$ through the barren-control and forest-control comparisons (Fig. 14c, d) generally match the results from the $T_{d2}$ and $Q_{E}$ spatial analyses (Figs. 10b, d, 12a, c). Small differences are noted across non-karst areas (point Y), but negative differences ranging from − 0.4 to − 0.8 g $\hbox {kg}^{-1}$ are also shown for the barren experiment over karst areas (Figs. 10a, 14c; points X and Z). This vertical cross-section supports the results for the barren experiment initiating drier near-surface conditions (Figs. 9e, 10b, 14c), which is not as clear at point X as at Z, since the precipitation system has moved into point X by this time. The forest experiment shows larger positive differences of 0.4 to 1.2 g $\hbox {kg}^{-1}$, indicating moister surface conditions (Figs. 9e, 10d, 14d). As noted previously, larger magnitudes of differences are found mostly across the karst areas (points X and Z) and within the surface layer with little to no differences aloft (Figs. 10a, 14a–d).

• (b) Equivalent Potential Temperature

Equivalent potential temperature ($\theta _{e})$ or moist static energy differences for both the barren and forest experiments yield further stability information (e.g., Pielke 2001) (Fig. 14e, f), where, as mentioned above, the barren experiment provides positive differences in near-surface temperature across karst regions (points X and Z). Likewise, the barren experiment results in large positive differences in $\theta _{e}$ of 0.4–$1\,{^{\circ }}\hbox {C}$ across the surface over the karst areas (Fig. 14e; points X and Z). Although there is a drying effect from the barren experiment over the karst areas, which may reduce $\theta _{e}$, the warming effect obviously plays a dominant role in the changes of $\theta _{e}$. The changes of $\theta _{e}$ are just the opposite for the forest experiment, where the above analysis shows negative differences in temperature (a cooling effect) across the surface, but larger positive differences for $Q_{v}$ (points X and Z; compare Fig. 14b, d with a, c). However, when considering $\theta _{e}$, the cross-sectional analysis reveals strong negative differences of − 0.6 to $-1\,{^{\circ }}\hbox {C}$ across the karst areas, especially near the surface, where the cooling effect is the strongest (point Z; compare Fig. 14b with f). Vertical profiles of $\theta _{e}$ relate to the potential instability of the atmosphere (e.g., Petty 2008). The $\theta _{e}$ values within the boundary layer imply that a barren surface increases the potential instability (from the warming and increased near-surface $\theta _{e}$ over the karst areas), while forest cover decreases the potential instability near the surface.

• (c) Vertical Circulation

The vertical circulation within the cross-sectional plane helps determine if any significant low-level circulations are generated from the experiments (Fig. 14e, f). Both the barren and forest experiments generate differences as large as 0.5 m $\hbox {s}^{-1}$ in the horizontal and 2.5 mm $\hbox {s}^{-1}$ in the vertical velocity components, with largest changes found in the karst area (point Z) and in the vicinity of the precipitation system (points X and Y). For the forest experiment, near-surface cooling and the decreased potential instability (as seen from $\theta _{e})$ leads to an overall enhanced downdraft over both point Z and the precipitation system area, resulting in near-surface flow divergence at points X and Z, so that the rising motion dominates at point Y (the non-karst area). The barren experiment shows less pronounced flow patterns (Fig. 14e) than the forest experiment, while weak circulation patterns opposite to that of the forest experiment are still discernable. The vertical circulation patterns suggest a correspondence to the precipitation patterns in the barren and forest experiments. At 0600 UTC 29 September 2008, the precipitation system at point X extends into part of the non-karst areas of point Y, where all model-simulated precipitation is similar (Figs. 3, 14). Recall that both the control and forest experiments overestimate the total precipitation at locations with heavy rainfall, which are mostly located near the non-karst areas of point Y. Consistent with Quintanar et al. (2008) and Suarez et al. (2014), the enhanced updraft for the forest experiment at point Y directly leads to enhanced precipitation, while the barren experiment improves the simulation of precipitation by correcting the overestimation seen in the control and forest experiments (see the discussion in Sect. 3.1).

• (d) Convective Available Potential Energy and Associated Instability

As discussed above in Sect. 3.2, the differences in maximum CAPE values of atmospheric columns are mainly the result of the large synoptic-scale progression of the precipitation system, with no obvious impacts from the localized land-surface conditions. However, the case is different when analyzing CAPE values along cross-sections and within the planetary boundary layer. Figure 14g, h show CAPE (of an air parcel at each grid point) differences within the lower layers of the atmosphere from the barren-control and forest-control comparisons, respectively. The leading edge of the precipitation line can easily be distinguished as very large differences occur there (Figs. 10a, 14g, h), with mostly very small differences occurring across the non-karst areas in the barren experiment ahead of this line (point Y, Figs. 10a, 14g). Vertical profiles give more interesting results over karst areas (points X and Z) as more frequent negative CAPE values are found in the barren experiment near the surface. The forest experiment provides similar impacts as the barren experiment, but with more positive differences in CAPE values over the karst areas (Fig. 14h).

As the cross-sections of CAPE and $Q_{v}$ values (compare Fig. 14g, h, with c, d) show patterns that align well, we suggest that the humidity plays a dominant role in determining the magnitude of CAPE, which agrees with earlier studies (e.g., Pielke 2001; Collow et al. 2014). With the drying effect of karst areas in the barren experiment, the values of CAPE decrease, and, consequently, the instability is suppressed, which further leads to the reduction in precipitation. Similarly, the wetting effect of the forest experiment leads to increased CAPE values, local instability and, consequently, enhanced precipitation.

4 Discussion and Conclusions

The impacts of karst landscapes on five precipitation events and the related atmospheric variables are assessed by comparing modelling results from different land types for simulating rainfall over karst and non-karst areas. Since existing models do not distinguish between karst and non-karst areas, the experiments help determine which existing land types in the model, along with their physical parameters, result in improved rainfall simulations in karst regions. Note that the changes introduced in the modelling experiments are limited to karst regions only. Subsequently, by using relatively similar barren land cover and sandy-soil conditions from the existing model to mimic certain karst characteristics, along with a contrasting forest land cover, the WRF model reveals a potential influence from the karst terrain under various weather conditions. Even though small perturbations at the initiation times of the modelling runs may cause small changes to the simulations, both the barren and forest land covers provide feedback through the exchange of heat and moisture at the surface, and show the potential for modified convective development based on several convective parameters, including $T_2, T_{d2}, T_{air}, Q_{v,}\theta _{e}$, and CAPE.

Overall, as shown in Fig. 15, the impacts of land cover and soil types over karst regions on the boundary layer are summarized as a simplified conceptual model (Winchester et al. 2017). The barren experiment results in the largest changes in both $T_2$ and $T_{d2}$, where a strong warming effect occurs with an intense drying effect across the karst region. These results contradict those of the forest experiment, as lower $T_2$ with much wetter near-surface conditions are found over karst areas. The drying effect for the barren experiment is more prominent during the day, while the warming effect is significant during both day and night. Analysis for both latent and sensible heat fluxes further supports these findings, as a large decrease in near-surface moisture is apparent for the barren experiment, while a slight increase is seen in the forest and sandy-soil experiments. The warming and cooling effects in the barren and forest experiments are linked to increased and decreased sensible heat fluxes, respectively. The warming effect for the barren experiment over the karst areas ultimately leads to increased potential instability, while the forest experiment gives the opposite result, with a decrease in potential instability due to surface cooling. These thermally-induced instabilities related to vertical circulation patterns enhance (e.g., in the forest experiment) or suppress (e.g., in the barren experiment) large-scale convection traversing non-karst and karst boundaries. In contrast, the values of CAPE show a close relationship with atmospheric humidity, while being related to the local instability. Thus, the drying effect for the barren experiment leads to a decrease in the values of CAPE, as well as instability, and contribute to the correction of the overestimation of precipitation in the control experiment. Again, the forest experiment produces the opposite effect.

Fig. 15

A simplified conceptual model of atmospheric responses within the boundary layer to different land cover/soil types over karst regions (note: the changes are all relative to the control experiment)

While the carbonate rocks composing karst landscapes cover some 18% of the land area of the USA (Weary and Doctor 2014) within a range of climates, and have been shown to influence land–atmosphere interactions, a full set of karst-related inputs for a land-surface model for atmospheric simulations have not yet been developed. Our research builds on recent studies using existing model input parameters to explore relationships between karst areas and land-cover types for the possible improvement in model representation and the simulation of precipitation. The use of the barren and sandy-soil land covers in the model represent one aspect of typical karst hydrologic conditions, wherein thin soils and highly permeable bedrock beneath often result in rapid drainage through the soil, and provide a basis for developing an optimal land-cover parametrization for karst terrain.

We recommend: (1) future work to develop methods for realistically representing karst landscapes; (2) field campaigns to collect data to further understand and quantify karst hydrology and model verification; (3) the inclusion of karst soil hydrological processes in models (see introduction); (4) the introduction of appropriate model tables representing soil hydrological properties; (5) appropriate descriptions of vertical water transport through the soils and bedrock of karst landscapes, including the fluxes of water vapour (Gonzalez et al. 2012; 6) modifications in land-cover and soil types, and their testing through experiments under various weather conditions; and (7) close collaboration between karst hydrologists and atmospheric scientists during model development.

Since the conclusions from our five cases could still be somewhat biased, seasonal or even longer periods of simulation are recommended. Although it is quite common to have a short model spin-up time, we recognize the need for much longer model (especially the land-surface model) spin-up times of weeks to years in duration (Cosgrove et al. 2003; Rodell et al. 2005; Chen et al. 2007; Case et al. 2008; Santanello et al. 2013; Angevine et al. 2014; Best and Grimmond 2014; Lawston et al. 2015), which is particularly helpful in improving model hydrology and flux estimations, and is typically conducted by running the land-surface model offline.